Lectures in nonlinear mechanics and chaos theory
Stetz, Albert W
2016-01-01
This elegant book presents a rigorous introduction to the theory of nonlinear mechanics and chaos. It turns out that many simple mechanical systems suffer from a peculiar malady. They are deterministic in the sense that their motion can be described with partial differential equations, but these equations have no proper solutions and the behavior they describe can be wildly unpredictable. This is implicit in Newtonian physics, and although it was analyzed in the pioneering work of Poincaré in the 19th century, its full significance has only been realized since the advent of modern computing. This book follows this development in the context of classical mechanics as it is usually taught in most graduate programs in physics. It starts with the seminal work of Laplace, Hamilton, and Liouville in the early 19th century and shows how their formulation of mechanics inevitably leads to systems that cannot be 'solved' in the usual sense of the word. It then discusses perturbation theory which, rather than providing...
Ancient and Current Chaos Theories
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Güngör Gündüz
2006-07-01
Full Text Available Chaos theories developed in the last three decades have made very important contributions to our understanding of dynamical systems and natural phenomena. The meaning of chaos in the current theories and in the past is somewhat different from each other. In this work, the properties of dynamical systems and the evolution of chaotic systems were discussed in terms of the views of ancient philosophers. The meaning of chaos in Anaximenes’ philosophy and its role in the Ancient natural philosophy has been discussed in relation to other natural philosophers such as of Anaximander, Parmenides, Heraclitus, Empedocles, Leucippus (i.e. atomists and Aristotle. In addition, the fundamental concepts of statistical mechanics and the current chaos theories were discussed in relation to the views in Ancient natural philosophy. The roots of the scientific concepts such as randomness, autocatalysis, nonlinear growth, information, pattern, etc. in the Ancient natural philosophy were investigated.
[Shedding light on chaos theory].
Chou, Shieu-Ming
2004-06-01
Gleick (1987) said that only three twentieth century scientific theories would be important enough to continue be of use in the twenty-first century: The Theory of Relativity, Quantum Theory, and Chaos Theory. Chaos Theory has become a craze which is being used to forge a new scientific system. It has also been extensively applied in a variety of professions. The purpose of this article is to introduce chaos theory and its nursing applications. Chaos is a sign of regular order. This is to say that chaos theory emphasizes the intrinsic potential for regular order within disordered phenomena. It is to be hoped that this article will inspire more nursing scientists to apply this concept to clinical, research, or administrative fields in our profession.
Advances in chaos theory and intelligent control
Vaidyanathan, Sundarapandian
2016-01-01
The book reports on the latest advances in and applications of chaos theory and intelligent control. Written by eminent scientists and active researchers and using a clear, matter-of-fact style, it covers advanced theories, methods, and applications in a variety of research areas, and explains key concepts in modeling, analysis, and control of chaotic and hyperchaotic systems. Topics include fractional chaotic systems, chaos control, chaos synchronization, memristors, jerk circuits, chaotic systems with hidden attractors, mechanical and biological chaos, and circuit realization of chaotic systems. The book further covers fuzzy logic controllers, evolutionary algorithms, swarm intelligence, and petri nets among other topics. Not only does it provide the readers with chaos fundamentals and intelligent control-based algorithms; it also discusses key applications of chaos as well as multidisciplinary solutions developed via intelligent control. The book is a timely and comprehensive reference guide for graduate s...
Erçetin, Şefika; Tekin, Ali
2014-01-01
The present work investigates global politics and political implications of social science and management with the aid of the latest complexity and chaos theories. Until now, deterministic chaos and nonlinear analysis have not been a focal point in this area of research. This book remedies this deficiency by utilizing these methods in the analysis of the subject matter. The authors provide the reader a detailed analysis on politics and its associated applications with the help of chaos theory, in a single edited volume.
Chaos Theory and Post Modernism
Snell, Joel
2009-01-01
Chaos theory is often associated with post modernism. However, one may make the point that both terms are misunderstood. The point of this article is to define both terms and indicate their relationship. Description: Chaos theory is associated with a definition of a theory dealing with variables (butterflies) that are not directly related to a…
Dynamical chaos: systems of classical mechanics
International Nuclear Information System (INIS)
Loskutov, A Yu
2007-01-01
This article is a methodological manual for those who are interested in chaotic dynamics. An exposition is given on the foundations of the theory of deterministic chaos that originates in classical mechanics systems. Fundamental results obtained in this area are presented, such as elements of the theory of nonlinear resonance and the Kolmogorov-Arnol'd-Moser theory, the Poincare-Birkhoff fixed-point theorem, and the Mel'nikov method. Particular attention is given to the analysis of the phenomena underlying the self-similarity and nature of chaos: splitting of separatrices and homoclinic and heteroclinic tangles. Important properties of chaotic systems - unpredictability, irreversibility, and decay of temporal correlations - are described. Models of classical statistical mechanics with chaotic properties, which have become popular in recent years - billiards with oscillating boundaries - are considered. It is shown that if a billiard has the property of well-developed chaos, then perturbations of its boundaries result in Fermi acceleration. But in nearly-integrable billiard systems, excitations of the boundaries lead to a new phenomenon in the ensemble of particles, separation of particles in accordance their velocities. If the initial velocity of the particles exceeds a certain critical value characteristic of the given billiard geometry, the particles accelerate; otherwise, they decelerate. (methodological notes)
Using chaos theory: the implications for nursing.
Haigh, Carol
2002-03-01
The purpose of this paper is to review chaos theory and to examine the role that it may have in the discipline of nursing. In this paper, the fundamental ingredients of chaotic thinking are outlined. The earlier days of chaos thinking were characterized by an almost exclusively physiological focus. By the 21st century, nurse theorists were applying its principles to the organization and evaluation of care delivery with varying levels of success. Whilst the biological use of chaos has focused on pragmatic approaches to knowledge enhancement, nursing has often focused on the mystical aspects of chaos as a concept. The contention that chaos theory has yet to find a niche within nursing theory and practice is examined. The application of chaotic thinking across nursing practice, nursing research and statistical modelling is reviewed. The use of chaos theory as a way of identifying the attractor state of specific systems is considered and the suggestion is made that it is within statistical modelling of services that chaos theory is most effective.
Meaning Finds a Way: Chaos (Theory) and Composition
Kyburz, Bonnie Lenore
2004-01-01
The explanatory power provided by the chaos theory is explored. A dynamic and reciprocal relationship between culture and chaos theory indicates that the progressive cultural work may be formed by the cross-disciplinary resonance of chaos theory.
Chaos theory in geophysics: past, present and future
International Nuclear Information System (INIS)
Sivakumar, B.
2004-01-01
The past two decades of research on chaos theory in geophysics has brought about a significant shift in the way we view geophysical phenomena. Research on chaos theory in geophysics continues to grow at a much faster pace, with applications to a wide variety of geophysical phenomena and geophysical problems. In spite of our success in understanding geophysical phenomena also from a different (i.e. chaotic) perspective, there still seems to be lingering suspicions on the scope of chaos theory in geophysics. The goal of this paper is to present a comprehensive account of the achievements and status of chaos theory in geophysics, and to disseminate the hope and scope for the future. A systematic review of chaos theory in geophysics, covering a wide spectrum of geophysical phenomena studied (e.g. rainfall, river flow, sediment transport, temperature, pressure, tree ring series, etc.), is presented to narrate our past achievements not only in understanding and predicting geophysical phenomena but also in improving the chaos identification and prediction techniques. The present state of chaos research in geophysics (in terms of geophysical phenomena, problems, and chaos methods) and potential for future improvements (in terms of where, why and possibly how) are also highlighted. Our popular views of nature (i.e. stochastic and deterministic), and of geophysical phenomena in particular, are discussed, and the usefulness of chaos theory as a bridge between such views is also put forth
Recent development of chaos theory in topological dynamics
Li, Jian; Ye, Xiangdong
2015-01-01
We give a summary on the recent development of chaos theory in topological dynamics, focusing on Li-Yorke chaos, Devaney chaos, distributional chaos, positive topological entropy, weakly mixing sets and so on, and their relationships.
Towards chaos criterion in quantum field theory
Kuvshinov, V. I.; Kuzmin, A. V.
2002-01-01
Chaos criterion for quantum field theory is proposed. Its correspondence with classical chaos criterion in semi-classical regime is shown. It is demonstrated for real scalar field that proposed chaos criterion can be used to investigate stability of classical solutions of field equations.
Applying Chaos Theory to Careers: Attraction and Attractors
Pryor, Robert G. L.; Bright, Jim E. H.
2007-01-01
This article presents the Chaos Theory of Careers with particular reference to the concepts of "attraction" and "attractors". Attractors are defined in terms of characteristic trajectories, feedback mechanisms, end states, ordered boundedness, reality visions and equilibrium and fluctuation. The identified types of attractors (point, pendulum,…
Application of Chaos Theory to Engine Systems
Matsumoto, Kazuhiro; Diebner, Hans H.; Tsuda, Ichiro; Hosoi, Yukiharu
2008-01-01
We focus on the control issue for engine systems from the perspective of chaos theory, which is based on the fact that engine systems have a low-dimensional chaotic dynamics. Two approaches are discussed: controlling chaos and harnessing chaos, respectively. We apply Pyragas' chaos control method to an actual engine system. The experimental results show that the chaotic motion of an engine system may be stabilized to a periodic motion. Alternatively, harnessing chaos for engine systems is add...
The Chaos Theory of Careers: A User's Guide
Bright, Jim E. H.; Pryor, Robert G. L.
2005-01-01
The purpose of this article is to set out the key elements of the Chaos Theory of Careers. The complexity of influences on career development presents a significant challenge to traditional predictive models of career counseling. Chaos theory can provide a more appropriate description of career behavior, and the theory can be applied with clients…
Chaos Theory as a Model for Managing Issues and Crises.
Murphy, Priscilla
1996-01-01
Uses chaos theory to model public relations situations in which the salient feature is volatility of public perceptions. Discusses the premises of chaos theory and applies them to issues management, the evolution of interest groups, crises, and rumors. Concludes that chaos theory is useful as an analogy to structure image problems and to raise…
Does chaos theory have major implications for philosophy of medicine?
Holm, S
2002-12-01
In the literature it is sometimes claimed that chaos theory, non-linear dynamics, and the theory of fractals have major implications for philosophy of medicine, especially for our analysis of the concept of disease and the concept of causation. This paper gives a brief introduction to the concepts underlying chaos theory and non-linear dynamics. It is then shown that chaos theory has only very minimal implications for the analysis of the concept of disease and the concept of causation, mainly because the mathematics of chaotic processes entail that these processes are fully deterministic. The practical unpredictability of chaotic processes, caused by their extreme sensitivity to initial conditions, may raise practical problems in diagnosis, prognosis, and treatment, but it raises no major theoretical problems. The relation between chaos theory and the problem of free will is discussed, and it is shown that chaos theory may remove the problem of predictability of decisions, but does not solve the problem of free will. Chaos theory may thus be very important for our understanding of physiological processes, and specific disease entities, without having any major implications for philosophy of medicine.
Oestreicher, Christian
2007-01-01
Whether every effect can be precisely linked to a given cause or to a list of causes has been a matter of debate for centuries, particularly during the 17th century, when astronomers became capable of predicting the trajectories of planets. Recent mathematical models applied to physics have included the idea that given phenomena cannot be predicted precisely, although they can be predicted to some extent, in line with the chaos theory. Concepts such as deterministic models, sensitivity to initial conditions, strange attractors, and fractal dimensions are inherent to the development of this theory A few situations involving normal or abnormal endogenous rhythms in biology have been analyzed following the principles of chaos theory. This is particularly the case with cardiac arrhythmias, but less so with biological clocks and circadian rhythms.
Oestreicher, Christian
2007-01-01
Whether every effect can be precisely linked to a given cause or to a list of causes has been a matter of debate for centuries, particularly during the 17th century when astronomers became capable of predicting the trajectories of planets. Recent mathematical models applied to physics have included the idea that given phenomena cannot be predicted precisely although they can be predicted to some extent in line with the chaos theory Concepts such as deterministic models, sensitivity to initial conditions, strange attractors, and fractal dimensions are inherent to the development of this theory, A few situations involving normal or abnormal endogenous rhythms in biology have been analyzed following the principles of chaos theory This is particularly the case with cardiac arrhythmias, but less so with biological clocks and circadian rhythms. PMID:17969865
Applying Chaos Theory to Lesson Planning and Delivery
Cvetek, Slavko
2008-01-01
In this article, some of the ways in which thinking about chaos theory can help teachers and student-teachers to accept uncertainty and randomness as natural conditions in the classroom are considered. Building on some key features of complex systems commonly attributed to chaos theory (e.g. complexity, nonlinearity, sensitivity to initial…
International Nuclear Information System (INIS)
Friedrich, H.
1992-01-01
Rapid growth in the study of nonlinear dynamics and chaos in classical mechanics, has led physicists to reappraise their abandonment of this definition of atomic theory in favour of quantum mechanics adopted earlier this century. The concept of chaos in classical mechanics is examined in this paper and manifestations of chaos in quantum mechanics are explored. While quantum mechanics teaches that atomic particles must not be pictured as moving sharply in defined orbits, these precise orbits can be used to describe essential features of the measurable quantum mechanical spectra. (UK)
Chaos theory: A fascinating concept for oncologists
International Nuclear Information System (INIS)
Denis, F.; Letellier, C.
2012-01-01
The oncologist is confronted daily by questions related to the fact that any patient presents a specific evolution for his cancer: he is challenged by very different, unexpected and often unpredictable outcomes, in some of his patients. The mathematical approach used today to describe this evolution has recourse to statistics and probability laws: such an approach does not ultimately apply to one particular patient, but to a given more or less heterogeneous population. This approach therefore poorly characterizes the dynamics of this disease and does not allow to state whether a patient is cured, to predict if he will relapse and when this could occur, and in what form, nor to predict the response to treatment and, in particular, to radiation therapy. Chaos theory, not well known by oncologists, could allow a better understanding of these issues. Developed to investigate complex systems producing behaviours that cannot be predicted due to a great sensitivity to initial conditions, chaos theory is rich of suitable concepts for a new approach of cancer dynamics. This article is three-fold: to provide a brief introduction to chaos theory, to clarify the main connecting points between chaos and carcinogenesis and to point out few promising research perspectives, especially in radiotherapy. (authors)
The Application of Chaos Theory to the Career-Plateaued Worker.
Duffy, Jean Ann
2000-01-01
Applies some of the principles of chaos theory to career-plateaued workers on the basis of a case study. Concludes that chaos theory provides career practitioners a useful application for working with this type of client. (Author/JDM)
Quantum signatures of chaos or quantum chaos?
International Nuclear Information System (INIS)
Bunakov, V. E.
2016-01-01
A critical analysis of the present-day concept of chaos in quantum systems as nothing but a “quantum signature” of chaos in classical mechanics is given. In contrast to the existing semi-intuitive guesses, a definition of classical and quantum chaos is proposed on the basis of the Liouville–Arnold theorem: a quantum chaotic system featuring N degrees of freedom should have M < N independent first integrals of motion (good quantum numbers) specified by the symmetry of the Hamiltonian of the system. Quantitative measures of quantum chaos that, in the classical limit, go over to the Lyapunov exponent and the classical stability parameter are proposed. The proposed criteria of quantum chaos are applied to solving standard problems of modern dynamical chaos theory.
Quantum signatures of chaos or quantum chaos?
Energy Technology Data Exchange (ETDEWEB)
Bunakov, V. E., E-mail: bunakov@VB13190.spb.edu [St. Petersburg State University (Russian Federation)
2016-11-15
A critical analysis of the present-day concept of chaos in quantum systems as nothing but a “quantum signature” of chaos in classical mechanics is given. In contrast to the existing semi-intuitive guesses, a definition of classical and quantum chaos is proposed on the basis of the Liouville–Arnold theorem: a quantum chaotic system featuring N degrees of freedom should have M < N independent first integrals of motion (good quantum numbers) specified by the symmetry of the Hamiltonian of the system. Quantitative measures of quantum chaos that, in the classical limit, go over to the Lyapunov exponent and the classical stability parameter are proposed. The proposed criteria of quantum chaos are applied to solving standard problems of modern dynamical chaos theory.
Chaos theory for clinical manifestations in multiple sclerosis.
Akaishi, Tetsuya; Takahashi, Toshiyuki; Nakashima, Ichiro
2018-06-01
Multiple sclerosis (MS) is a demyelinating disease which characteristically shows repeated relapses and remissions irregularly in the central nervous system. At present, the pathological mechanism of MS is unknown and we do not have any theories or mathematical models to explain its disseminated patterns in time and space. In this paper, we present a new theoretical model from a viewpoint of complex system with chaos model to reproduce and explain the non-linear clinical and pathological manifestations in MS. First, we adopted a discrete logistic equation with non-linear dynamics to prepare a scalar quantity for the strength of pathogenic factor at a specific location of the central nervous system at a specific time to reflect the negative feedback in immunity. Then, we set distinct minimum thresholds in the above-mentioned scalar quantity for demyelination possibly causing clinical relapses and for cerebral atrophy. With this simple model, we could theoretically reproduce all the subtypes of relapsing-remitting MS, primary progressive MS, and secondary progressive MS. With the sensitivity to initial conditions and sensitivity to minute change in parameters of the chaos theory, we could also reproduce the spatial dissemination. Such chaotic behavior could be reproduced with other similar upward-convex functions with appropriate set of initial conditions and parameters. In conclusion, by applying chaos theory to the three-dimensional scalar field of the central nervous system, we can reproduce the non-linear outcome of the clinical course and explain the unsolved disseminations in time and space of the MS patients. Copyright © 2018 Elsevier Ltd. All rights reserved.
A Chaos Theory Perspective on International Migration
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Anca Tănasie
2017-12-01
Full Text Available This paper aims at providing a different approach to international migration analysis, beyond classical models previously proposed by specialized literature. Chaos theory is getting more and more applied into macroeconomics once traditional linear models or even previous dynamic analysis become less suitable. Modern science sees chaos as unpredictable evolution, maybe even disorder. Still, chaos has got its own rules and can describe many dynamic phenomena within our world. Thus, we test whether international migration data falls under the rules of chaos and whether recent developments within the “European migration crisis” (the total daily migration inflows towards the coasts of Italy, by sea, from January 2014 to April 2017 could be described as chaotic.
[Chaos theory: a fascinating concept for oncologists].
Denis, F; Letellier, C
2012-05-01
The oncologist is confronted daily by questions related to the fact that any patient presents a specific evolution for his cancer: he is challenged by very different, unexpected and often unpredictable outcomes, in some of his patients. The mathematical approach used today to describe this evolution has recourse to statistics and probability laws: such an approach does not ultimately apply to one particular patient, but to a given more or less heterogeneous population. This approach therefore poorly characterizes the dynamics of this disease and does not allow to state whether a patient is cured, to predict if he will relapse and when this could occur, and in what form, nor to predict the response to treatment and, in particular, to radiation therapy. Chaos theory, not well known by oncologists, could allow a better understanding of these issues. Developed to investigate complex systems producing behaviours that cannot be predicted due to a great sensitivity to initial conditions, chaos theory is rich of suitable concepts for a new approach of cancer dynamics. This article is three-fold: to provide a brief introduction to chaos theory, to clarify the main connecting points between chaos and carcinogenesis and to point out few promising research perspectives, especially in radiotherapy. Copyright © 2012 Société française de radiothérapie oncologique (SFRO). Published by Elsevier SAS. All rights reserved.
Onset of dynamical chaos in topologically massive gauge theories
International Nuclear Information System (INIS)
Giansanti, A.; Simic, P.D.
1988-01-01
The onset of dynamical chaos is studied numerically in (2+1)-dimensional non-Abelian field theory with the Chern-Simons topological term. In the limit of strong fields, slowly varying in space (spatially homogeneous fields), this theory is an analog to a system of three charged particles moving in a plane in an orthogonal magnetic field and under the influence of a quartic potential. The ''phase transition'' (order chaos) is observed within a narrow energy range. The threshold of the transition depends on the sign of the angular momentum of the field reflecting parity violation in the underlying field theory. The transition region is investigated in some detail and the hyperfine structure of order-chaos-order-... transitions is observed suggesting the necessity of probabilistic description
Chaos Theory and International Relations
2016-12-01
King Oscar II 12 James E. Glenn, Chaos Theory: The Essentials for Military Applications (Newport, RI...Adolf Hitler in Germany, Alexander’s conquest of the Persian Empire, the arrival of Attila to Europe, the onset of the two Gulf Wars, the Arab Spring
Chaos Theory and Its Application to Education: Mehmet Akif Ersoy University Case
Akmansoy, Vesile; Kartal, Sadik
2014-01-01
Discussions have arisen regarding the application of the new paradigms of chaos theory to social sciences as compared to physical sciences. This study examines what role chaos theory has within the education process and what effect it has by describing the views of university faculty regarding chaos and education. The participants in this study…
An introduction to chaos theory in CFD
Pulliam, Thomas H.
1990-01-01
The popular subject 'chaos theory' has captured the imagination of a wide variety of scientists and engineers. CFD has always been faced with nonlinear systems and it is natural to assume that nonlinear dynamics will play a role at sometime in such work. This paper will attempt to introduce some of the concepts and analysis procedures associated with nonlinear dynamics theory. In particular, results from computations of an airfoil at high angle of attack which exhibits a sequence of bifurcations for single frequency unsteady shedding through period doublings cascading into low dimensional chaos are used to present and demonstrate various aspects of nonlinear dynamics in CFD.
Riemannian geometry of Hamiltonian chaos: hints for a general theory.
Cerruti-Sola, Monica; Ciraolo, Guido; Franzosi, Roberto; Pettini, Marco
2008-10-01
We aim at assessing the validity limits of some simplifying hypotheses that, within a Riemmannian geometric framework, have provided an explanation of the origin of Hamiltonian chaos and have made it possible to develop a method of analytically computing the largest Lyapunov exponent of Hamiltonian systems with many degrees of freedom. Therefore, a numerical hypotheses testing has been performed for the Fermi-Pasta-Ulam beta model and for a chain of coupled rotators. These models, for which analytic computations of the largest Lyapunov exponents have been carried out in the mentioned Riemannian geometric framework, appear as paradigmatic examples to unveil the reason why the main hypothesis of quasi-isotropy of the mechanical manifolds sometimes breaks down. The breakdown is expected whenever the topology of the mechanical manifolds is nontrivial. This is an important step forward in view of developing a geometric theory of Hamiltonian chaos of general validity.
Bright, Jim E. H.; Pryor, Robert G. L.
2011-01-01
The Chaos Theory of Careers (CTC; Pryor & Bright, 2011) construes both individuals and the contexts in which they develop their careers in terms of complex dynamical systems. Such systems perpetually operate under influences of stability and change both internally and in relation to each other. The CTC introduces new concepts to account for…
International Nuclear Information System (INIS)
Kinnebrock, Werner
2011-01-01
The past century changed the classical, scientific way of view enormously. The quantum theory broke with the imagination of continuity of all dynamical processes and gave space to completely new, nearly revolutionary approaches of thinking. Einstein's relativity theory put the absoluteness of time and space as well as the general validity of the Euclidean geometry in question. The absolute calculability, as it was formulated by Laplace, was by the influence of chaos theory proven as illusion. Computers made by the Mandelbrot set the presentation of new esthetic and never seen structures. Hilbert's century program of a complete formalization of mathematics failed because of the famous law of Goedel. It is the demand of this book to present all these theories and conclusions easily understandably and entertainingly.
Pryor, Robert; Bright, Jim
2004-01-01
This paper highlights five challenges to the accepted wisdom in career development theory and practice. It presents the chaos theory of careers and argues that the chaos theory provides a more complete and authentic account of human behaviour. The paper argues that positivism, reductionism and assumptions of linearity are inappropriate for…
Quantum mechanical suppression of chaos
International Nuclear Information System (INIS)
Bluemel, R.; Smilansky, U.
1990-01-01
The relation between determinism and predictability is the central issue in the study of 'deterministic chaos'. Much knowledge has been accumulated in the past 10 years about the chaotic dynamics of macroscopic (classical) systems. The implications of chaos in the microscopic quantum world is examined, in other words, how to reconcile the correspondence principle with the inherent uncertainties which reflect the wave nature of quantum dynamics. Recent atomic physics experiments demonstrate clearly that chaos is relevant to the microscopic world. In particular, such experiments emphasise the urgent need to clarify the genuine quantum mechanism which imposes severe limitations on quantum dynamics, and renders it so very different from its classical counterpart. (author)
A Framework for Chaos Theory Career Counselling
Pryor, Robert G. L.
2010-01-01
Theory in career development counselling provides a map that counsellors can use to understand and structure the career counselling process. It also provides a means to communicate this understanding and structuring to their clients as part of the counselling intervention. The chaos theory of careers draws attention to the complexity,…
Chaos Theory and James Joyce's "ulysses": Leopold Bloom as a Human COMPLEX@SYSTEM^
Mackey, Peter Francis
1995-01-01
These four ideas apply as much to our lives as to the life of Leopold Bloom: (1) A trivial decision can wholly change a life. (2) A chance encounter can dramatically alter life's course. (3) A contingent nexus exists between consciousness and environment. (4) A structure of meaning helps us interpret life's chaos. These ideas also relate to a contemporary science called by some "chaos theory." The connection between Ulysses and chaos theory enhances our understanding of Bloom's day; it also suggests that this novel may be about the real process of life itself. The first chapter explains how Joyce's own essays and comments to friends compel attention to the links between Ulysses and chaos theory. His scientific contemporaries anticipated chaos theory, and their ideas seem to have rubbed off on him. We see this in his sense of trivial things and chance, his modernistic organizational impulses, and the contingent nature of Bloom's experience. The second chapter studies what chaos theory and Joyce's ideas tell us about "Ithaca," the episode which particularly implicates our processes of interpreting this text as well as life itself as we face their chaos. The third chapter examines Bloom's close feel for the aboriginal world, a contingency that clarifies his vulnerability to trivial changes. The fourth chapter studies how Bloom's stream of consciousness unfolds--from his chance encounters with trivial things. Beneath this stream's seeming chaos, Bloom's distinct personality endures, similar to how Joyce's schemas give Ulysses an imbedded, underlying order. The fifth chapter examines how trivial perturbations, such as Lyons' misunderstanding about "Throwaway," produce small crises for Bloom, exacerbating his seeming impotence before his lonely "fate.". The final chapter analyzes Bloom's views that fate and chance dictate his life. His views provide an opportunity to explore the implications chaos theory has for our understanding of free will and determinism. Ultimately
CHAOS THEORY OF LAW: PENJELASAN ATAS KETERATURAN DAN KETIDAKTERATURAN DALAM HUKUM
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. Sudjito
2015-02-01
Full Text Available It is of no posibilitiy to understand the complex reality of law by means of linear-mechanistic approach used to be ulitilized in rechtsdogmatiek or legal-positivism which is still dominant in the teaching of law. It needs our readiness to see the world of law not as in order but in chaos; and this is the basic reason to present the Chaos theory of law. It is hoped that this theory will enable us to explore and explain the law throroughly. Thus the law science will be the total science which does not limit itself to the positive law, the state law or the lawyer’s law. Furthermore this chaos theory is expected to give better description and comprehension of law. Order and disorder are not opposant, or white-black dichotomy, but they are interrelated, interwoven and having mutual fulfilment in a sustainably and continually change process. The Chaos theory of law, thus, constitutes a theory which is qualified to give good explanation of the complex reality of law and provide the best solution to the critical condition of law in our country.
Directory of Open Access Journals (Sweden)
Tamás Meszéna
2017-04-01
Full Text Available We are faced with chaotic processes in many segments of our life: meteorology, environmental pollution, financial and economic processes, sociology, mechanics, electronics, biology, chemistry. The spreading of high-performance computers and the development of simulation methods made the examination of these processes easily available. Regular, periodic motions (pendulum, harmonic oscillatory motion, bouncing ball, as taught at secondary level, become chaotic even due minor changes. If it is true that the most considerable achievements of twentieth century physics were the theory of relativity, quantum mechanics and chaos theory, then it is presumably time to think about, examine and test how and to what extent chaos can be presented to the students. Here I would like to introduce a 12 lesson long facultative curriculum framework on chaos designed for students aged seventeen. The investigation of chaos phenomenon in this work is based on a freeware, “Dynamics Solver”. This software, with some assistance from the teacher, is suitable for classroom use at secondary level.
Meso-structures of dynamical chaos and E-infinity theory
International Nuclear Information System (INIS)
Mukhamedov, A.M.
2009-01-01
A novel proposal is made to develop a unified theory of dynamical chaos using an idea of extra-coordinates. It is supposed that chaos is capable to translate influences from quantum level of description to the classical macroscopic one and vise versa. The notion of macroscopically prepared microstates is proposed to determine a special case of extra-coordinates induced by cooperative effects at quantum resolution of dynamical events. Meso-structures mediating quantum and classical appearances of chaotic motion are studied in the light of E-infinity theory.
Chaos in nuclei: Theory and experiment
Muñoz, L.; Molina, R. A.; Gómez, J. M. G.
2018-05-01
During the last three decades the quest for chaos in nuclei has been quite intensive, both with theoretical calculations using nuclear models and with detailed analyses of experimental data. In this paper we outline the concept and characteristics of quantum chaos in two different approaches, the random matrix theory fluctuations and the time series fluctuations. Then we discuss the theoretical and experimental evidence of chaos in nuclei. Theoretical calculations, especially shell-model calculations, have shown a strongly chaotic behavior of bound states in regions of high level density. The analysis of experimental data has shown a strongly chaotic behavior of nuclear resonances just above the one-nucleon emission threshold. For bound states, combining experimental data of a large number of nuclei, a tendency towards chaotic motion is observed in spherical nuclei, while deformed nuclei exhibit a more regular behavior associated to the collective motion. On the other hand, it had never been possible to observe chaos in the experimental bound energy levels of any single nucleus. However, the complete experimental spectrum of the first 151 states up to excitation energies of 6.20 MeV in the 208Pb nucleus have been recently identified and the analysis of its spectral fluctuations clearly shows the existence of chaotic motion.
Generalized Statistical Mechanics at the Onset of Chaos
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Alberto Robledo
2013-11-01
Full Text Available Transitions to chaos in archetypal low-dimensional nonlinear maps offer real and precise model systems in which to assess proposed generalizations of statistical mechanics. The known association of chaotic dynamics with the structure of Boltzmann–Gibbs (BG statistical mechanics has suggested the potential verification of these generalizations at the onset of chaos, when the only Lyapunov exponent vanishes and ergodic and mixing properties cease to hold. There are three well-known routes to chaos in these deterministic dissipative systems, period-doubling, quasi-periodicity and intermittency, which provide the setting in which to explore the limit of validity of the standard BG structure. It has been shown that there is a rich and intricate behavior for both the dynamics within and towards the attractors at the onset of chaos and that these two kinds of properties are linked via generalized statistical-mechanical expressions. Amongst the topics presented are: (i permanently growing sensitivity fluctuations and their infinite family of generalized Pesin identities; (ii the emergence of statistical-mechanical structures in the dynamics along the routes to chaos; (iii dynamical hierarchies with modular organization; and (iv limit distributions of sums of deterministic variables. The occurrence of generalized entropy properties in condensed-matter physical systems is illustrated by considering critical fluctuations, localization transition and glass formation. We complete our presentation with the description of the manifestations of the dynamics at the transitions to chaos in various kinds of complex systems, such as, frequency and size rank distributions and complex network images of time series. We discuss the results.
Application of Chaos Theory in Trucks' Overloading Enforcement
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Abbas Mahmoudabadi
2013-01-01
Full Text Available Trucks' overloading is considered as one of the most substantial concerns in road transport due to a possible road surface damage, as well as, are less reliable performance of trucks' braking system. Sufficient human resource and adequate time scheduling are to be planned for surveying trucks' overloading; hence, it seems required to prepare an all-around model to be able to predict the number of overloaded vehicles. In the present research work, the concept of chaos theory has been utilized to predict the ratio of trucks which might be guessed overloaded. The largest Lyapunov exponent is utilized to determine the presence of chaos using experimental data and concluded that the ratio of overloaded trucks reflects chaotic behavior. The prediction based on chaos theory is compared with the results of simple smoothing and moving average methods according to the well-known criterion of mean square errors. The results have also revealed that the chaotic prediction model would act more capably comparing the analogous methods including simple smoothing and moving average to predict the ratio of passing trucks to be possibly overloaded.
Models and applications of chaos theory in modern sciences
Zeraoulia, Elhadj
2011-01-01
This book presents a select group of papers that provide a comprehensive view of the models and applications of chaos theory in medicine, biology, ecology, economy, electronics, mechanical, and the human sciences. Covering both the experimental and theoretical aspects of the subject, it examines a range of current topics of interest. It considers the problems arising in the study of discrete and continuous time chaotic dynamical systems modeling the several phenomena in nature and society-highlighting powerful techniques being developed to meet these challenges that stem from the area of nonli
Chaos theory perspective for industry clusters development
Yu, Haiying; Jiang, Minghui; Li, Chengzhang
2016-03-01
Industry clusters have outperformed in economic development in most developing countries. The contributions of industrial clusters have been recognized as promotion of regional business and the alleviation of economic and social costs. It is no doubt globalization is rendering clusters in accelerating the competitiveness of economic activities. In accordance, many ideas and concepts involve in illustrating evolution tendency, stimulating the clusters development, meanwhile, avoiding industrial clusters recession. The term chaos theory is introduced to explain inherent relationship of features within industry clusters. A preferred life cycle approach is proposed for industrial cluster recessive theory analysis. Lyapunov exponents and Wolf model are presented for chaotic identification and examination. A case study of Tianjin, China has verified the model effectiveness. The investigations indicate that the approaches outperform in explaining chaos properties in industrial clusters, which demonstrates industrial clusters evolution, solves empirical issues and generates corresponding strategies.
Paulson, Eric J.
2005-01-01
This theoretical article examines reading processes using chaos theory as an analogy. Three principles of chaos theory are identified and discussed, then related to reading processes as revealed through eye movement research. Used as an analogy, the chaos theory principle of sensitive dependence contributes to understanding the difficulty in…
On chaos in quantum mechanics: The two meanings of sensitive dependence
International Nuclear Information System (INIS)
Ingraham, R.L.; Luna Acosta, G.A.
1993-08-01
Sensitive dependence on initial conditions, the most important signature of chaos, can mean failure of Lyapunov stability, the primary meaning adopted in dynamical systems theory, or the presence of positive Lyapunov exponents, the meaning favored in physics. These are not equivalent in general. We show that there is sensitive dependence in quantum mechanics in the sense of violation of Lyapunov stability for maps of the state vector like involving unbounded operators A. This is true even for bounded quantum systems, where the corresponding Lyapunov exponents are all zero. Experiments to reveal this sensitive dependence, a definite though unfamiliar prediction of quantum mechanics, should be devised. It may also invalidate the usual assumption of linear response theory in quantum statistical mechanics in some cases. (author) 13 refs
Borrowed knowledge chaos theory and the challenge of learning across disciplines
Kellert, Stephen H
2009-01-01
What happens to scientific knowledge when researchers outside the natural sciences bring elements of the latest trend across disciplinary boundaries for their own purposes? Researchers in fields from anthropology to family therapy and traffic planning employ the concepts, methods, and results of chaos theory to harness the disciplinary prestige of the natural sciences, to motivate methodological change or conceptual reorganization within their home discipline, and to justify public policies and aesthetic judgments.Using the recent explosion in the use (and abuse) of chaos theory, Borrowed Knowledge and the Challenge of Learning across Disciplines examines the relationship between science and other disciplines as well as the place of scientific knowledge within our broader culture. Stephen H. Kellert's detailed investigation of the myriad uses of chaos theory reveals serious problems that can arise in the interchange between science and other knowledge-making pursuits, as well as opportunities for constructive...
Application of Chaos Theory to Psychological Models
Blackerby, Rae Fortunato
This dissertation shows that an alternative theoretical approach from physics--chaos theory--offers a viable basis for improved understanding of human beings and their behavior. Chaos theory provides achievable frameworks for potential identification, assessment, and adjustment of human behavior patterns. Most current psychological models fail to address the metaphysical conditions inherent in the human system, thus bringing deep errors to psychological practice and empirical research. Freudian, Jungian and behavioristic perspectives are inadequate psychological models because they assume, either implicitly or explicitly, that the human psychological system is a closed, linear system. On the other hand, Adlerian models that require open systems are likely to be empirically tenable. Logically, models will hold only if the model's assumptions hold. The innovative application of chaotic dynamics to psychological behavior is a promising theoretical development because the application asserts that human systems are open, nonlinear and self-organizing. Chaotic dynamics use nonlinear mathematical relationships among factors that influence human systems. This dissertation explores these mathematical relationships in the context of a sample model of moral behavior using simulated data. Mathematical equations with nonlinear feedback loops describe chaotic systems. Feedback loops govern the equations' value in subsequent calculation iterations. For example, changes in moral behavior are affected by an individual's own self-centeredness, family and community influences, and previous moral behavior choices that feed back to influence future choices. When applying these factors to the chaos equations, the model behaves like other chaotic systems. For example, changes in moral behavior fluctuate in regular patterns, as determined by the values of the individual, family and community factors. In some cases, these fluctuations converge to one value; in other cases, they diverge in
Philosophical perspectives on quantum chaos: Models and interpretations
Bokulich, Alisa Nicole
2001-09-01
The problem of quantum chaos is a special case of the larger problem of understanding how the classical world emerges from quantum mechanics. While we have learned that chaos is pervasive in classical systems, it appears to be almost entirely absent in quantum systems. The aim of this dissertation is to determine what implications the interpretation of quantum mechanics has for attempts to explain the emergence of classical chaos. There are three interpretations of quantum mechanics that have set out programs for solving the problem of quantum chaos: the standard interpretation, the statistical interpretation, and the deBroglie-Bohm causal interpretation. One of the main conclusions of this dissertation is that an interpretation alone is insufficient for solving the problem of quantum chaos and that the phenomenon of decoherence must be taken into account. Although a completely satisfactory solution of the problem of quantum chaos is still outstanding, I argue that the deBroglie-Bohm interpretation with the help of decoherence outlines the most promising research program to pursue. In addition to making a contribution to the debate in the philosophy of physics concerning the interpretation of quantum mechanics, this dissertation reveals two important methodological lessons for the philosophy of science. First, issues of reductionism and intertheoretic relations cannot be divorced from questions concerning the interpretation of the theories involved. Not only is the exploration of intertheoretic relations a central part of the articulation and interpretation of an individual theory, but the very terms used to discuss intertheoretic relations, such as `state' and `classical limit', are themselves defined by particular interpretations of the theory. The second lesson that emerges is that, when it comes to characterizing the relationship between classical chaos and quantum mechanics, the traditional approaches to intertheoretic relations, namely reductionism and
Nee, Sean
2018-05-01
Survival analysis in biology and reliability theory in engineering concern the dynamical functioning of bio/electro/mechanical units. Here we incorporate effects of chaotic dynamics into the classical theory. Dynamical systems theory now distinguishes strong and weak chaos. Strong chaos generates Type II survivorship curves entirely as a result of the internal operation of the system, without any age-independent, external, random forces of mortality. Weak chaos exhibits (a) intermittency and (b) Type III survivorship, defined as a decreasing per capita mortality rate: engineering explicitly defines this pattern of decreasing hazard as 'infant mortality'. Weak chaos generates two phenomena from the normal functioning of the same system. First, infant mortality- sensu engineering-without any external explanatory factors, such as manufacturing defects, which is followed by increased average longevity of survivors. Second, sudden failure of units during their normal period of operation, before the onset of age-dependent mortality arising from senescence. The relevance of these phenomena encompasses, for example: no-fault-found failure of electronic devices; high rates of human early spontaneous miscarriage/abortion; runaway pacemakers; sudden cardiac death in young adults; bipolar disorder; and epilepsy.
Using simplified Chaos Theory to manage nursing services.
Haigh, Carol A
2008-04-01
The purpose of this study was to evaluate the part simplified chaos theory could play in the management of nursing services. As nursing care becomes more complex, practitioners need to become familiar with business planning and objective time management. There are many time-limited methods that facilitate this type of planning but few that can help practitioners to forecast the end-point outcome of the service they deliver. A growth model was applied to a specialist service to plot service trajectory. Components of chaos theory can play a role in forecasting service outcomes and consequently the impact upon the management of such services. The ability to (1) track the trajectory of a service and (2) manipulate that trajectory by introducing new variables can allow managers to forward plan for service development and to evaluate the effectiveness of a service by plotting its end-point state.
The butterfly and the tornado: chaos theory and climate change
International Nuclear Information System (INIS)
Madrid, Carlos
2013-01-01
In this book, the author addresses two topics: the theory of chaos, and climate change. The first chapters propose a prehistory and history of chaos, from Newton, Laplace and Lorenz and their controversies as far as prehistory of chaos is concerned, and with different works performed during the twentieth century (Hadamard, Birkhoff, van der Pol, and so on, until Lorenz, the MIT meteorologist and the discovery of the Butterfly Effect, and more recent works by Yorke and Feigenbaum about the logistic equation and the transition to chaos) as far as recent history is concerned. The next chapter describes the deterministic chaos by introducing non linear dynamic systems and distinguishing three regimes: steady, periodic or chaotic. The second part addresses climate change, outlines that global warming is a reality, that the main origin is the increase of greenhouse effect, and that CO 2 emissions related to human activity are the main origin of this additional greenhouse effect. The author notably recalls the controversy about the analysis of the global average temperature curve, discusses the assessment of average temperatures from a statistical point of view and in relationship with the uneven distribution of survey stations. The last chapter discusses the numerical modelling of time and climate, and the validity of the Butterfly Effect. The author also proposes a brief overview of the IPCC, discusses the emergence of an international climate policy (UN convention, Kyoto protocol), evokes the use of game theory to ensure a convergence of treaties, and analyses the economic situation of several countries (including Spain) since the Kyoto protocol
CHAOS THEORY, GLOBAL SYSTEMIC CHANGE, AND HYBRID WARS
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A. Korybko
2016-01-01
Full Text Available The global system is being rocked by the dueling ambitions of two competing blocs, with the US and its allies fighting to reinforce their unipolar system while Russia and its partners struggle to forge a multipolar future. The rapidity and scope with which events are unfolding makes it overwhelming for the casual observer to make sense of all of the complex processes currently at play, and truth be told, it’s understandable that all of this can appear confusing. In an attempt to clarify the present state of global affairs and forecast the direction that it’s all headed in, the article begins by explaining the nature of chaos theory and describing how it’s applicable to conceptualizing contemporary international relations. Afterwards, the idea of “chaos sequencing” is proposed, which in essence is a model that can be used in understanding the process of chaotic change. Following that, the article addresses the topic of global systemic change and includes the most relevant examples for how this relates to the present day. Next, the research combines these two aforementioned elements (chaos theory and global systemic change and presents a forward-looking geopolitical analysis that incorporates cutting-edge Hybrid War theory and aims to put the New Cold War into its proper perspective. Finally, the article ends on a suggestive note in encouraging analysts to study the authors’ conceptualization of Hybrid War in order to better prepare themselves for understanding and responding to forthcoming international events.
Replication of chaos in neural networks, economics and physics
Akhmet, Marat
2016-01-01
This book presents detailed descriptions of chaos for continuous-time systems. It is the first-ever book to consider chaos as an input for differential and hybrid equations. Chaotic sets and chaotic functions are used as inputs for systems with attractors: equilibrium points, cycles and tori. The findings strongly suggest that chaos theory can proceed from the theory of differential equations to a higher level than previously thought. The approach selected is conducive to the in-depth analysis of different types of chaos. The appearance of deterministic chaos in neural networks, economics and mechanical systems is discussed theoretically and supported by simulations. As such, the book offers a valuable resource for mathematicians, physicists, engineers and economists studying nonlinear chaotic dynamics.
On the suppression of chaos in quantum and classical physics
International Nuclear Information System (INIS)
Fried, H.M.; Gabellini, Y.
1997-01-01
A brief outline is presented of an example of potential-theory quantum chaos, which is suppressed by the full radiative corrections of quantum field theory. A similar mechanism may be devised and applied to classically chaotic systems, and provides an example in which an explicit diminution of the original chaos becomes apparent. (author)
Organisational Leadership and Chaos Theory: Let's Be Careful
Galbraith, Peter
2004-01-01
This article addresses issues associated with applications of ideas from "chaos theory" to educational administration and leadership as found in the literature. Implications are considered in relation to claims concerning the behaviour of non-linear dynamic systems, and to the nature of the interpretations and recommendations that are made. To aid…
The Value of Failing in Career Development: A Chaos Theory Perspective
Pryor, Robert G. L.; Bright, James E. H.
2012-01-01
Failing is a neglected topic in career development theory and counselling practice. Most theories see failing as simply the opposite of success and something to be avoided. It is contended that the Chaos Theory of Careers with its emphasis on complexity, uncertainty and consequent human imitations, provides a conceptually coherent account of…
Short-term data forecasting based on wavelet transformation and chaos theory
Wang, Yi; Li, Cunbin; Zhang, Liang
2017-09-01
A sketch of wavelet transformation and its application was given. Concerning the characteristics of time sequence, Haar wavelet was used to do data reduction. After processing, the effect of “data nail” on forecasting was reduced. Chaos theory was also introduced, a new chaos time series forecasting flow based on wavelet transformation was proposed. The largest Lyapunov exponent was larger than zero from small data sets, it verified the data change behavior still met chaotic behavior. Based on this, chaos time series to forecast short-term change behavior could be used. At last, the example analysis of the price from a real electricity market showed that the forecasting method increased the precision of the forecasting more effectively and steadily.
Controlling chaos in permanent magnet synchronous motor based on finite-time stability theory
International Nuclear Information System (INIS)
Du-Qu, Wei; Bo, Zhang
2009-01-01
This paper reports that the performance of permanent magnet synchronous motor (PMSM) degrades due to chaos when its systemic parameters fall into a certain area. To control the undesirable chaos in PMSM, a nonlinear controller, which is simple and easy to be constructed, is presented to achieve finite-time chaos control based on the finite-time stability theory. Computer simulation results show that the proposed controller is very effective. The obtained results may help to maintain the industrial servo driven system's security operation. (general)
Chaos Theory as a Planning Tool for Community-Based Educational Experiences for Health Students.
Velde, Beth P.; Greer, Annette G.; Lynch, Deirdre C.; Escott-Stump, Sylvia
2002-01-01
Chaos theory, which attempts to understand underlying order where none is apparent, was applied to an interdisciplinary rural health training program for health professionals. Similar programs should anticipate systemic flux between order and chaos and pay attention to information flow, degree of diversity, richness of connectivity, contained…
Chaos Criminology: A critical analysis
McCarthy, Adrienne L.
There has been a push since the early 1980's for a paradigm shift in criminology from a Newtonian-based ontology to one of quantum physics. Primarily this effort has taken the form of integrating Chaos Theory into Criminology into what this thesis calls 'Chaos Criminology'. However, with the melding of any two fields, terms and concepts need to be translated properly, which has yet to be done. In addition to proving a translation between fields, this thesis also uses a set of criteria to evaluate the effectiveness of the current use of Chaos Theory in Criminology. While the results of the theory evaluation reveal that the current Chaos Criminology work is severely lacking and in need of development, there is some promise in the development of Marx's dialectical materialism with Chaos Theory.
Group Chaos Theory: A Metaphor and Model for Group Work
Rivera, Edil Torres; Wilbur, Michael; Frank-Saraceni, James; Roberts-Wilbur, Janice; Phan, Loan T.; Garrett, Michael T.
2005-01-01
Group phenomena and interactions are described through the use of the chaos theory constructs and characteristics of sensitive dependence on initial conditions, phase space, turbulence, emergence, self-organization, dissipation, iteration, bifurcation, and attractors and fractals. These constructs and theoretical tenets are presented as applicable…
Menstruation, perimenopause, and chaos theory.
Derry, Paula S; Derry, Gregory N
2012-01-01
This article argues that menstruation, including the transition to menopause, results from a specific kind of complex system, namely, one that is nonlinear, dynamical, and chaotic. A complexity-based perspective changes how we think about and research menstruation-related health problems and positive health. Chaotic systems are deterministic but not predictable, characterized by sensitivity to initial conditions and strange attractors. Chaos theory provides a coherent framework that qualitatively accounts for puzzling results from perimenopause research. It directs attention to variability within and between women, adaptation, lifespan development, and the need for complex explanations of disease. Whether the menstrual cycle is chaotic can be empirically tested, and a summary of our research on 20- to 40-year-old women is provided.
Complexity, Chaos, and Nonlinear Dynamics: A New Perspective on Career Development Theory
Bloch, Deborah P.
2005-01-01
The author presents a theory of career development drawing on nonlinear dynamics and chaos and complexity theories. Career is presented as a complex adaptive entity, a fractal of the human entity. Characteristics of complex adaptive entities, including (a) autopiesis, or self-regeneration; (b) open exchange; (c) participation in networks; (d)…
The chaos avant-garde memories of the early days of chaos theory
Abraham, Ralph H
2001-01-01
This book is an authoritative and unique reference for the history of chaos theory, told by the pioneers themselves. It also provides an excellent historical introduction to the concepts. There are eleven contributions, and six of them are published here for the first time - two by Steve Smale, three by Yoshisuke Ueda, and one each by Ralph Abraham, Edward Lorenz, Christian Mira, Floris Takens, T Y Li and James A Yorke, and Otto E Rossler. Contents: On How I Got Started in Dynamical Systems 1959-1962 (S Smale); Finding a Horseshoe on the Beaches of Rio (S Smale); Strange Attractors and the Ori
Keaten, James A.
This paper offers a model that integrates chaos theory and cybernetics, which can be used to describe the structure of decision making within small groups. The paper begins with an overview of cybernetics and chaos. Definitional characteristics of cybernetics are reviewed along with salient constructs, such as goal-seeking, feedback, feedback…
A New Technique in saving Fingerprint with low volume by using Chaos Game and Fractal Theory
Directory of Open Access Journals (Sweden)
Maryam Ashourzadeh
2010-12-01
Full Text Available Fingerprint is one of the simplest and most reliable biometric features of human for identification. In this study by using fractal theory and by the assistance of Chaos Game a new fractal is made from fingerprint. While making the new fractal by using Chaos Game mechanism some parameters, which can be used in identification process, can be deciphered. For this purpose, a fractal is made for each fingerprint, we save 10 parameters for every fingerprint, which have necessary information for identity, as said before. So we save 10 decimal parameters with 0.02 accuracy instead of saving the picture of a fingerprint or some parts of it. Now we improve the great volume of fingerprint pictures by using this model which employs fractal for knowing the personality
International Nuclear Information System (INIS)
Steiner, F.
1994-01-01
A short historical overview is given on the development of our knowledge of complex dynamical systems with special emphasis on ergodicity and chaos, and on the semiclassical quantization of integrable and chaotic systems. The general trace formular is discussed as a sound mathematical basis for the semiclassical quantization of chaos. Two conjectures are presented on the basis of which it is argued that there are unique fluctuation properties in quantum mechanics which are universal and, in a well defined sense, maximally random if the corresponding classical system is strongly chaotic. These properties constitute the quantum mechanical analogue of the phenomenon of chaos in classical mechanics. Thus quantum chaos has been found. (orig.)
Chaos in World Politics: A Reflection
Ferreira, Manuel Alberto Martins; Filipe, José António Candeias Bonito; Coelho, Manuel F. P.; Pedro, Isabel C.
Chaos theory results from natural scientists' findings in the area of non-linear dynamics. The importance of related models has increased in the last decades, by studying the temporal evolution of non-linear systems. In consequence, chaos is one of the concepts that most rapidly have been expanded in what research topics respects. Considering that relationships in non-linear systems are unstable, chaos theory aims to understand and to explain this kind of unpredictable aspects of nature, social life, the uncertainties, the nonlinearities, the disorders and confusion, scientifically it represents a disarray connection, but basically it involves much more than that. The existing close relationship between change and time seems essential to understand what happens in the basics of chaos theory. In fact, this theory got a crucial role in the explanation of many phenomena. The relevance of this kind of theories has been well recognized to explain social phenomena and has permitted new advances in the study of social systems. Chaos theory has also been applied, particularly in the context of politics, in this area. The goal of this chapter is to make a reflection on chaos theory - and dynamical systems such as the theories of complexity - in terms of the interpretation of political issues, considering some kind of events in the political context and also considering the macro-strategic ideas of states positioning in the international stage.
Chaos and Crisis: Propositions for a General Theory of Crisis Communication.
Seeger, Matthew W.
2002-01-01
Presents key concepts of chaos theory (CT) as a general framework for describing organizational crisis and crisis communication. Discusses principles of predictability, sensitive dependence on initial conditions, bifurcation as system breakdown, emergent self-organization, and fractals and strange attractors as principles of organization. Explores…
Cutright, Marc, Ed.
This anthology considers some ways that chaos theory might be not only a descriptive metaphor for the conditions of leadership, planning, and policy in higher education, but also a prescriptive metaphor that might be used to improve these functions and others. The essays are: (1) "Introduction: Metaphor, Chaos Theory, and This Book" (Marc…
Nuclear spectroscopy and quantum chaos
International Nuclear Information System (INIS)
Sakata, Fumihiko; Marumori, Toshio; Hashimoto, Yukio; Yamamoto, Yoshifumi; Tsukuma, Hidehiko; Iwasawa, Kazuo.
1990-05-01
In this paper, a recent development of INS-TSUKUBA joint research project on large-amplitude collective motion is summerized. The classical theory of nuclear collective dynamics formulated within the time-dependent Hartree-Fock theory is recapitulated and decisive role of the level crossing in the single-particle dynamics on the order-to-chaos transition of collective motion is discussed in detail. Extending the basic idea of the classical theory, we discuss a quantum theory of nuclear collective dynamics which allows us to properly define a concept of quantum chaos for each eigenfunction. By using numerical calculation, we illustrate what the quantum chaos for each eigenfunction means and its relation to usual definition based on the random matrix theory. (author)
Universality in quantum chaos and the one-parameter scaling theory.
García-García, Antonio M; Wang, Jiao
2008-02-22
The one-parameter scaling theory is adapted to the context of quantum chaos. We define a generalized dimensionless conductance, g, semiclassically and then study Anderson localization corrections by renormalization group techniques. This analysis permits a characterization of the universality classes associated to a metal (g-->infinity), an insulator (g-->0), and the metal-insulator transition (g-->g(c)) in quantum chaos provided that the classical phase space is not mixed. According to our results the universality class related to the metallic limit includes all the systems in which the Bohigas-Giannoni-Schmit conjecture holds but automatically excludes those in which dynamical localization effects are important. The universality class related to the metal-insulator transition is characterized by classical superdiffusion or a fractal spectrum in low dimensions (d < or = 2). Several examples are discussed in detail.
Positive Maladjustment as a Transition from Chaos to Order
Laycraft, Krystyna
2009-01-01
Dabrowski's theory of positive disintegration describes patterns and explains mechanisms of human development and has been successfully applied to understanding of gifted individuals. This article shows how the concepts of chaos theory and self-organization such as the sensitivity to initial conditions, positive and negative feedback, bifurcation…
Integrability and chaos in quantum systems (as viewed from geometry and dynamical symmetry)
International Nuclear Information System (INIS)
Zhang, Wei-Min.
1989-01-01
It is known that the development and deep understanding of modern interaction theory and classical mechanics are made through geometry and symmetry. Yet, quantum mechanics which was regarded to be the microscopic theory of classical mechanics and achieved the crowning success in interpreting the entire microscopic world was developed purely from algebraic methods. In this thesis, the author will study the geometry and dynamical symmetry in quantum systems, from which the question of integrability and chaos are explicitly addressed. First of all, the quantum dynamical degrees of freedom and quantum integrability are precisely defined and the inherent geometrical structure of quantum systems is explored from the fundamental structure of quantum theory. Such a geometrical structure can provide a framework to simultaneously build quantum and classical mechanics. The quantum-classical correspondence is then explicitly deduced. The dynamics of quantum system before it reaches the classical limit is formulated. Thus, the classical chaos is proven to be a special limiting phenomena of quantum systems and the dynamics before the system reaches its classical chaos is explored. The latter is the first step to seek the quantum manifestation of chaos. The relationship between integrability and dynamical symmetry are studied and some universal properties are discovered: a dynamical system (both quantum and classical) in integrable if it possesses a dynamical symmetry. Chaos will occur if the system undergoes a dynamical symmetry breaking and is accompanied by a structural phase transition. Thus, the concept of dynamical symmetry can be used to predict the general behaviors of a system. The theoretical underpinnings developed in this thesis are verified by many basic quantum mechanical examples
Renormalisation in Quantum Mechanics, Quantum Instantons and Quantum Chaos
Jirari, H.; Kröger, H.; Luo, X. Q.; Moriarty, K. J. M.
2001-01-01
We suggest how to construct non-perturbatively a renormalized action in quantum mechanics. We discuss similarties and differences with the standard effective action. We propose that the new quantum action is suitable to define and compute quantum instantons and quantum chaos.
Developing Integrated Arts Curriculum in Hong Kong: Chaos Theory at Work?
Wong, Marina
2013-01-01
This article reports the development of integrated arts curriculum in two Hong Kong secondary schools over a 9-year period. Initial findings display a range of individual responses to educational change that are both non-predictable and non-linear. Chaos theory is used to explain these varied responses in terms of bifurcations. The findings of…
Introduction to the focus issue: fifty years of chaos: applied and theoretical.
Hikihara, Takashi; Holmes, Philip; Kambe, Tsutomu; Rega, Giuseppe
2012-12-01
The discovery of deterministic chaos in the late nineteenth century, its subsequent study, and the development of mathematical and computational methods for its analysis have substantially influenced the sciences. Chaos is, however, only one phenomenon in the larger area of dynamical systems theory. This Focus Issue collects 13 papers, from authors and research groups representing the mathematical, physical, and biological sciences, that were presented at a symposium held at Kyoto University from November 28 to December 2, 2011. The symposium, sponsored by the International Union of Theoretical and Applied Mechanics, was called 50 Years of Chaos: Applied and Theoretical. Following some historical remarks to provide a background for the last 50 years, and for chaos, this Introduction surveys the papers and identifies some common themes that appear in them and in the theory of dynamical systems.
Soft Measurement Modeling Based on Chaos Theory for Biochemical Oxygen Demand (BOD
Directory of Open Access Journals (Sweden)
Junfei Qiao
2016-12-01
Full Text Available The precision of soft measurement for biochemical oxygen demand (BOD is always restricted due to various factors in the wastewater treatment plant (WWTP. To solve this problem, a new soft measurement modeling method based on chaos theory is proposed and is applied to BOD measurement in this paper. Phase space reconstruction (PSR based on Takens embedding theorem is used to extract more information from the limited datasets of the chaotic system. The WWTP is first testified as a chaotic system by the correlation dimension (D, the largest Lyapunov exponents (λ1, the Kolmogorov entropy (K of the BOD and other water quality parameters time series. Multivariate chaotic time series modeling method with principal component analysis (PCA and artificial neural network (ANN is then adopted to estimate the value of the effluent BOD. Simulation results show that the proposed approach has higher accuracy and better prediction ability than the corresponding modeling approaches not based on chaos theory.
International Nuclear Information System (INIS)
Cejnar, P.
2007-01-01
Chaos is a name given in physics to a branch which, within classical mechanics, studies the consequences of sensitive dependences of the behavior of physical systems on the starting conditions, i.e., the 'butterfly wing effect'. However, how to describe chaotic behavior in the world of quantum particles? It appears that quantum mechanics does not admit the sensitive dependence on the starting conditions, and moreover, predicts a substantial suppression of chaos also at the macroscopic level. Still, the quantum properties of systems that are chaotic in terms of classical mechanics differ basically from the properties of classically arranged systems. This topic is studied by a field of physics referred to as quantum chaos. (author)
Chaos control using sliding-mode theory
International Nuclear Information System (INIS)
Nazzal, Jamal M.; Natsheh, Ammar N.
2007-01-01
Chaos control means to design a controller that is able to mitigating or eliminating the chaos behavior of nonlinear systems that experiencing such phenomenon. In this paper, a nonlinear Sliding-Mode Controller (SMC) is presented. Two nonlinear chaotic systems are chosen to be our case study in this paper, the well known Chua's circuit and Lorenz system. The study shows the effectiveness of the designed nonlinear Sliding-Mode Controller
Shiftwork: A Chaos Theory of Careers Agenda for Change in Career Counseling
Bright, Jim E. H.; Pryor, Robert G. L.
2008-01-01
This paper presents the implications of the Chaos Theory of Careers for career counselling in the form of Shiftwork. Shiftwork represents an expanded paradigm of career counselling based on complexity, change and uncertainty. Eleven paradigm shifts for careers counselling are outlined to incorporate into contemporary practice pattern making, an…
Harnessing quantum transport by transient chaos.
Yang, Rui; Huang, Liang; Lai, Ying-Cheng; Grebogi, Celso; Pecora, Louis M
2013-03-01
Chaos has long been recognized to be generally advantageous from the perspective of control. In particular, the infinite number of unstable periodic orbits embedded in a chaotic set and the intrinsically sensitive dependence on initial conditions imply that a chaotic system can be controlled to a desirable state by using small perturbations. Investigation of chaos control, however, was largely limited to nonlinear dynamical systems in the classical realm. In this paper, we show that chaos may be used to modulate or harness quantum mechanical systems. To be concrete, we focus on quantum transport through nanostructures, a problem of considerable interest in nanoscience, where a key feature is conductance fluctuations. We articulate and demonstrate that chaos, more specifically transient chaos, can be effective in modulating the conductance-fluctuation patterns. Experimentally, this can be achieved by applying an external gate voltage in a device of suitable geometry to generate classically inaccessible potential barriers. Adjusting the gate voltage allows the characteristics of the dynamical invariant set responsible for transient chaos to be varied in a desirable manner which, in turn, can induce continuous changes in the statistical characteristics of the quantum conductance-fluctuation pattern. To understand the physical mechanism of our scheme, we develop a theory based on analyzing the spectrum of the generalized non-Hermitian Hamiltonian that includes the effect of leads, or electronic waveguides, as self-energy terms. As the escape rate of the underlying non-attracting chaotic set is increased, the imaginary part of the complex eigenenergy becomes increasingly large so that pointer states are more difficult to form, making smoother the conductance-fluctuation pattern.
Energy Technology Data Exchange (ETDEWEB)
Kinnebrock, Werner [Fachhochschule Rheinland-Pfalz (Germany)
2011-07-01
The past century changed the classical, scientific way of view enormously. The quantum theory broke with the imagination of continuity of all dynamical processes and gave space to completely new, nearly revolutionary approaches of thinking. Einstein's relativity theory put the absoluteness of time and space as well as the general validity of the Euclidean geometry in question. The absolute calculability, as it was formulated by Laplace, was by the influence of chaos theory proven as illusion. Computers made by the Mandelbrot set the presentation of new esthetic and never seen structures. Hilbert's century program of a complete formalization of mathematics failed because of the famous law of Goedel. It is the demand of this book to present all these theories and conclusions easily understandably and entertainingly.
Game as a Career Metaphor: A Chaos Theory Career Counselling Application
Pryor, Robert George Leslie; Bright, Jim E. H.
2009-01-01
The potential of game as a career metaphor for use in counselling is explored and it is argued that it has been largely overlooked in the literature to date. This metaphor is then explicitly linked with the Chaos Theory of Careers (CTC), by showing how the notion of attractors within the CTC can be illustrated effectively using games metaphors.…
Chaos and random matrices in supersymmetric SYK
Hunter-Jones, Nicholas; Liu, Junyu
2018-05-01
We use random matrix theory to explore late-time chaos in supersymmetric quantum mechanical systems. Motivated by the recent study of supersymmetric SYK models and their random matrix classification, we consider the Wishart-Laguerre unitary ensemble and compute the spectral form factors and frame potentials to quantify chaos and randomness. Compared to the Gaussian ensembles, we observe the absence of a dip regime in the form factor and a slower approach to Haar-random dynamics. We find agreement between our random matrix analysis and predictions from the supersymmetric SYK model, and discuss the implications for supersymmetric chaotic systems.
Control and synchronization of chaos in nonlinear systems and prospects for application. Pt.1
International Nuclear Information System (INIS)
Fang Jinqing
1996-01-01
Main progress in one challenging subject of nonlinear science--control and synchronization of chaos in nonlinear systems are reviewed systematically, including recent advance in controlling and synchronizing hyperchaos. Current methods and principles of schemes of chaos control and synchronization are classified and summarized in detail. Potential prospects for application are commented both in theory and experiment. The whole review is divided into two parts. In the first one, subject on the mechanism and method of chaos control are analyzed and discussed extensively. In the second one, the synchronization of non-chaos, chaos, hyperchaos and their control and application are described. Main trends for development of the subject is mentioned. (101 refs.)
Challenging the dominant logic of Emergency Departments: guidelines from chaos theory.
Chinnis, A; White, K R
1999-01-01
Chaos is order without predictability (1 ). Any unfortunate patient who has recently made a trek to an Emergency Department (ED) or even better, has watched the immensely popular TV show, ER, knows that the visit can be a frustrating and a time consuming experience. The waits are so protracted that one can observe all cycles of birth, death, love, and romance in the waiting room. The process is tedious for the patient who must tell one's tale to a triage nurse, a registration clerk, the primary nurse, the nursing care partner, and finally the emergency physician. Then, the patient must face more delays while being pushed, ineffectively, in a horizontal fashion, through vertical functional silos of care, such as laboratory and radiology. The mind-set or dominant logic of this system of ED patient flow assumes that waits are acceptable and unavoidable, and that the function of the ED is to care for only the truly emergent patient. This dominant logic, coupled with the market constraints of population-based versus case-based payment mechanisms, has led to a declining trend in ED visits for the first time in 20 years (2). In order to improve the quality of ED care as well as to increase acceptability for patient and payer, the dominant logic must be challenged. An understanding of chaos theory and perception of the Emergency Department as a complex adaptive system foster methods for challenging the dominant logic.
Chaos the science of predictable random motion
Kautz, Richard
2011-01-01
Based on only elementary mathematics, this engaging account of chaos theory bridges the gap between introductions for the layman and college-level texts. It develops the science of dynamics in terms of small time steps, describes the phenomenon of chaos through simple examples, and concludes with a close look at a homoclinic tangle, the mathematical monster at the heart of chaos. The presentation is enhanced by many figures, animations of chaotic motion (available on a companion CD), and biographical sketches of the pioneers of dynamics and chaos theory. To ensure accessibility to motivated high school students, care has been taken to explain advanced mathematical concepts simply, including exponentials and logarithms, probability, correlation, frequency analysis, fractals, and transfinite numbers. These tools help to resolve the intriguing paradox of motion that is predictable and yet random, while the final chapter explores the various ways chaos theory has been put to practical use.
Mechanics from Newton's laws to deterministic chaos
Scheck, Florian
2018-01-01
This book covers all topics in mechanics from elementary Newtonian mechanics, the principles of canonical mechanics and rigid body mechanics to relativistic mechanics and nonlinear dynamics. It was among the first textbooks to include dynamical systems and deterministic chaos in due detail. As compared to the previous editions the present 6th edition is updated and revised with more explanations, additional examples and problems with solutions, together with new sections on applications in science. Symmetries and invariance principles, the basic geometric aspects of mechanics as well as elements of continuum mechanics also play an important role. The book will enable the reader to develop general principles from which equations of motion follow, to understand the importance of canonical mechanics and of symmetries as a basis for quantum mechanics, and to get practice in using general theoretical concepts and tools that are essential for all branches of physics. The book contains more than 150 problems ...
Pryor, Robert G. L.; Amundson, Norman E.; Bright, Jim E. H.
2008-01-01
The chaos theory of careers emphasizes both stability and change in its account of career development. This article outlines counseling strategies derived from this emphasis in terms of convergent or probability thinking and emergent or possibility thinking. These 2 perspectives are characterized, and practical counseling strategy implications are…
Making sense of social media communications with chaos theory
DEFF Research Database (Denmark)
Gyimóthy, Szilvia; Larson, Mia
, offering a few conceptual papers which adopt complexity theories to describe destination development patterns (Russel & Faulkner, 2000, 2004; Zahra & Ryan 2007). The purpose of this paper is to discuss the validity of chaos theory in the context of strategic communications, where new (social) media has...... changed the marketing landscape beyond recognition. The exponential growth of social media platforms has led to weakened marketer control (and greater consumer sovereignty) over information about organisations and their products. In this new communications paradigm (Muniz & Schau 2007), information...... media channels. Social media users serve as gatekeepers, opting for which fluctuations to pay attention to, which to ignore. The challenge is then to establish a framework of unfolding communication patterns on social media which can eventually explain the collective behaviour of bloggers, twitters...
Effect of smoothing on robust chaos.
Deshpande, Amogh; Chen, Qingfei; Wang, Yan; Lai, Ying-Cheng; Do, Younghae
2010-08-01
In piecewise-smooth dynamical systems, situations can arise where the asymptotic attractors of the system in an open parameter interval are all chaotic (e.g., no periodic windows). This is the phenomenon of robust chaos. Previous works have established that robust chaos can occur through the mechanism of border-collision bifurcation, where border is the phase-space region where discontinuities in the derivatives of the dynamical equations occur. We investigate the effect of smoothing on robust chaos and find that periodic windows can arise when a small amount of smoothness is present. We introduce a parameter of smoothing and find that the measure of the periodic windows in the parameter space scales linearly with the parameter, regardless of the details of the smoothing function. Numerical support and a heuristic theory are provided to establish the scaling relation. Experimental evidence of periodic windows in a supposedly piecewise linear dynamical system, which has been implemented as an electronic circuit, is also provided.
International Nuclear Information System (INIS)
Whelan, N.D.
1993-01-01
Random Matrix Theory successfully describes the statistics of the low-lying spectra of some nuclei but not of others. It is currently believed that this theory applies to systems in which the corresponding classical motion is chaotic. This conjecture is tested for collective nuclei by studying the Interacting Boson Model. Quantum and classical measures of chaos are proposed and found to be in agreement throughout the parameter space of the model. For some parameter values the measures indicate the presence of a previously unknown approximate symmetry. A phenomenon called partial dynamical symmetry is explored and shown to lead to a suppression of chaos. A time dependent function calculated from the quantum spectrum is discussed. This function is sensitive to the extent of chaos and provides a robust method of analyzing experimental spectra
COPD self-management supportive care: chaos and complexity theory.
Cornforth, Amber
This paper uses the emergent theories of chaos and complexity to explore the self-management supportive care of chronic obstructive pulmonary disease (COPD) patients within the evolving primary care setting. It discusses the concept of self-management support, the complexity of the primary care context and consultations, smoking cessation, and the impact of acute exacerbations and action planning. The author hopes that this paper will enable the acquisition of new insight and better understanding in this clinical area, as well as support meaningful learning and facilitate more thoughtful, effective and high quality patient-centred care within the context of primary care.
International Nuclear Information System (INIS)
Luo, Shaohua; Sun, Quanping; Cheng, Wei
2016-01-01
This paper addresses chaos control of the micro-electro- mechanical resonator by using adaptive dynamic surface technology with extended state observer. To reveal the mechanism of the micro- electro-mechanical resonator, the phase diagrams and corresponding time histories are given to research the nonlinear dynamics and chaotic behavior, and Homoclinic and heteroclinic chaos which relate closely with the appearance of chaos are presented based on the potential function. To eliminate the effect of chaos, an adaptive dynamic surface control scheme with extended state observer is designed to convert random motion into regular motion without precise system model parameters and measured variables. Putting tracking differentiator into chaos controller solves the ‘explosion of complexity’ of backstepping and poor precision of the first-order filters. Meanwhile, to obtain high performance, a neural network with adaptive law is employed to approximate unknown nonlinear function in the process of controller design. The boundedness of all the signals of the closed-loop system is proved in theoretical analysis. Finally, numerical simulations are executed and extensive results illustrate effectiveness and robustness of the proposed scheme.
Chaos applications in telecommunications
Stavroulakis, Peter
2005-01-01
IntroductionPeter StavroulakisChaotic Signal Generation and Transmission Antonio Cândido Faleiros,Waldecir João Perrella,TâniaNunes Rabello,Adalberto Sampaio Santos, andNeiYoshihiro SomaChaotic Transceiver Design Arthur Fleming-DahlChaos-Based Modulation and DemodulationTechniques Francis C.M. Lau and Chi K. TseA Chaos Approach to Asynchronous DS-CDMASystems S. Callegari, G. Mazzini, R. Rovatti, and G. SettiChannel Equalization in Chaotic CommunicationSystems Mahmut CiftciOptical Communications using ChaoticTechniques Gregory D. VanWiggerenAPPENDIX AFundamental Concepts of the Theory ofChaos a
2012 Symposium on Chaos, Complexity and Leadership
Erçetin, Şefika
2014-01-01
These proceedings from the 2012 symposium on "Chaos, complexity and leadership" reflect current research results from all branches of Chaos, Complex Systems and their applications in Management. Included are the diverse results in the fields of applied nonlinear methods, modeling of data and simulations, as well as theoretical achievements of Chaos and Complex Systems. Also highlighted are Leadership and Management applications of Chaos and Complexity Theory.
THEORY OF SECULAR CHAOS AND MERCURY'S ORBIT
International Nuclear Information System (INIS)
Lithwick, Yoram; Wu Yanqin
2011-01-01
We study the chaotic orbital evolution of planetary systems, focusing on secular (i.e., orbit-averaged) interactions, which dominate on long timescales. We first focus on the evolution of a test particle that is forced by multiple planets. To linear order in eccentricity and inclination, its orbit precesses with constant frequencies. But nonlinearities modify the frequencies, and can shift them into and out of resonance with either the planets' eigenfrequencies (forming eccentricity or inclination secular resonances), or with linear combinations of those frequencies (forming mixed high-order secular resonances). The overlap of these nonlinear secular resonances drives secular chaos. We calculate the locations and widths of nonlinear secular resonances, display them together on a newly developed map (the 'map of the mean momenta'), and find good agreement between analytical and numerical results. This map also graphically demonstrates how chaos emerges from overlapping secular resonances. We then apply this newfound understanding to Mercury to elucidate the origin of its orbital chaos. We find that since Mercury's two free precession frequencies (in eccentricity and inclination) lie within ∼25% of two other eigenfrequencies in the solar system (those of the Jupiter-dominated eccentricity mode and the Venus-dominated inclination mode), secular resonances involving these four modes overlap and cause Mercury's chaos. We confirm this with N-body integrations by showing that a slew of these resonant angles alternately librate and circulate. Our new analytical understanding allows us to calculate the criterion for Mercury to become chaotic: Jupiter and Venus must have eccentricity and inclination of a few percent. The timescale for Mercury's chaotic diffusion depends sensitively on the forcing. As it is, Mercury appears to be perched on the threshold for chaos, with an instability timescale comparable to the lifetime of the solar system.
General practice and the new science emerging from the theories of 'chaos' and complexity.
Griffiths, F; Byrne, D
1998-01-01
This paper outlines the general practice world view and introduces the main features of the theories of 'chaos' and complexity. From this, analogies are drawn between general practice and the theories, which suggest a different way of understanding general practice and point to future developments in general practice research. A conceptual and practical link between qualitative and quantitative methods of research is suggested. Methods of combining data about social context with data about in...
Some open questions in 'wave chaos'
International Nuclear Information System (INIS)
Nonnenmacher, Stéphane
2008-01-01
The subject area referred to as 'wave chaos', 'quantum chaos' or 'quantum chaology' has been investigated mostly by the theoretical physics community in the last 30 years. The questions it raises have more recently also attracted the attention of mathematicians and mathematical physicists, due to connections with number theory, graph theory, Riemannian, hyperbolic or complex geometry, classical dynamical systems, probability, etc. After giving a rough account on 'what is quantum chaos?', I intend to list some pending questions, some of them having been raised a long time ago, some others more recent. The choice of problems (and of references) is of course partial and personal. (open problem)
Nuclear physics, symmetries, and quantum chaos
International Nuclear Information System (INIS)
Bunakov, V.E.
1999-01-01
The reasons why the problem of chaos is of great topical interest in modern physics are briefly summarized, and it is indicated that ambiguities in the concept of quantum chaos present the greatest difficulties in these realms. The theory of random matrices and strength functions are generalized to demonstrate that chaotization of a system is associated with the violation of its symmetries. A criterion of quantum chaoticity is formulated in terms of the spreading width Γ spr . In the classical limit, this criterion reduces to Lyapunov's stability criteria. It is shown that the proposed criterion is applicable to standard problems of the modern theory of dynamical chaos
Nonlinear dynamics and quantum chaos an introduction
Wimberger, Sandro
2014-01-01
The field of nonlinear dynamics and chaos has grown very much over the last few decades and is becoming more and more relevant in different disciplines. This book presents a clear and concise introduction to the field of nonlinear dynamics and chaos, suitable for graduate students in mathematics, physics, chemistry, engineering, and in natural sciences in general. It provides a thorough and modern introduction to the concepts of Hamiltonian dynamical systems' theory combining in a comprehensive way classical and quantum mechanical description. It covers a wide range of topics usually not found in similar books. Motivations of the respective subjects and a clear presentation eases the understanding. The book is based on lectures on classical and quantum chaos held by the author at Heidelberg University. It contains exercises and worked examples, which makes it ideal for an introductory course for students as well as for researchers starting to work in the field.
Chaos Theory as a Model for Life Transitions Counseling: Nonlinear Dynamics and Life's Changes
Bussolari, Cori J.; Goodell, Judith A.
2009-01-01
Chaos theory is presented for counselors working with clients experiencing life transitions. It is proposed as a model that considers disorder, unpredictability, and lack of control as normal parts of transition processes. Nonlinear constructs from physics are adapted for use in counseling. The model provides a method clients can use to…
Colloquium: Random matrices and chaos in nuclear spectra
International Nuclear Information System (INIS)
Papenbrock, T.; Weidenmueller, H. A.
2007-01-01
Chaos occurs in quantum systems if the statistical properties of the eigenvalue spectrum coincide with predictions of random-matrix theory. Chaos is a typical feature of atomic nuclei and other self-bound Fermi systems. How can the existence of chaos be reconciled with the known dynamical features of spherical nuclei? Such nuclei are described by the shell model (a mean-field theory) plus a residual interaction. The question is answered using a statistical approach (the two-body random ensemble): The matrix elements of the residual interaction are taken to be random variables. Chaos is shown to be a generic feature of the ensemble and some of its properties are displayed, emphasizing those which differ from standard random-matrix theory. In particular, the existence of correlations among spectra carrying different quantum numbers is demonstrated. These are subject to experimental verification
Chaos and Christianity: A Response to Butz and a Biblical Alternative.
Watts, Richard E.; Trusty, Jerry
1997-01-01
M.R. Butz's position regarding chaos theory and Christianity is reviewed. The compatibility of biblical theology and the sciences is discussed. Parallels between chaos theory and the philosophical perspective of Soren Kierkegaard are explored. A biblical model is offered for counselors in assisting Christian clients in embracing chaos. (Author/EMK)
Chaos vibration of pinion and rack steering trapezoidal mechanism containing two clearances
Wei, Daogao; Wang, Yu; Jiang, Tong; Zheng, Sifa; Zhao, Wenjing; Pan, Zhijie
2017-08-01
The multi-clearances of breaking type steering trapezoidal mechanism joints influences vehicle steering stability. Hence, to ascertain the influence of clearance value on steering stability, this paper takes the steering mechanism of a certain vehicle type as a prototype that can be simplified into a planar six-bar linkage, then establishes the system dynamic differential equations after considering the two clearances of tie rods and the steering knuckle arms. The influence of the clearance parameters on the movement stability of the steering mechanism is studied using a numerical computation method. Results show that when the two clearances are equal, the planar movement of the tie rods changes from period-doubling to chaos as the clearances increase. When the two clearances are 0.25 mm and 1.5 mm respectively, the planar movements of the two side tie rods come into chaos, causing the steering stability to deteriorate. Moreover, with the increase of clearances, turning moment fluctuates more intensively and the peak value increases.
Advanced mechanics from Euler's determinism to Arnold's chaos
Rajeev, S G
2013-01-01
Classical Mechanics is the oldest and best understood part of physics. This does not mean that it is cast in marble yet, a museum piece to be admired from a distance. Instead, mechanics continues to be an active area of research by physicists and mathematicians. Every few years, we need to re-evaluate the purpose of learning mechanics and look at old material in the light of modern developments. Once you have learned basic mechanics (Newton's laws, the solution of the Kepler problem) and quantum mechanics (the Schrodinger equation, hydrogen atom) it is time to go back and relearn classical mechanics in greater depth. It is the intent of this book to take you through the ancient (the original meaning of "classical") parts of the subject quickly: the ideas started by Euler and ending roughly with Poincare. We then take up the developments of twentieth century physics that have largely to do with chaos and discrete time evolution (the basis of numerical solutions).
Quantum chaos theory and the spectrum of ideal-MHD instabilities in toroidal plasmas
International Nuclear Information System (INIS)
Dewar, Robert L.; Carolin, Nuehrenberg; Tatsuno, Tomoya
2004-01-01
In a fully 3-D system such as a stellarator, the toroidal mode number n ceases to be a good quantum number - all ns within a given mode family being coupled. It is found that the discrete spectrum of unstable ideal MHD (magnetohydrodynamic) instabilities ceases to exist unless MHD is modified (regularized) by introducing a short-perpendicular-wavelength cutoff. Attempts to use ray tracing to estimate the regularized MHD spectrum fail due to the occurrence of chaotic ray trajectories. In quantum chaos theory, strong chaos in the semiclassical limit leads to eigenvalue statistics the same as those of a suitable ensemble of random matrices. For instance, the probability distribution function for the separation between neighboring eigenvalues is as derived from random matrix theory and goes to zero at zero separation. This contrasts with the Poissonian distribution found in separable systems, showing that a signature of quantum chaos is level repulsion. In order to determine whether eigenvalues of the regularized MHD problem obey the same statistics as those of the Schroedinger equation in both the separable 1-D case and the chaotic 3-D cases, we have assembled data sets of ideal MHD eigenvalues for a Suydam-unstable cylindrical (1-D) equilibrium using Mathematica and a Mercier-unstable (3-D) equilibrium using the CAS3D code. In the 1-D case, we find that the unregularized Suydam-approximation spectrum has an anomalous peak at zero eigenvalue separation. On the other hand, regularization by restricting the domain of κsub(perpendicular) recovers the expected Poissonian distribution. In the 3-D case we find strong evidence of level repulsion within mode families, but mixing mode families produces Poissonian statistics. (author)
Chaos in the atomic and subatomic world
International Nuclear Information System (INIS)
Nussenzveig, H.M.
1992-01-01
This work discusses the possibility of the existence of chaos in the quantum level. In the macroscopic scale, chaos can be explained by the use of classical mechanics. The problem is to know whether there is any manifestation of chaos in the evolution of a system following the quantum mechanical laws. (A.C.A.S.)
On quantum chaos, stochastic webs and localization in a quantum mechanical kick system
International Nuclear Information System (INIS)
Engel, U.M.
2007-01-01
In this study quantum chaos is discussed using the kicked harmonic oscillator as a model system. The kicked harmonic oscillator is characterized by an exceptional scenario of weak chaos: In the case of resonance between the frequency of the harmonic oscillator and the frequency of the periodic forcing, stochastic webs in phase space are generated by the classical dynamics. For the quantum dynamics of this system it is shown that the resulting Husimi distributions in quantum phase space exhibit the same web-like structures as the classical webs. The quantum dynamics is characterized by diffusive energy growth - just as the classical dynamics in the channels of the webs. In the case of nonresonance, the classically diffusive dynamics is found to be quantum mechanically suppressed. This bounded energy growth, which corresponds to localization in quantum phase space, is explained analytically by mapping the system onto the Anderson model. In this way, within the context of quantum chaos, the kicked harmonic oscillator is characterized by exhibiting its noteworthy geometrical and dynamical properties both classically and quantum mechanically, while at the same time there are also very distinct quantum deviations from classical properties, the most prominent example being quantum localization. (orig.)
The transition to chaos conservative classical systems and quantum manifestations
Reichl, Linda E
2004-01-01
This book provides a thorough and comprehensive discussion of classical and quantum chaos theory for bounded systems and for scattering processes Specific discussions include • Noether’s theorem, integrability, KAM theory, and a definition of chaotic behavior • Area-preserving maps, quantum billiards, semiclassical quantization, chaotic scattering, scaling in classical and quantum dynamics, dynamic localization, dynamic tunneling, effects of chaos in periodically driven systems and stochastic systems • Random matrix theory and supersymmetry The book is divided into several parts Chapters 2 through 4 deal with the dynamics of nonlinear conservative classical systems Chapter 5 and several appendices give a thorough grounding in random matrix theory and supersymmetry techniques Chapters 6 and 7 discuss the manifestations of chaos in bounded quantum systems and open quantum systems respectively Chapter 8 focuses on the semiclassical description of quantum systems with underlying classical chaos, and Chapt...
Improved PSO algorithm based on chaos theory and its application to design flood hydrograph
Directory of Open Access Journals (Sweden)
Si-Fang Dong
2010-06-01
Full Text Available The deficiencies of basic particle swarm optimization (bPSO are its ubiquitous prematurity and its inability to seek the global optimal solution when optimizing complex high-dimensional functions. To overcome such deficiencies, the chaos-PSO (COSPSO algorithm was established by introducing the chaos optimization mechanism and a global particle stagnation-disturbance strategy into bPSO. In the improved algorithm, chaotic movement was adopted for the particles' initial movement trajectories to replace the former stochastic movement, and the chaos factor was used to guide the particles' path. When the global particles were stagnant, the disturbance strategy was used to keep the particles in motion. Five benchmark optimizations were introduced to test COSPSO, and they proved that COSPSO can remarkably improve efficiency in optimizing complex functions. Finally, a case study of COSPSO in calculating design flood hydrographs demonstrated the applicability of the improved algorithm.
2nd International Symposium on Chaos, Complexity and Leadership
Banerjee, Santo
2015-01-01
These proceedings from the 2013 symposium on "Chaos, complexity and leadership" reflect current research results from all branches of Chaos, Complex Systems and their applications in Management. Included are the diverse results in the fields of applied nonlinear methods, modeling of data and simulations, as well as theoretical achievements of Chaos and Complex Systems. Also highlighted are Leadership and Management applications of Chaos and Complexity Theory.
Experimental Induction of Genome Chaos.
Ye, Christine J; Liu, Guo; Heng, Henry H
2018-01-01
Genome chaos, or karyotype chaos, represents a powerful survival strategy for somatic cells under high levels of stress/selection. Since the genome context, not the gene content, encodes the genomic blueprint of the cell, stress-induced rapid and massive reorganization of genome topology functions as a very important mechanism for genome (karyotype) evolution. In recent years, the phenomenon of genome chaos has been confirmed by various sequencing efforts, and many different terms have been coined to describe different subtypes of the chaotic genome including "chromothripsis," "chromoplexy," and "structural mutations." To advance this exciting field, we need an effective experimental system to induce and characterize the karyotype reorganization process. In this chapter, an experimental protocol to induce chaotic genomes is described, following a brief discussion of the mechanism and implication of genome chaos in cancer evolution.
Genome chaos: survival strategy during crisis.
Liu, Guo; Stevens, Joshua B; Horne, Steven D; Abdallah, Batoul Y; Ye, Karen J; Bremer, Steven W; Ye, Christine J; Chen, David J; Heng, Henry H
2014-01-01
Genome chaos, a process of complex, rapid genome re-organization, results in the formation of chaotic genomes, which is followed by the potential to establish stable genomes. It was initially detected through cytogenetic analyses, and recently confirmed by whole-genome sequencing efforts which identified multiple subtypes including "chromothripsis", "chromoplexy", "chromoanasynthesis", and "chromoanagenesis". Although genome chaos occurs commonly in tumors, both the mechanism and detailed aspects of the process are unknown due to the inability of observing its evolution over time in clinical samples. Here, an experimental system to monitor the evolutionary process of genome chaos was developed to elucidate its mechanisms. Genome chaos occurs following exposure to chemotherapeutics with different mechanisms, which act collectively as stressors. Characterization of the karyotype and its dynamic changes prior to, during, and after induction of genome chaos demonstrates that chromosome fragmentation (C-Frag) occurs just prior to chaotic genome formation. Chaotic genomes seem to form by random rejoining of chromosomal fragments, in part through non-homologous end joining (NHEJ). Stress induced genome chaos results in increased karyotypic heterogeneity. Such increased evolutionary potential is demonstrated by the identification of increased transcriptome dynamics associated with high levels of karyotypic variance. In contrast to impacting on a limited number of cancer genes, re-organized genomes lead to new system dynamics essential for cancer evolution. Genome chaos acts as a mechanism of rapid, adaptive, genome-based evolution that plays an essential role in promoting rapid macroevolution of new genome-defined systems during crisis, which may explain some unwanted consequences of cancer treatment.
National Research Council Canada - National Science Library
Morris, Jr, Gerald W
2007-01-01
.... The study investigates whether chaos theory, part of complexity science, can extract information from Katrina contracting data to help managers make better logistics decisions during disaster relief operations...
Random matrices and chaos in nuclear physics: Nuclear structure
International Nuclear Information System (INIS)
Weidenmueller, H. A.; Mitchell, G. E.
2009-01-01
Evidence for the applicability of random-matrix theory to nuclear spectra is reviewed. In analogy to systems with few degrees of freedom, one speaks of chaos (more accurately, quantum chaos) in nuclei whenever random-matrix predictions are fulfilled. An introduction into the basic concepts of random-matrix theory is followed by a survey over the extant experimental information on spectral fluctuations, including a discussion of the violation of a symmetry or invariance property. Chaos in nuclear models is discussed for the spherical shell model, for the deformed shell model, and for the interacting boson model. Evidence for chaos also comes from random-matrix ensembles patterned after the shell model such as the embedded two-body ensemble, the two-body random ensemble, and the constrained ensembles. All this evidence points to the fact that chaos is a generic property of nuclear spectra, except for the ground-state regions of strongly deformed nuclei.
Loss of 'complexity' and aging. Potential applications of fractals and chaos theory to senescence
Lipsitz, L. A.; Goldberger, A. L.
1992-01-01
The concept of "complexity," derived from the field of nonlinear dynamics, can be adapted to measure the output of physiologic processes that generate highly variable fluctuations resembling "chaos." We review data suggesting that physiologic aging is associated with a generalized loss of such complexity in the dynamics of healthy organ system function and hypothesize that such loss of complexity leads to an impaired ability to adapt to physiologic stress. This hypothesis is supported by observations showing an age-related loss of complex variability in multiple physiologic processes including cardiovascular control, pulsatile hormone release, and electroencephalographic potentials. If further research supports this hypothesis, measures of complexity based on chaos theory and the related geometric concept of fractals may provide new ways to monitor senescence and test the efficacy of specific interventions to modify the age-related decline in adaptive capacity.
On the Mechanisms Behind Chaos
DEFF Research Database (Denmark)
Lindberg, Erik
2006-01-01
behind the chaotic behavior, e.g. one group is based on the sudden interrupt of inductive currents, another group is based on the sudden parallel coupling of capacitors with different voltages, and a third group may be based on multiplication of signals. An example of chaos based on disturbance...
International Nuclear Information System (INIS)
Chen Yun; Wu Xiaofeng; Liu Zhong
2009-01-01
This paper studies global synchronization of non-autonomous chaotic electro-mechanical gyrostat systems via variable substitution control. A master-slave non-autonomous synchronization scheme with variable substitution control is mathematically presented. Based on the scheme, some sufficient algebraic criteria for global chaos synchronization of master and slave electro-mechanical gyrostat systems via various single-variable coupling are derived. The effectiveness of the obtained criteria is numerically illustrated by the examples.
Common prescriptions for psychology derived from dialectical materialism and chaos theory.
Gilgen, A R
2000-04-01
During the entire Soviet period (1917-1991), Russian psychologists labored to create a psychology which would be consonant with Marxist-Leninist assumptions derived from dialectical materialism. Some of their early prescriptions, in particular those put forward by Konstantin N. Kornilov in the 1920s and early 1930s, are identical to strategies being advanced by contemporary American psychologists who propose that chaos theory and nonlinear meta-modeling techniques in general, given advances in computer and television technologies, can be designed for research capable of dealing with the complexities, nonlinearities, self-organizational processes, and abrupt transformations characteristic of human psychological functioning.
Jiang, Xingxing; Cheng, Mengfan; Luo, Fengguang; Deng, Lei; Fu, Songnian; Ke, Changjian; Zhang, Minming; Tang, Ming; Shum, Ping; Liu, Deming
2016-12-12
A novel electro-optic chaos source is proposed on the basis of the reverse-time chaos theory and an analog-digital hybrid feedback loop. The analog output of the system can be determined by the numeric states of shift registers, which makes the system robust and easy to control. The dynamical properties as well as the complexity dependence on the feedback parameters are investigated in detail. The correlation characteristics of the system are also studied. Two improving strategies which were established in digital field and analog field are proposed to conceal the time-delay signature. The proposed scheme has the potential to be used in radar and optical secure communication systems.
Semiconductor Lasers Stability, Instability and Chaos
Ohtsubo, Junji
2013-01-01
This third edition of “Semiconductor Lasers, Stability, Instability and Chaos” was significantly extended. In the previous edition, the dynamics and characteristics of chaos in semiconductor lasers after the introduction of the fundamental theory of laser chaos and chaotic dynamics induced by self-optical feedback and optical injection was discussed. Semiconductor lasers with new device structures, such as vertical-cavity surface-emitting lasers and broad-area semiconductor lasers, are interesting devices from the viewpoint of chaotic dynamics since they essentially involve chaotic dynamics even in their free-running oscillations. These topics are also treated with respect to the new developments in the current edition. Also the control of such instabilities and chaos control are critical issues for applications. Another interesting and important issue of semiconductor laser chaos in this third edition is chaos synchronization between two lasers and the application to optical secure communication. One o...
International Nuclear Information System (INIS)
Loskutov, Alexander
2010-01-01
This review introduces most of the concepts used in the study of chaotic phenomena in nonlinear systems and has as its objective to summarize the current understanding of results from the theory of chaotic dynamical systems and to describe the original ideas underlying the study of deterministic chaos. The presentation relies on informal analysis, with abstract mathematical ideas visualized geometrically or by examples from physics. Hyperbolic dynamics, homoclinic trajectories and tangencies, wild hyperbolic sets, and different types of attractors which appear in dynamical systems are considered. The key aspects of ergodic theory are discussed, and the basic statistical properties of chaotic dynamical systems are described. The fundamental difference between stochastic dynamics and deterministic chaos is explained. The review concludes with an investigation of the possibility of studying complex systems on the basis of the analysis of registered signals, i.e. the generated time series. (reviews of topical problems)
Energy Technology Data Exchange (ETDEWEB)
Tél, Tamás [Institute for Theoretical Physics, Eötvös University, and MTA-ELTE Theoretical Physics Research Group, Pázmány P. s. 1/A, Budapest H-1117 (Hungary)
2015-09-15
We intend to show that transient chaos is a very appealing, but still not widely appreciated, subfield of nonlinear dynamics. Besides flashing its basic properties and giving a brief overview of the many applications, a few recent transient-chaos-related subjects are introduced in some detail. These include the dynamics of decision making, dispersion, and sedimentation of volcanic ash, doubly transient chaos of undriven autonomous mechanical systems, and a dynamical systems approach to energy absorption or explosion.
Tél, Tamás
2015-09-01
We intend to show that transient chaos is a very appealing, but still not widely appreciated, subfield of nonlinear dynamics. Besides flashing its basic properties and giving a brief overview of the many applications, a few recent transient-chaos-related subjects are introduced in some detail. These include the dynamics of decision making, dispersion, and sedimentation of volcanic ash, doubly transient chaos of undriven autonomous mechanical systems, and a dynamical systems approach to energy absorption or explosion.
Fundamental link between system theory and statistical mechanics
International Nuclear Information System (INIS)
Atmanspacher, H.; Scheingraber, H.
1987-01-01
A fundamental link between system theory and statistical mechanics has been found to be established by the Kolmogorov entropy. By this quantity the temporal evolution of dynamical systems can be classified into regular, chaotic, and stochastic processes. Since K represents a measure for the internal information creation rate of dynamical systems, it provides an approach to irreversibility. The formal relationship to statistical mechanics is derived by means of an operator formalism originally introduced by Prigogine. For a Liouville operator L and an information operator M tilde acting on a distribution in phase space, it is shown that i[L, M tilde] = KI (I = identity operator). As a first consequence of this equivalence, a relation is obtained between the chaotic correlation time of a system and Prigogine's concept of a finite duration of presence. Finally, the existence of chaos in quantum systems is discussed with respect to the existence of a quantum mechanical time operator
Relativistic quantum chaos-An emergent interdisciplinary field.
Lai, Ying-Cheng; Xu, Hong-Ya; Huang, Liang; Grebogi, Celso
2018-05-01
Quantum chaos is referred to as the study of quantum manifestations or fingerprints of classical chaos. A vast majority of the studies were for nonrelativistic quantum systems described by the Schrödinger equation. Recent years have witnessed a rapid development of Dirac materials such as graphene and topological insulators, which are described by the Dirac equation in relativistic quantum mechanics. A new field has thus emerged: relativistic quantum chaos. This Tutorial aims to introduce this field to the scientific community. Topics covered include scarring, chaotic scattering and transport, chaos regularized resonant tunneling, superpersistent currents, and energy level statistics-all in the relativistic quantum regime. As Dirac materials have the potential to revolutionize solid-state electronic and spintronic devices, a good understanding of the interplay between chaos and relativistic quantum mechanics may lead to novel design principles and methodologies to enhance device performance.
Applications of chaos and nonlinear dynamics in science and engineering
Rondoni, Lamberto; Mitra, Mala
Chaos and nonlinear dynamics initially developed as a new emergent field with its foundation in physics and applied mathematics. The highly generic, interdisciplinary quality of the insights gained in the last few decades has spawned myriad applications in almost all branches of science and technology—and even well beyond. Wherever the quantitative modeling and analysis of complex, nonlinear phenomena are required, chaos theory and its methods can play a key role. This second volume concentrates on reviewing further relevant, contemporary applications of chaotic nonlinear systems as they apply to the various cutting-edge branches of engineering. This encompasses, but is not limited to, topics such as the spread of epidemics; electronic circuits; chaos control in mechanical devices; secure communication; and digital watermarking. Featuring contributions from active and leading research groups, this collection is ideal both as a reference work and as a ‘recipe book’ full of tried and tested, successf...
International Nuclear Information System (INIS)
Lee, Sang-Bong.
1993-09-01
Quantum manifestation of classical chaos has been one of the extensively studied subjects for more than a decade. Yet clear understanding of its nature still remains to be an open question partly due to the lack of a canonical definition of quantum chaos. The classical definition seems to be unsuitable in quantum mechanics partly because of the Heisenberg quantum uncertainty. In this regard, quantum chaos is somewhat misleading and needs to be clarified at the very fundamental level of physics. Since it is well known that quantum mechanics is more fundamental than classical mechanics, the quantum description of classically chaotic nature should be attainable in the limit of large quantum numbers. The focus of my research, therefore, lies on the correspondence principle for classically chaotic systems. The chaotic damped driven pendulum is mainly studied numerically using the split operator method that solves the time-dependent Schroedinger equation. For classically dissipative chaotic systems in which (multi)fractal strange attractors often emerge, several quantum dissipative mechanisms are also considered. For instance, Hoover's and Kubo-Fox-Keizer's approaches are studied with some computational analyses. But the notion of complex energy with non-Hermiticity is extensively applied. Moreover, the Wigner and Husimi distribution functions are examined with an equivalent classical distribution in phase-space, and dynamical properties of the wave packet in configuration and momentum spaces are also explored. The results indicate that quantum dynamics embraces classical dynamics although the classicalquantum correspondence fails to be observed in the classically chaotic regime. Even in the semi-classical limits, classically chaotic phenomena would eventually be suppressed by the quantum uncertainty
4th international interdisciplinary chaos symposium
Banerjee, Santo; Caglar, Suleyman; Ozer, Mehmet; Chaos and complex systems
2013-01-01
Complexity Science and Chaos Theory are fascinating areas of scientific research with wide-ranging applications. The interdisciplinary nature and ubiquity of complexity and chaos are features that provides scientists with a motivation to pursue general theoretical tools and frameworks. Complex systems give rise to emergent behaviors, which in turn produce novel and interesting phenomena in science, engineering, as well as in the socio-economic sciences. The aim of all Symposia on Chaos and Complex Systems (CCS) is to bring together scientists, engineers, economists and social scientists, and to discuss the latest insights and results obtained in the area of corresponding nonlinear-system complex (chaotic) behavior. Especially for the “4th International Interdisciplinary Chaos Symposium on Chaos and Complex Systems,” which took place April 29th to May 2nd, 2012 in Antalya, Turkey, the scope of the symposium had been further enlarged so as to encompass the presentation of work from circuits to econophysic...
A fast chaos-based image encryption scheme with a dynamic state variables selection mechanism
Chen, Jun-xin; Zhu, Zhi-liang; Fu, Chong; Yu, Hai; Zhang, Li-bo
2015-03-01
In recent years, a variety of chaos-based image cryptosystems have been investigated to meet the increasing demand for real-time secure image transmission. Most of them are based on permutation-diffusion architecture, in which permutation and diffusion are two independent procedures with fixed control parameters. This property results in two flaws. (1) At least two chaotic state variables are required for encrypting one plain pixel, in permutation and diffusion stages respectively. Chaotic state variables produced with high computation complexity are not sufficiently used. (2) The key stream solely depends on the secret key, and hence the cryptosystem is vulnerable against known/chosen-plaintext attacks. In this paper, a fast chaos-based image encryption scheme with a dynamic state variables selection mechanism is proposed to enhance the security and promote the efficiency of chaos-based image cryptosystems. Experimental simulations and extensive cryptanalysis have been carried out and the results prove the superior security and high efficiency of the scheme.
Quantum chaos: Statistical relaxation in discrete spectrum
International Nuclear Information System (INIS)
Chirikov, B.V.
1991-01-01
The controversial phenomenon of quantum chaos is discussed using the quantized standard map, or the kicked rotator, as a simple model. The relation to the classical dynamical chaos is tracked down on the basis of the correspondence principle. Various mechanisms of the quantum suppression of classical chaos are considered with an application to the excitation and ionization of Rydberg atoms in a microwave field. Several definitions of the quantum chaos are discussed. (author). 27 refs
Earnshow, R; Jones, H
1991-01-01
This volume is based upon the presentations made at an international conference in London on the subject of 'Fractals and Chaos'. The objective of the conference was to bring together some of the leading practitioners and exponents in the overlapping fields of fractal geometry and chaos theory, with a view to exploring some of the relationships between the two domains. Based on this initial conference and subsequent exchanges between the editors and the authors, revised and updated papers were produced. These papers are contained in the present volume. We thank all those who contributed to this effort by way of planning and organisation, and also all those who helped in the production of this volume. In particular, we wish to express our appreciation to Gerhard Rossbach, Computer Science Editor, Craig Van Dyck, Production Director, and Nancy A. Rogers, who did the typesetting. A. J. Crilly R. A. Earnshaw H. Jones 1 March 1990 Introduction Fractals and Chaos The word 'fractal' was coined by Benoit Mandelbrot i...
Strong chaos in one-dimensional quantum system
International Nuclear Information System (INIS)
Yang, C.-D.; Wei, C.-H.
2008-01-01
According to the Poincare-Bendixson theorem, a minimum of three autonomous equations is required to exhibit deterministic chaos. Because a one-dimensional quantum system is described by only two autonomous equations using de Broglie-Bohm's trajectory interpretation, chaos in one-dimensional quantum systems has long been considered impossible. We will prove in this paper that chaos phenomenon does exist in one-dimensional quantum systems, if the domain of quantum motions is extended to complex space by noting that the quantum world is actually characterized by a four-dimensional complex spacetime according to the E (∞) theory. Furthermore, we point out that the interaction between the real and imaginary parts of complex trajectories produces a new chaos phenomenon unique to quantum systems, called strong chaos, which describes the situation that quantum trajectories may emerge and diverge spontaneously without any perturbation in the initial position
Chaos, decoherence and quantum cosmology
International Nuclear Information System (INIS)
Calzetta, Esteban
2012-01-01
In this topical review we discuss the connections between chaos, decoherence and quantum cosmology. We understand chaos as classical chaos in systems with a finite number of degrees of freedom, decoherence as environment induced decoherence and quantum cosmology as the theory of the Wheeler-DeWitt equation or else the consistent history formulation thereof, first in mini super spaces and later through its extension to midi super spaces. The overall conclusion is that consideration of decoherence is necessary (and probably sufficient) to sustain an interpretation of quantum cosmology based on the wavefunction of the Universe adopting a Wentzel-Kramers-Brillouin form for large Universes, but a definitive account of the semiclassical transition in classically chaotic cosmological models is not available in the literature yet. (topical review)
Semiconductor lasers stability, instability and chaos
Ohtsubo, Junji
2017-01-01
This book describes the fascinating recent advances made concerning the chaos, stability and instability of semiconductor lasers, and discusses their applications and future prospects in detail. It emphasizes the dynamics in semiconductor lasers by optical and electronic feedback, optical injection, and injection current modulation. Applications of semiconductor laser chaos, control and noise, and semiconductor lasers are also demonstrated. Semiconductor lasers with new structures, such as vertical-cavity surface-emitting lasers and broad-area semiconductor lasers, are intriguing and promising devices. Current topics include fast physical number generation using chaotic semiconductor lasers for secure communication, development of chaos, quantum-dot semiconductor lasers and quantum-cascade semiconductor lasers, and vertical-cavity surface-emitting lasers. This fourth edition has been significantly expanded to reflect the latest developments. The fundamental theory of laser chaos and the chaotic dynamics in se...
Chaos and fractals. Applications to nuclear engineering
International Nuclear Information System (INIS)
Clausse, A.; Delmastro, D.F.
1990-01-01
This work presents a description of the research lines carried out by the authors on chaos and fractal theories, oriented to the nuclear field. The possibilities that appear in the nuclear security branch where the information deriving from chaos and fractal techniques may help to the development of better criteria and more reliable designs, are of special importance. (Author) [es
Chaos in electric drive systems analysis control and application
Chau, K T
2011-01-01
In Chaos in Electric Drive Systems: Analysis, Control and Application authors Chau and Wang systematically introduce an emerging technology of electrical engineering that bridges abstract chaos theory and practical electric drives. The authors consolidate all important information in this interdisciplinary technology, including the fundamental concepts, mathematical modeling, theoretical analysis, computer simulation, and hardware implementation. The book provides comprehensive coverage of chaos in electric drive systems with three main parts: analysis, control and application. Corresponding drive systems range from the simplest to the latest types: DC, induction, synchronous reluctance, switched reluctance, and permanent magnet brushless drives.The first book to comprehensively treat chaos in electric drive systemsReviews chaos in various electrical engineering technologies and drive systemsPresents innovative approaches to stabilize and stimulate chaos in typical drivesDiscusses practical application of cha...
Chaos and the quantum: how nonlinear effects can explain certain quantum paradoxes
Energy Technology Data Exchange (ETDEWEB)
McHarris, Wm C, E-mail: mcharris@chemistry.msu.edu [Departments of Chemistry and Physics/Astronomy, Michigan State University, East Lansing, MI 48824 (United States)
2011-07-08
In recent years we have suggested that many of the so-called paradoxes resulting from the Copenhagen interpretation of quantum mechanics could well have more logical parallels based in nonlinear dynamics and chaos theory. Perhaps quantum mechanics might not be strictly linear as has been commonly postulated, and indeed, during the past year experimentalists have discovered signatures of chaos in a definitely quantum system. As an illustration of what can go wrong when quantum effects are forced into a linear interpretation, I examine Bell-type inequalities. In conventional derivations of such inequalities, classical systems are found to impose upper limits on the statistical correlations between, say, the properties of a pair of separated but entangled particles, whereas quantum systems allow greater correlations. Numerous experiments have upheld the quantum predictions (greater statistical correlations than allowed classically), which has led to inferences such as the instantaneous transmission of information between effectively infinitely separated particles - Einstein's 'spooky action-at-a-distance', incompatible with relativity. I argue that there is nothing wrong with the quantum mechanical side of such derivations (the usual point of attack by those attempting to debunk Bell-type arguments), but implicit in the derivations on the classical side is the assumption of independent, uncorrelated particles. As a result, one is comparing uncorrelated probabilities versus conditional probabilities rather than comparing classical versus quantum mechanics, making moot the experimental inferences. Further, nonlinear classical systems are known to exhibit correlations that can easily be as great as and overlap with quantum correlations - so-called nonextensive thermodynamics with its nonadditive entropy has verified this with numerous examples. Perhaps quantum mechanics does contain fundamental nonlinear elements. Nonlinear dynamics and chaos theory could
Chaos and the quantum: how nonlinear effects can explain certain quantum paradoxes
International Nuclear Information System (INIS)
McHarris, Wm C
2011-01-01
In recent years we have suggested that many of the so-called paradoxes resulting from the Copenhagen interpretation of quantum mechanics could well have more logical parallels based in nonlinear dynamics and chaos theory. Perhaps quantum mechanics might not be strictly linear as has been commonly postulated, and indeed, during the past year experimentalists have discovered signatures of chaos in a definitely quantum system. As an illustration of what can go wrong when quantum effects are forced into a linear interpretation, I examine Bell-type inequalities. In conventional derivations of such inequalities, classical systems are found to impose upper limits on the statistical correlations between, say, the properties of a pair of separated but entangled particles, whereas quantum systems allow greater correlations. Numerous experiments have upheld the quantum predictions (greater statistical correlations than allowed classically), which has led to inferences such as the instantaneous transmission of information between effectively infinitely separated particles - Einstein's 'spooky action-at-a-distance', incompatible with relativity. I argue that there is nothing wrong with the quantum mechanical side of such derivations (the usual point of attack by those attempting to debunk Bell-type arguments), but implicit in the derivations on the classical side is the assumption of independent, uncorrelated particles. As a result, one is comparing uncorrelated probabilities versus conditional probabilities rather than comparing classical versus quantum mechanics, making moot the experimental inferences. Further, nonlinear classical systems are known to exhibit correlations that can easily be as great as and overlap with quantum correlations - so-called nonextensive thermodynamics with its nonadditive entropy has verified this with numerous examples. Perhaps quantum mechanics does contain fundamental nonlinear elements. Nonlinear dynamics and chaos theory could well provide a
Conceptual Models and Theory-Embedded Principles on Effective Schooling.
Scheerens, Jaap
1997-01-01
Reviews models and theories on effective schooling. Discusses four rationality-based organization theories and a fifth perspective, chaos theory, as applied to organizational functioning. Discusses theory-embedded principles flowing from these theories: proactive structuring, fit, market mechanisms, cybernetics, and self-organization. The…
Linear Matrix Inequality Based Fuzzy Synchronization for Fractional Order Chaos
Directory of Open Access Journals (Sweden)
Bin Wang
2015-01-01
Full Text Available This paper investigates fuzzy synchronization for fractional order chaos via linear matrix inequality. Based on generalized Takagi-Sugeno fuzzy model, one efficient stability condition for fractional order chaos synchronization or antisynchronization is given. The fractional order stability condition is transformed into a set of linear matrix inequalities and the rigorous proof details are presented. Furthermore, through fractional order linear time-invariant (LTI interval theory, the approach is developed for fractional order chaos synchronization regardless of the system with uncertain parameters. Three typical examples, including synchronization between an integer order three-dimensional (3D chaos and a fractional order 3D chaos, anti-synchronization of two fractional order hyperchaos, and the synchronization between an integer order 3D chaos and a fractional order 4D chaos, are employed to verify the theoretical results.
Equilibrium paths analysis of materials with rheological properties by using the chaos theory
Bednarek, Paweł; Rządkowski, Jan
2018-01-01
The numerical equilibrium path analysis of the material with random rheological properties by using standard procedures and specialist computer programs was not successful. The proper solution for the analysed heuristic model of the material was obtained on the base of chaos theory elements and neural networks. The paper deals with mathematical reasons of used computer programs and also are elaborated the properties of the attractor used in analysis. There are presented results of conducted numerical analysis both in a numerical and in graphical form for the used procedures.
Routes to chaos in continuous mechanical systems. Part 1: Mathematical models and solution methods
International Nuclear Information System (INIS)
Awrejcewicz, J.; Krysko, V.A.; Papkova, I.V.; Krysko, A.V.
2012-01-01
In this work chaotic dynamics of continuous mechanical systems such as flexible plates and shallow shells is studied. Namely, a wide class of the mentioned objects is analyzed including flexible plates and cylinder-like panels of infinite length, rectangular spherical and cylindrical shells, closed cylindrical shells, axially symmetric plates, as well as spherical and conical shells. The considered problems are solved by the Bubnov–Galerkin and higher approximation Ritz methods. Convergence and validation of those methods are studied. The Cauchy problems are solved mainly by the fourth Runge-Kutta method, although all variants of the Runge-Kutta methods are considered. New scenarios of transition from regular to chaotic orbits are detected, analyzed and discussed. First part of the paper is devoted to the validation of results obtained. This is why the same infinite length problem is reduced to that of a finite dimension through the FDM (Finite Difference Method) with the approximation order of O(c 2 ), BGM (Bubnov–Galerkin Method) or RM (Ritz Method) with higher approximations. We pay attention not only to convergence of the mentioned methods regarding the number of partitions of the interval [0, 1] in the FDM or regarding the number of terms in the series applied either in the BGM or RM methods, but we also compare the results obtained via the mentioned different approaches. Furthermore, a so called practical convergence of different Runge-Kutta type methods are tested starting from the second and ending with the eighth order. Second part of the work is devoted to a study of routes to chaos in the so far mentioned mechanical objects. For this purpose the so-called “dynamical charts” are constructed versus control parameters {q 0 , ω p }, where q 0 denotes the loading amplitude, and ω p is the loading frequency. The charts are constructed through analyses of frequency power spectra and the largest Lyapunov exponent (LE). Analysis of the mentioned charts
International Nuclear Information System (INIS)
Chirikov, B.V.
1990-01-01
Classification of chaotic patterns in classical Hamiltonian systems is given as a series of levels with increasing disorder. Hamiltonian dynamics is presented, including the renormalization chaos, based upon the fairly simple resonant theory. First estimates for the critical structure and related statistical anomalies in arbitrary dimensions are discussed. 49 refs
Decoherence, determinism and chaos
International Nuclear Information System (INIS)
Noyes, H.P.
1994-01-01
The author claims by now to have made his case that modern work on fractals and chaos theory has already removed the presumption that classical physics is 'deterministic'. Further, he claims that in so far as classical relativistic field theory (i.e. electromagnetism and gravitation) are scale invariant, they are self-consistent only if the idea of 'test-particle' is introduced from outside the theory. Einstein spent the last years of his life trying to use singularities in the metric as 'particles' or to get them out of the non-linearities in a grand unified theory -- in vain. So classical physics in this sense cannot be the fundamental theory. However, the author claims to have shown that if he introduces a 'scale invariance bounded from below' by measurement accuracy, then Tanimura's generalization of the Feynman proof as reconstructed by Dyson allows him to make a consistent classical theory for decoherent sources sinks. Restoring coherence to classical physics via relativistic action-at-a distance is left as a task for the future. Relativistic quantum mechanics, properly reconstructed from a finite and discrete basis, emerges in much better shape. The concept of 'particles has to be replaced by NO-YES particulate events, and particle-antiparticle pair creation and annihilation properly formulated
Subcritical Multiplicative Chaos for Regularized Counting Statistics from Random Matrix Theory
Lambert, Gaultier; Ostrovsky, Dmitry; Simm, Nick
2018-05-01
For an {N × N} Haar distributed random unitary matrix U N , we consider the random field defined by counting the number of eigenvalues of U N in a mesoscopic arc centered at the point u on the unit circle. We prove that after regularizing at a small scale {ɛN > 0}, the renormalized exponential of this field converges as N \\to ∞ to a Gaussian multiplicative chaos measure in the whole subcritical phase. We discuss implications of this result for obtaining a lower bound on the maximum of the field. We also show that the moments of the total mass converge to a Selberg-like integral and by taking a further limit as the size of the arc diverges, we establish part of the conjectures in Ostrovsky (Nonlinearity 29(2):426-464, 2016). By an analogous construction, we prove that the multiplicative chaos measure coming from the sine process has the same distribution, which strongly suggests that this limiting object should be universal. Our approach to the L 1-phase is based on a generalization of the construction in Berestycki (Electron Commun Probab 22(27):12, 2017) to random fields which are only asymptotically Gaussian. In particular, our method could have applications to other random fields coming from either random matrix theory or a different context.
The foundations of chaos revisited from Poincaré to recent advancements
2016-01-01
With contributions from a number of pioneering researchers in the field, this collection is aimed not only at researchers and scientists in nonlinear dynamics but also at a broader audience interested in understanding and exploring how modern chaos theory has developed since the days of Poincaré. This book was motivated by and is an outcome of the CHAOS 2015 meeting held at the Henri Poincaré Institute in Paris, which provided a perfect opportunity to gain inspiration and discuss new perspectives on the history, development and modern aspects of chaos theory. Henri Poincaré is remembered as a great mind in mathematics, physics and astronomy. His works, well beyond their rigorous mathematical and analytical style, are known for their deep insights into science and research in general, and the philosophy of science in particular. The Poincaré conjecture (only proved in 2006) along with his work on the three-body problem are considered to be the foundation of modern chaos theory.
Collective diffusion and quantum chaos in holography
Wu, Shao-Feng; Wang, Bin; Ge, Xian-Hui; Tian, Yu
2018-05-01
We define a particular combination of charge and heat currents that is decoupled with the heat current. This "heat-decoupled" (HD) current can be transported by diffusion at long distances, when some thermoelectric conductivities and susceptibilities satisfy a simple condition. Using the diffusion condition together with the Kelvin formula, we show that the HD diffusivity can be same as the charge diffusivity and also the heat diffusivity. We illustrate that such mechanism is implemented in a strongly coupled field theory, which is dual to a Lifshitz gravity with the dynamical critical index z =2 . In particular, it is exhibited that both charge and heat diffusivities build the relationship to the quantum chaos. Moreover, we study the HD diffusivity without imposing the diffusion condition. In some homogeneous holographic lattices, it is found that the diffusivity/chaos relation holds independently of any parameters, including the strength of momentum relaxation, chemical potential, or temperature. We also show a counter example of the relation and discuss its limited universality.
Ray and wave chaos in underwater acoustic waveguides
International Nuclear Information System (INIS)
Virovlyansky, Anatolii L; Makarov, Denis V; Prants, Sergei V
2012-01-01
In the 1990s, the study of the chaotic behavior of ray trajectories in inhomogeneous waveguides emerged as a new field in ocean acoustics. It turned out that at ranges on the order of or larger than 1000 km ray chaos is well developed and should be taken into account when describing long-range sound propagation in the ocean. The theoretical analysis of ray chaos and of its finite-wavelength manifestation, wave chaos, is to a large extent based on well-known methods and ideas from the theory of dynamical and quantum chaos. Concrete examples are used to review the results obtained in this field over the last two decades. (reviews of topical problems)
International Nuclear Information System (INIS)
Muñoz, L; Fernández-Ramírez, C; Relaño, A; Retamosa, J
2012-01-01
In the last decade quantum chaos has become a well established discipline with outreach to different fields, from condensed-matter to nuclear physics. The most important signature of quantum chaos is the statistical analysis of the energy spectrum, which distinguishes between systems with integrable and chaotic classical analogues. In recent years, spectral statistical techniques inherited from quantum chaos have been applied successfully to the baryon spectrum revealing its likely chaotic behaviour even at the lowest energies. However, the theoretical spectra present a behaviour closer to the statistics of integrable systems which makes theory and experiment statistically incompatible. The usual statement of missing resonances in the experimental spectrum when compared to the theoretical ones cannot account for the discrepancies. In this communication we report an improved analysis of the baryon spectrum, taking into account the low statistics and the error bars associated with each resonance. Our findings give a major support to the previous conclusions. Besides, analogue analyses are performed in the experimental meson spectrum, with comparison to theoretical models.
Chaos, complexity, and random matrices
Cotler, Jordan; Hunter-Jones, Nicholas; Liu, Junyu; Yoshida, Beni
2017-11-01
Chaos and complexity entail an entropic and computational obstruction to describing a system, and thus are intrinsically difficult to characterize. In this paper, we consider time evolution by Gaussian Unitary Ensemble (GUE) Hamiltonians and analytically compute out-of-time-ordered correlation functions (OTOCs) and frame potentials to quantify scrambling, Haar-randomness, and circuit complexity. While our random matrix analysis gives a qualitatively correct prediction of the late-time behavior of chaotic systems, we find unphysical behavior at early times including an O(1) scrambling time and the apparent breakdown of spatial and temporal locality. The salient feature of GUE Hamiltonians which gives us computational traction is the Haar-invariance of the ensemble, meaning that the ensemble-averaged dynamics look the same in any basis. Motivated by this property of the GUE, we introduce k-invariance as a precise definition of what it means for the dynamics of a quantum system to be described by random matrix theory. We envision that the dynamical onset of approximate k-invariance will be a useful tool for capturing the transition from early-time chaos, as seen by OTOCs, to late-time chaos, as seen by random matrix theory.
Kac-Moody algebras and controlled chaos
International Nuclear Information System (INIS)
Wesley, Daniel H
2007-01-01
Compactification can control chaotic Mixmaster behaviour in gravitational systems with p-form matter: we consider this in light of the connection between supergravity models and Kac-Moody algebras. We show that different compactifications define 'mutations' of the algebras associated with the noncompact theories. We list the algebras obtained in this way, and find novel examples of wall systems determined by Lorentzian (but not hyperbolic) algebras. Cosmological models with a smooth pre-big bang phase require that chaos is absent: we show that compactification alone cannot eliminate chaos in the simplest compactifications of the heterotic string on a Calabi-Yau, or M theory on a manifold of G 2 holonomy. (fast track communication)
A quantum harmonic oscillator and strong chaos
International Nuclear Information System (INIS)
Oprocha, Piotr
2006-01-01
It is known that many physical systems which do not exhibit deterministic chaos when treated classically may exhibit such behaviour if treated from the quantum mechanics point of view. In this paper, we will show that an annihilation operator of the unforced quantum harmonic oscillator exhibits distributional chaos as introduced in B Schweizer and J SmItal (1994 Trans. Am. Math. Soc. 344 737-54). Our approach strengthens previous results on chaos in this model and provides a very powerful tool to measure chaos in other (quantum or classical) models
Application of chaos and fractals to computer vision
Farmer, Michael E
2014-01-01
This book provides a thorough investigation of the application of chaos theory and fractal analysis to computer vision. The field of chaos theory has been studied in dynamical physical systems, and has been very successful in providing computational models for very complex problems ranging from weather systems to neural pathway signal propagation. Computer vision researchers have derived motivation for their algorithms from biology and physics for many years as witnessed by the optical flow algorithm, the oscillator model underlying graphical cuts and of course neural networks. These algorithm
Chaos analysis and chaotic EMI suppression of DC-DC converters
Zhang, Bo
2014-01-01
Introduces chaos theory, its analytical methods and the means to apply chaos to the switching power supply design DC-DC converters are typical switching systems which have plenty of nonlinear behaviors, such as bifurcation and chaos. The nonlinear behaviors of DC-DC converters have been studied heavily over the past 20 years, yet researchers are still unsure of the practical application of bifurcations and chaos in switching converters. The electromagnetic interference (EMI), which resulted from the high rates of changes of voltage and current, has become a major design criterion in DC-DC co
Temporal epilepsy seizures monitoring and prediction using cross-correlation and chaos theory.
Haddad, Tahar; Ben-Hamida, Naim; Talbi, Larbi; Lakhssassi, Ahmed; Aouini, Sadok
2014-01-01
Temporal seizures due to hippocampal origins are very common among epileptic patients. Presented is a novel seizure prediction approach employing correlation and chaos theories. The early identification of seizure signature allows for various preventive measures to be undertaken. Electro-encephalography signals are spectrally broken down into the following sub-bands: delta; theta; alpha; beta; and gamma. The proposed approach consists of observing a high correlation level between any pair of electrodes for the lower frequencies and a decrease in the Lyapunov index (chaos or entropy) for the higher frequencies. Power spectral density and statistical analysis tools were used to determine threshold levels for the lower frequencies. After studying all five sub-bands, the analysis has revealed that the seizure signature can be extracted from the delta band and the high frequencies. High frequencies are defined as both the gamma band and the ripples occurring within the 60-120 Hz sub-band. To validate the proposed approach, six patients from both sexes and various age groups with temporal epilepsies originating from the hippocampal area were studied using the Freiburg database. An average seizure prediction of 30 min, an anticipation accuracy of 72%, and a false-positive rate of 0% were accomplished throughout 200 h of recording time.
Markov transitions and the propagation of chaos
International Nuclear Information System (INIS)
Gottlieb, A.
1998-01-01
The propagation of chaos is a central concept of kinetic theory that serves to relate the equations of Boltzmann and Vlasov to the dynamics of many-particle systems. Propagation of chaos means that molecular chaos, i.e., the stochastic independence of two random particles in a many-particle system, persists in time, as the number of particles tends to infinity. We establish a necessary and sufficient condition for a family of general n-particle Markov processes to propagate chaos. This condition is expressed in terms of the Markov transition functions associated to the n-particle processes, and it amounts to saying that chaos of random initial states propagates if it propagates for pure initial states. Our proof of this result relies on the weak convergence approach to the study of chaos due to Sztitman and Tanaka. We assume that the space in which the particles live is homomorphic to a complete and separable metric space so that we may invoke Prohorov's theorem in our proof. We also show that, if the particles can be in only finitely many states, then molecular chaos implies that the specific entropies in the n-particle distributions converge to the entropy of the limiting single-particle distribution
Peake, Sharon; McDowall, Almuth
2012-01-01
In a rapidly changing world of work, little research exists on mid-career transitions. We investigated these using the open-systems approach of chaos theory as a guiding metaphor and conducted interviews with seven mid-career individuals chosen for their experience of a significant mid-career transition. Four common themes were identified through…
Stick-slip chaos in a mechanical oscillator with dry friction
Kousaka, Takuji; Asahara, Hiroyuki; Inaba, Naohiko
2018-03-01
This study analyzes a forced mechanical dynamical system with dry friction that can generate chaotic stick-slip vibrations. We find that the dynamics proposed by Yoshitake et al. [Trans. Jpn. Soc. Mech. Eng. C 61, 768 (1995)] can be expressed as a nonautonomous constraint differential equation owing to the static friction force. The object is constrained to the surface of a moving belt by a static friction force from when it sticks to the surface until the force on the object exceeds the maximal static friction force. We derive a 1D Poincaré return map from the constrained mechanical system, and prove numerically that this 1D map has an absolutely continuous invariant measure and a positive Lyapunov exponent, providing strong evidence for chaos.
Hampson, Karen M; Cufflin, Matthew P; Mallen, Edward A H
2017-08-01
When fixating on a stationary object, the power of the eye's lens fluctuates. Studies have suggested that changes in these so-called microfluctuations in accommodation may be a factor in the onset and progression of short-sightedness. Like many physiological signals, the fluctuations in the power of the lens exhibit chaotic behaviour. A breakdown or reduction in chaos in physiological systems indicates stress to the system or pathology. The purpose of this study was to determine whether the chaos in fluctuations of the power of the lens changes with refractive error, i.e. how short-sighted a subject is, and/or accommodative demand, i.e. the effective distance of the object that is being viewed. Six emmetropes (EMMs, non-short-sighted), six early-onset myopes (EOMs, onset of short-sightedness before the age of 15), and six late-onset myopes (LOMs, onset of short-sightedness after the age of 15) took part in the study. Accommodative microfluctuations were measured at 22 Hz using an SRW-5000 autorefractor at accommodative demands of 1 D (dioptres), 2 D, and 3 D. Chaos theory analysis was used to determine the embedding lag, embedding dimension, limit of predictability, and Lyapunov exponent. Topological transitivity was also tested for. For comparison, the power spectrum and standard deviation were calculated for each time record. The EMMs had a statistically significant higher Lyapunov exponent than the LOMs ([Formula: see text] vs. [Formula: see text]) and a lower embedding dimension than the LOMs ([Formula: see text] vs. [Formula: see text]). There was insufficient evidence (non-significant p value) of a difference between EOMs and EMMs or EOMs and LOMs. The majority of time records were topologically transitive. There was insufficient evidence of accommodative demand having an effect. Power spectrum analysis and assessment of the standard deviation of the fluctuations failed to discern differences based on refractive error. Chaos differences in accommodation
International Nuclear Information System (INIS)
Bohigas, Oriol
2005-01-01
Are there quantum signatures, for instance in the spectral properties, of the underlying regular or chaotic nature of the corresponding classical motion? Are there universality classes? Within this framework the merging of two at first sight seemingly disconnected fields, namely random matrix theories (RMT) and quantum chaos (QC), is briefly described. Periodic orbit theory (POT) plays a prominent role. Emphasis is given to compound nucleus resonances and binding energies, whose shell effects are examined from this perspective. Several aspects are illustrated with Riemann's ζ-function, which has become a testing ground for RMT, QC, POT, and their relationship
Energy Technology Data Exchange (ETDEWEB)
Bohigas, Oriol [Laboratoire de Physique Theorique et Modeles Statistiques, Orsay (France)
2005-04-18
Are there quantum signatures, for instance in the spectral properties, of the underlying regular or chaotic nature of the corresponding classical motion? Are there universality classes? Within this framework the merging of two at first sight seemingly disconnected fields, namely random matrix theories (RMT) and quantum chaos (QC), is briefly described. Periodic orbit theory (POT) plays a prominent role. Emphasis is given to compound nucleus resonances and binding energies, whose shell effects are examined from this perspective. Several aspects are illustrated with Riemann's {zeta}-function, which has become a testing ground for RMT, QC, POT, and their relationship.
Chaos concepts, control and constructive use
Bolotin, Yurii; Yanovsky, Vladimir
2017-01-01
This book offers a short and concise introduction to the many facets of chaos theory. While the study of chaotic behavior in nonlinear, dynamical systems is a well-established research field with ramifications in all areas of science, there is a lot to be learnt about how chaos can be controlled and, under appropriate conditions, can actually be constructive in the sense of becoming a control parameter for the system under investigation, stochastic resonance being a prime example. The present work stresses the latter aspects and, after recalling the paradigm changes introduced by the concept of chaos, leads the reader skillfully through the basics of chaos control by detailing the relevant algorithms for both Hamiltonian and dissipative systems, among others. The main part of the book is then devoted to the issue of synchronization in chaotic systems, an introduction to stochastic resonance, and a survey of ratchet models. In this second, revised and enlarged edition, two more chapters explore the many interf...
Quantum chaos in the Heisenberg picture
International Nuclear Information System (INIS)
McKellar, B.H.J.; Lancaster, M.; McCaw, J.
2000-01-01
Full text: We explore the possibility of defining quantum chaos in the algebra of quantum mechanical operators. The simple definition of the Lyapunov exponent in terms of a metric on that algebra has the expected properties for the quantum logistic map, as we confirm for the simple spin 1 system. We then show numerically and analytically that the Hamiltonian evolution of finite spin systems does not lead to chaos in this definition, and investigate alternative definitions of quantum chaos in the algebra of operators
Czech Academy of Sciences Publication Activity Database
Beran, Zdeněk; Čelikovský, Sergej
2013-01-01
Roč. 23, č. 5 (2013), 1350084-1-1350084-9 ISSN 0218-1274 R&D Projects: GA ČR GA13-20433S Institutional support: RVO:67985556 Keywords : Hyperspace * chaos * shadowing * Bernoulli shift Subject RIV: BC - Control Systems Theory Impact factor: 1.017, year: 2013 http://library.utia.cas.cz/separaty/2013/TR/beran-0392926.pdf
Nuclear physics and ideas of quantum chaos
International Nuclear Information System (INIS)
Zelevinsky, V.G.
2002-01-01
The field nowadays called 'many-body quantum chaos' was started in 1939 with the article by I.I. Gurevich studying the regularities of nuclear spectra. The field has been extensively developed recently, both mathematically and in application to mesoscopic systems and quantum fields. We argue that nuclear physics and the theory of quantum chaos are mutually beneficial. Many ideas of quantum chaos grew up from the factual material of nuclear physics; this enrichment still continues to take place. On the other hand, many phenomena in nuclear structure and reactions, as well as the general problem of statistical physics of finite strongly interacting systems, can be understood much deeper with the help of ideas and methods borrowed from the field of quantum chaos. A brief review of the selected topics related to the recent development is presented
Controllable chaos in hybrid electro-optomechanical systems
Wang, Mei; Lü, Xin-You; Ma, Jin-Yong; Xiong, Hao; Si, Liu-Gang; Wu, Ying
2016-01-01
We investigate the nonlinear dynamics of a hybrid electro-optomechanical system (EOMS) that allows us to realize the controllable opto-mechanical nonlinearity by driving the microwave LC resonator with a tunable electric field. A controllable optical chaos is realized even without changing the optical pumping. The threshold and lifetime of the chaos could be optimized by adjusting the strength, frequency, or phase of the electric field. This study provides a method of manipulating optical chaos with an electric field. It may offer the prospect of exploring the controllable chaos in on-chip optoelectronic devices and its applications in secret communication. PMID:26948505
Controllable chaos in hybrid electro-optomechanical systems.
Wang, Mei; Lü, Xin-You; Ma, Jin-Yong; Xiong, Hao; Si, Liu-Gang; Wu, Ying
2016-03-07
We investigate the nonlinear dynamics of a hybrid electro-optomechanical system (EOMS) that allows us to realize the controllable opto-mechanical nonlinearity by driving the microwave LC resonator with a tunable electric field. A controllable optical chaos is realized even without changing the optical pumping. The threshold and lifetime of the chaos could be optimized by adjusting the strength, frequency, or phase of the electric field. This study provides a method of manipulating optical chaos with an electric field. It may offer the prospect of exploring the controllable chaos in on-chip optoelectronic devices and its applications in secret communication.
Rydberg Atoms in Strong Fields: a Testing Ground for Quantum Chaos.
Courtney, Michael
1995-01-01
Rydberg atoms in strong static electric and magnetic fields provide experimentally accessible systems for studying the connections between classical chaos and quantum mechanics in the semiclassical limit. This experimental accessibility has motivated the development of reliable quantum mechanical solutions. This thesis uses both experimental and computed quantum spectra to test the central approaches to quantum chaos. These central approaches consist mainly of developing methods to compute the spectra of quantum systems in non -perturbative regimes, correlating statistical descriptions of eigenvalues with the classical behavior of the same Hamiltonian, and the development of semiclassical methods such as periodic-orbit theory. Particular emphasis is given to identifying the spectral signature of recurrences --quantum wave packets which follow classical orbits. The new findings include: the breakdown of the connection between energy-level statistics and classical chaos in odd-parity diamagnetic lithium, the discovery of the signature of very long period orbits in atomic spectra, quantitative evidence for the scattering of recurrences by the alkali -metal core, quantitative description of the behavior of recurrences near bifurcations, and a semiclassical interpretation of the evolution of continuum Stark spectra. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.).
Scaling of chaos in strongly nonlinear lattices.
Mulansky, Mario
2014-06-01
Although it is now understood that chaos in complex classical systems is the foundation of thermodynamic behavior, the detailed relations between the microscopic properties of the chaotic dynamics and the macroscopic thermodynamic observations still remain mostly in the dark. In this work, we numerically analyze the probability of chaos in strongly nonlinear Hamiltonian systems and find different scaling properties depending on the nonlinear structure of the model. We argue that these different scaling laws of chaos have definite consequences for the macroscopic diffusive behavior, as chaos is the microscopic mechanism of diffusion. This is compared with previous results on chaotic diffusion [M. Mulansky and A. Pikovsky, New J. Phys. 15, 053015 (2013)], and a relation between microscopic chaos and macroscopic diffusion is established.
Application of chaos theory to the particle dynamics of asymmetry-induced transport
Eggleston, D. L.
2018-03-01
The techniques of chaos theory are employed in an effort to better understand the complex single-particle dynamics of asymmetry-induced transport in non-neutral plasmas. The dynamical equations are re-conceptualized as describing time-independent trajectories in a four-dimensional space consisting of the radius r, rotating frame angle ψ, axial position z, and axial velocity v. Results include the identification of an integral of the motion, fixed-point analysis of the dynamical equations, the construction and interpretation of Poincaré sections to visualize the dynamics, and, for the case of chaotic motion, numerical calculation of the largest Lyapunov exponent. Chaotic cases are shown to be associated with the overlap of resonance islands formed by the applied asymmetry.
Bounding the space of holographic CFTs with chaos
Energy Technology Data Exchange (ETDEWEB)
Perlmutter, Eric [Department of Physics, Princeton University,Jadwin Hall, Princeton, NJ 08544 (United States)
2016-10-13
Thermal states of quantum systems with many degrees of freedom are subject to a bound on the rate of onset of chaos, including a bound on the Lyapunov exponent, λ{sub L}≤2π/β. We harness this bound to constrain the space of putative holographic CFTs and their would-be dual theories of AdS gravity. First, by studying out-of-time-order four-point functions, we discuss how λ{sub L}=2π/β in ordinary two-dimensional holographic CFTs is related to properties of the OPE at strong coupling. We then rule out the existence of unitary, sparse two-dimensional CFTs with large central charge and a set of higher spin currents of bounded spin; this implies the inconsistency of weakly coupled AdS{sub 3} higher spin gravities without infinite towers of gauge fields, such as the SL(N) theories. This fits naturally with the structure of higher-dimensional gravity, where finite towers of higher spin fields lead to acausality. On the other hand, unitary CFTs with classical W{sub ∞}[λ] symmetry, dual to 3D Vasiliev or hs[λ] higher spin gravities, do not violate the chaos bound, instead exhibiting no chaos: λ{sub L}=0. Independently, we show that such theories violate unitarity for |λ|>2. These results encourage a tensionless string theory interpretation of the 3D Vasiliev theory.
Schuster, H G
2008-01-01
This long-awaited revised second edition of the standard reference on the subject has been considerably expanded to include such recent developments as novel control schemes, control of chaotic space-time patterns, control of noisy nonlinear systems, and communication with chaos, as well as promising new directions in research. The contributions from leading international scientists active in the field provide a comprehensive overview of our current level of knowledge on chaos control and its applications in physics, chemistry, biology, medicine, and engineering. In addition, they show the overlap with the traditional field of control theory in the engineering community.An interdisciplinary approach of interest to scientists and engineers working in a number of areas
Topological organization of (low-dimensional) chaos
International Nuclear Information System (INIS)
Tufillaro, N.B.
1992-01-01
Recent progress toward classifying low-dimensional chaos measured from time series data is described. This classification theory assigns a template to the time series once the time series is embedded in three dimensions. The template describes the primary folding and stretching mechanisms of phase space responsible for the chaotic motion. Topological invariants of the unstable periodic orbits in the closure of the strange set are calculated from the (reconstructed) template. These topological invariants must be consistent with ampersand ny model put forth to describe the time series data, and are useful in invalidating (or gaining confidence in) any model intended to describe the dynamical system generating the time series
Approximate motion integrals and the quantum chaos problem
International Nuclear Information System (INIS)
Bunakov, V.E.; Ivanov, I.B.
2001-01-01
One discusses the problem of occurrence and seek for the motion integrals in the stationary quantum mechanics and its relation to the quantum chaos. One studies decomposition of quantum numbers and derives the criterion of chaos. To seek the motion integrals one applies the convergence method. One derived the approximate integrals in the Hennone-Hales problem. One discusses the problem of compatibility of chaos and integrability [ru
Directory of Open Access Journals (Sweden)
Nuray Mercan
2012-01-01
Full Text Available Some words, which are basic cues of determining actors of current time-likeglobalization and information age-, change, speed, competition, and diversitybecame nearly catchwords. All the world, have been grazing from the limitedperception of history about place and time and have been facing the fact that thefuture is changing totally in different axis. This orbit has differentcoordinates,tools and methods and it is unavoidable. Likewise, basic dynamics ofinformation age are not being able to explain with the paradigms of industrialage. In whole world, new coordinates of information age which guide a new era-so ist paradigm-is becoming chaos theory, its captains are becoming differentleaders of different geographies. “Butterfly Effect”, another concept , which isrelated to “Chos Theory”of Edward N. Lorenz, can define as small changes ininitial datas in a system can cause big and unknown results. Globalization andinformation age make butterfly effect common. In this study, from the point of “ A butterfly’s flapping in Amazon Forest can cause a storm in USA” view, possibleeffects of chaos theory and butterfly effect to social life and to organizations willbe evaluated.,In the first part of this researchwill explainedchaos theory,inthethesecond part will mentionedfrom dominant metaphors in the past andfuture organizations ,inthethird part will analyzedmodel of chaos managementorganization.
Wave chaos in acoustics and elasticity
International Nuclear Information System (INIS)
Tanner, Gregor; Soendergaard, Niels
2007-01-01
Interpreting wave phenomena in terms of an underlying ray dynamics adds a new dimension to the analysis of linear wave equations. Forming explicit connections between spectra and wavefunctions on the one hand and the properties of a related ray dynamics on the other hand is a comparatively new research area, especially in elasticity and acoustics. The theory has indeed been developed primarily in a quantum context; it is increasingly becoming clear, however, that important applications lie in the field of mechanical vibrations and acoustics. We provide an overview over basic concepts in this emerging field of wave chaos. This ranges from ray approximations of the Green function to periodic orbit trace formulae and random matrix theory and summarizes the state of the art in applying these ideas in acoustics-both experimentally and from a theoretical/numerical point of view. (topical review)
Asymptotic chaos expansions in finance theory and practice
Nicolay, David
2014-01-01
Stochastic instantaneous volatility models such as Heston, SABR or SV-LMM have mostly been developed to control the shape and joint dynamics of the implied volatility surface. In principle, they are well suited for pricing and hedging vanilla and exotic options, for relative value strategies or for risk management. In practice however, most SV models lack a closed form valuation for European options. This book presents the recently developed Asymptotic Chaos Expansions methodology (ACE) which addresses that issue. Indeed its generic algorithm provides, for any regular SV model, the pure asymptotes at any order for both the static and dynamic maps of the implied volatility surface. Furthermore, ACE is programmable and can complement other approximation methods. Hence it allows a systematic approach to designing, parameterising, calibrating and exploiting SV models, typically for Vega hedging or American Monte-Carlo. Asymptotic Chaos Expansions in Finance illustrates the ACE approach for single underlyings (suc...
Riemannian theory of Hamiltonian chaos and Lyapunov exponents
Casetti, Lapo; Clementi, Cecilia; Pettini, Marco
1996-12-01
A nonvanishing Lyapunov exponent λ1 provides the very definition of deterministic chaos in the solutions of a dynamical system; however, no theoretical mean of predicting its value exists. This paper copes with the problem of analytically computing the largest Lyapunov exponent λ1 for many degrees of freedom Hamiltonian systems as a function of ɛ=E/N, the energy per degree of freedom. The functional dependence λ1(ɛ) is of great interest because, among other reasons, it detects the existence of weakly and strongly chaotic regimes. This aim, the analytic computation of λ1(ɛ), is successfully reached within a theoretical framework that makes use of a geometrization of Newtonian dynamics in the language of Riemannian differential geometry. An alternative point of view about the origin of chaos in these systems is obtained independently of the standard explanation based on homoclinic intersections. Dynamical instability (chaos) is here related to curvature fluctuations of the manifolds whose geodesics are natural motions and is described by means of the Jacobi-Levi-Civita equation (JLCE) for geodesic spread. In this paper it is shown how to derive from the JLCE an effective stability equation. Under general conditions, this effective equation formally describes a stochastic oscillator; an analytic formula for the instability growth rate of its solutions is worked out and applied to the Fermi-Pasta-Ulam β model and to a chain of coupled rotators. Excellent agreement is found between the theoretical prediction and numeric values of λ1(ɛ) for both models.
Chaos synchronization of a new chaotic system via nonlinear control
International Nuclear Information System (INIS)
Zhang Qunjiao; Lu Junan
2008-01-01
This paper investigates chaos synchronization of a new chaotic system [Lue J, Chen G, Cheng D. A new chaotic system and beyond: the generalized Lorenz-like system. Int J Bifurcat Chaos 2004;14:1507-37]. Two kinds of novel nonlinear controllers are designed based on the Lyapunov stability theory. It can be viewed as an improvement to the existing results of reference [Park JH. Chaos synchronization of a chaotic system via nonlinear control. Chaos, Solitons and Fractals 2005;25:579-84] because we use less controllers but realize a global and exponential asymptotical synchronization. Numerical simulations are provided to show the effectiveness and advantage of this method
Chaos in charged AdS black hole extended phase space
Chabab, M.; El Moumni, H.; Iraoui, S.; Masmar, K.; Zhizeh, S.
2018-06-01
We present an analytical study of chaos in a charged black hole in the extended phase space in the context of the Poincare-Melnikov theory. Along with some background on dynamical systems, we compute the relevant Melnikov function and find its zeros. Then we analyse these zeros either to identify the temporal chaos in the spinodal region, or to observe spatial chaos in the small/large black hole equilibrium configuration. As a byproduct, we derive a constraint on the Black hole' charge required to produce chaotic behaviour. To the best of our knowledge, this is the first endeavour to understand the correlation between chaos and phase picture in black holes.
Chaos synchronization of coupled hyperchaotic system
International Nuclear Information System (INIS)
Yang Lixin; Chu Yandong; Zhang Jiangang; Li Xianfeng
2009-01-01
Chaos synchronization, as an important topic, has become an active research subject in nonlinear science. Over the past two decades, chaos synchronization between nonlinear systems has been extensively studied, and many types of synchronization have been announced. This paper introduces synchronization of coupled hyperchaotic system, based on the Lapunov stability theory, asymptotic stability of the system is guaranteed by means of Lapunov function. The numerical simulation was provided in order to show the effectiveness of this method for the synchronization of the chaotic hyperchaotic Chen system and Rossler system.
Adventures in order and chaos : a scientific autobiography
Contopoulos, George
The field of Order and Chaos had a remarkable expansion in the last 50 years. The main reason was the use of computers, and the development of new theoretical methods that we call now 'the theory of chaos'. The author describes this fascinating period in a relaxed and sometimes humorous autobiographical way. He relates his interactions with many people in dynamical astronomy and he quotes several anecdotes from these interactions. He refers also to his experiences when he served in various international positions, such as general secretary of the IAU and chairman of the journal Astronomy and Astrophysics. In recent years the theory of chaos has been extended to new areas, like relativity, cosmology and quantum mechanics and it continues expanding in almost all branches of physics. The book describes many important ideas in this field in a simple way. It refers also to problems of more general interest, like writing papers and giving lectures and the interaction of authors and referees. Finally it gives some useful prospects for the future of dynamical astronomy and related fields. George Contopoulos, PhD U.Athens1953; Professor of Astronomy U.Thessaloniki 1957-75; U.Athens 1975-96; Emeritus 1996-; Member, Academy of Athens 1997-. Visiting Professor Yale U., Harvard U., MIT, Cornell U., U.Chicago, U.Maryland, U. Florida, Florida State U., U. Milan; Res. Associate, Yerkes Obs., Inst.Adv.Study Princeton, Inst.Space Studies, Goddard Flight Center, Columbia U., ESO. Author or Editor of 15 books, and about 250 papers on Galactic Dynamics, Relativity and Celestial Mechanics. Positions held: Gen.Secretary of the IAU; Director General Nat.Obs.of Greece, Pres.Hellenic Astron.Soc.; Nat.Representative of Greece in NATO, etc. Distinctions: Amer. Astron.Soc. Brouwer Prize; U.Chicago, Honorary Doctor's Degree; IAU, Pres. Commission 33 (Galaxy); Member Academia Europaea; Associate Royal Astron. Soc.; Chairman of the European Journal "Astronomy and Astrophysics"; Assoc. Editor of
Guastello, Stephen J
2009-07-01
The landmarks in the use of chaos and related constructs in psychology were entwined with the growing use of other nonlinear dynamical constructs, especially catastrophes and self-organization. The growth in substantive applications of chaos in psychology is partially related to the development of methodologies that work within the constraints of psychological data. The psychological literature includes rigorous theory with testable propositions, lighter-weight metaphorical uses of the construct, and colloquial uses of "chaos" with no particular theoretical intent. The current state of the chaos construct and supporting empirical research in psychological theory is summarized in neuroscience, psychophysics, psychomotor skill and other learning phenomena, clinical and abnormal psychology, and group dynamics and organizational behavior. Trends indicate that human systems do not remain chaotic indefinitely; they eventually self-organize, and the concept of the complex adaptive system has become prominent. Chaotic turbulence is generally higher in healthy systems compared to unhealthy systems, although opposite appears true in mood disorders. Group dynamics research shows trends consistent with the complex adaptive system, whereas organizational behavior lags behind in empirical studies relative to the quantity of its theory. Future directions for research involving the chaos construct and other nonlinear dynamics are outlined.
Hamiltonian Chaos and Fractional Dynamics
International Nuclear Information System (INIS)
Combescure, M
2005-01-01
This book provides an introduction and discussion of the main issues in the current understanding of classical Hamiltonian chaos, and of its fractional space-time structure. It also develops the most complex and open problems in this context, and provides a set of possible applications of these notions to some fundamental questions of dynamics: complexity and entropy of systems, foundation of classical statistical physics on the basis of chaos theory, and so on. Starting with an introduction of the basic principles of the Hamiltonian theory of chaos, the book covers many topics that can be found elsewhere in the literature, but which are collected here for the readers' convenience. In the last three parts, the author develops topics which are not typically included in the standard textbooks; among them are: - the failure of the traditional description of chaotic dynamics in terms of diffusion equations; - he fractional kinematics, its foundation and renormalization group analysis; - 'pseudo-chaos', i.e. kinetics of systems with weak mixing and zero Lyapunov exponents; - directional complexity and entropy. The purpose of this book is to provide researchers and students in physics, mathematics and engineering with an overview of many aspects of chaos and fractality in Hamiltonian dynamical systems. In my opinion it achieves this aim, at least provided researchers and students (mainly those involved in mathematical physics) can complement this reading with comprehensive material from more specialized sources which are provided as references and 'further reading'. Each section contains introductory pedagogical material, often illustrated by figures coming from several numerical simulations which give the feeling of what's going on, and thus is very useful to the reader who is not very familiar with the topics presented. Some problems are included at the end of most sections to help the reader to go deeper into the subject. My one regret is that the book does not
Chaos-based hash function (CBHF) for cryptographic applications
International Nuclear Information System (INIS)
Amin, Mohamed; Faragallah, Osama S.; Abd El-Latif, Ahmed A.
2009-01-01
As the core of cryptography, hash is the basic technique for information security. Many of the hash functions generate the message digest through a randomizing process of the original message. Subsequently, a chaos system also generates a random behavior, but at the same time a chaos system is completely deterministic. In this paper, an algorithm for one-way hash function construction based on chaos theory is introduced. Theoretical analysis and computer simulation indicate that the algorithm can satisfy all performance requirements of hash function in an efficient and flexible manner and secure against birthday attacks or meet-in-the-middle attacks, which is good choice for data integrity or authentication.
Chaos-based hash function (CBHF) for cryptographic applications
Energy Technology Data Exchange (ETDEWEB)
Amin, Mohamed [Dept. of Mathematics and Computer Science, Faculty of Science, Menoufia University, Shebin El-Koom 32511 (Egypt)], E-mail: mamin04@yahoo.com; Faragallah, Osama S. [Dept. of Computer Science and Engineering, Faculty of Electronic Engineering, Menoufia University, Menouf 32952 (Egypt)], E-mail: osam_sal@yahoo.com; Abd El-Latif, Ahmed A. [Dept. of Mathematics and Computer Science, Faculty of Science, Menoufia University, Shebin El-Koom 32511 (Egypt)], E-mail: ahmed_rahiem@yahoo.com
2009-10-30
As the core of cryptography, hash is the basic technique for information security. Many of the hash functions generate the message digest through a randomizing process of the original message. Subsequently, a chaos system also generates a random behavior, but at the same time a chaos system is completely deterministic. In this paper, an algorithm for one-way hash function construction based on chaos theory is introduced. Theoretical analysis and computer simulation indicate that the algorithm can satisfy all performance requirements of hash function in an efficient and flexible manner and secure against birthday attacks or meet-in-the-middle attacks, which is good choice for data integrity or authentication.
Bunimovich, Leonid A; Vela-Arevalo, Luz V
2015-09-01
"Chaos is found in greatest abundance wherever order is being sought.It always defeats order, because it is better organized"Terry PratchettA brief review is presented of some recent findings in the theory of chaotic dynamics. We also prove a statement that could be naturally considered as a dual one to the Poincaré theorem on recurrences. Numerical results demonstrate that some parts of the phase space of chaotic systems are more likely to be visited earlier than other parts. A new class of chaotic focusing billiards is discussed that clearly violates the main condition considered to be necessary for chaos in focusing billiards.
Quantum manifestations of chaos
International Nuclear Information System (INIS)
Borondo, F.; Benito, R.M.
1998-01-01
The correspondence between classical and quantum mechanics is considered both in the regular and chaotic regimes, and the main results regarding the quantum manifestations of chaos are reviewed. (Author) 16 refs
[Analysis of the heart sound with arrhythmia based on nonlinear chaos theory].
Ding, Xiaorong; Guo, Xingming; Zhong, Lisha; Xiao, Shouzhong
2012-10-01
In this paper, a new method based on the nonlinear chaos theory was proposed to study the arrhythmia with the combination of the correlation dimension and largest Lyapunov exponent, through computing and analyzing these two parameters of 30 cases normal heart sound and 30 cases with arrhythmia. The results showed that the two parameters of the heart sounds with arrhythmia were higher than those with the normal, and there was significant difference between these two kinds of heart sounds. That is probably due to the irregularity of the arrhythmia which causes the decrease of predictability, and it's more complex than the normal heart sound. Therefore, the correlation dimension and the largest Lyapunov exponent can be used to analyze the arrhythmia and for its feature extraction.
Directory of Open Access Journals (Sweden)
Shaohua Luo
2016-09-01
Full Text Available This paper addresses chaos suppression of the mechanical centrifugal flywheel governor system with output constraint and fully unknown parameters via adaptive dynamic surface control. To have a certain understanding of chaotic nature of the mechanical centrifugal flywheel governor system and subsequently design its controller, the useful tools like the phase diagrams and corresponding time histories are employed. By using tangent barrier Lyapunov function, a dynamic surface control scheme with neural network and tracking differentiator is developed to transform chaos oscillation into regular motion and the output constraint rule is not broken in whole process. Plugging second-order tracking differentiator into chaos controller tackles the “explosion of complexity” of backstepping and improves the accuracy in contrast with the first-order filter. Meanwhile, Chebyshev neural network with adaptive law whose input only depends on a subset of Chebyshev polynomials is derived to learn the behavior of unknown dynamics. The boundedness of all signals of the closed-loop system is verified in stability analysis. Finally, the results of numerical simulations illustrate effectiveness and exhibit the superior performance of the proposed scheme by comparing with the existing ADSC method.
Rank one chaos in a class of planar systems with heteroclinic cycle.
Chen, Fengjuan; Han, Maoan
2009-12-01
In this paper, we study rank one chaos in a class of planar systems with heteroclinic cycle. We first find a stable limit cycle inside the heteroclinic cycle. We then add an external periodic forcing to create rank one chaos. We follow a step-by-step procedure guided by the theory of rank one chaos to find experimental evidence of strange attractors with Sinai, Ruelle, and Bowen measures.
[Radiotherapy and chaos theory: the tit bird and the butterfly...].
Denis, F; Letellier, C
2012-09-01
Although the same simple laws govern cancer outcome (cell division repeated again and again), each tumour has a different outcome before as well as after irradiation therapy. The linear-quadratic radiosensitivity model allows an assessment of tumor sensitivity to radiotherapy. This model presents some limitations in clinical practice because it does not take into account the interactions between tumour cells and non-tumoral bystander cells (such as endothelial cells, fibroblasts, immune cells...) that modulate radiosensitivity and tumor growth dynamics. These interactions can lead to non-linear and complex tumor growth which appears to be random but that is not since there is not so many tumors spontaneously regressing. In this paper we propose to develop a deterministic approach for tumour growth dynamics using chaos theory. Various characteristics of cancer dynamics and tumor radiosensitivity can be explained using mathematical models of competing cell species. Copyright © 2012 Société française de radiothérapie oncologique (SFRO). Published by Elsevier SAS. All rights reserved.
The chaos theory and the quality assurance
International Nuclear Information System (INIS)
Aguilar, Omar; Domech More, Jesus
1999-01-01
In the present paper we suggest the importance that the new science of chaos offers in the analysis,design and improvement processes in the production of gamma shielding devices as part of the quality assurance system. A brief analysis of the influence of the errors of measures, the interactions between the process and its environment in determining of the basic behaviour of the process and its stability is done.(author)
Phase Locking and Chaos in a Josephson Junction Array Shunted by a Common Resistance
International Nuclear Information System (INIS)
Tie-Ge, Zhou; Jing, Mao; Ting-Shu, Liu; Yue, Lai; Shao-Lin, Yan
2009-01-01
The dynamics of a Josephson junction array shunted by a common resistance are investigated by using numerical methods. Coexistence of phase locking and chaos is observed in the system when the resistively and capacitively shunted junction model is adopted. The corresponding parameter ranges for phase locking and chaos are presented. When there are three resistively shunted junctions in the array, chaos is found for the first time and the parameter range for chaos is also presented. According to the theory of Chernikov and Schmidt, when there are four or more junctions in the array, the system exhibits chaotic behavior. Our results indicate that the theory of Chernikov and Schmidt is not exactly appropriate. (condensed matter: electronicstructure, electrical, magnetic, and opticalproperties)
Forgotten and neglected theories of Poincare
International Nuclear Information System (INIS)
Arnold, V.I.
2006-04-01
This paper describes a number of published and unpublished works of Henri Poincare that await continuation by the next generations of mathematicians: works on celestial mechanics, on topology, on the theory of chaos and dynamical systems, and on homology, intersections and links. Also discussed are the history of the theory of relativity and the theory of functions and the connection between the Poincare conjecture and the theory of knot invariants. (author)
MODELLING AND SIMULATING RISKS IN THE TRAINING OF THE HUMAN RESOURCES BY APPLYING THE CHAOS THEORY
Eugen ROTARESCU
2012-01-01
The article approaches the modelling and simulation of risks in the training of the human resources, as well as the forecast of the degree of human resources training impacted by risks by applying the mathematical tools offered by the Chaos Theory and mathematical statistics. We will highlight that the level of knowledge, skills and abilities of the human resources from an organization are autocorrelated in time and they depend on the level of a previous moment of the training, as well as on ...
Many-Body Quantum Chaos and Entanglement in a Quantum Ratchet
Valdez, Marc Andrew; Shchedrin, Gavriil; Heimsoth, Martin; Creffield, Charles E.; Sols, Fernando; Carr, Lincoln D.
2018-06-01
We uncover signatures of quantum chaos in the many-body dynamics of a Bose-Einstein condensate-based quantum ratchet in a toroidal trap. We propose measures including entanglement, condensate depletion, and spreading over a fixed basis in many-body Hilbert space, which quantitatively identify the region in which quantum chaotic many-body dynamics occurs, where random matrix theory is limited or inaccessible. With these tools, we show that many-body quantum chaos is neither highly entangled nor delocalized in the Hilbert space, contrary to conventionally expected signatures of quantum chaos.
Some studies on arithmetical chaos in classical and quantum mechanics
International Nuclear Information System (INIS)
Bolte, J.
1993-04-01
Several aspects of classical and quantum mechanics applied to a class of strongly chaotic systems are studied. The latter consists of single particles moving without external forces on surfaces of constant negative Gaussian curvature whose corresponding fundamental groups are supplied with an arithmetic structure. It is shown that the arithmetical features of the considered systems lead to exceptional properties of the corresponding spectra of lengths of closed geodesics (periodic orbits). The most significant one is an exponential growth of degeneracies in these geodesic length spectra. Furthermore, the arithmetical systems are distinguished by a structure that appears as a generalization of geometric symmetries. These pseudosymmetries occur in the quantization of the classical arithmetic systems as Hecke operators, which form an infinite algebra of self-adjoint operators commuting with the Hamiltonian. The statistical properties of quantum energies in the arithmetical systems have previously been identified as exceptional. They do not fit into the general scheme of random matrix theory. It is shown with the help of a simplified model for the spectral form factor how the spectral statistics in arithmetical quantum chaos can be understood by the properties of the corresponding classical geodesic length spectra. A decisive role is played by the exponentially increasing multiplicities of lengths. The model developed for the level spacings distribution and for the number variance is compared to the corresponding quantities obtained from quantum energies for a specific arithmetical system. Finally, the convergence properties of a representation for the Selberg zeta function as a Dirichlet series are studied. It turns out that the exceptional classical and quantum mechanical properties shared by the arithmetical systems prohibit a convergence of this important function in the physically interesting domain. (orig.)
Weak and strong chaos in Fermi-Pasta-Ulam models and beyond
Pettini, Marco; Casetti, Lapo; Cerruti-Sola, Monica; Franzosi, Roberto; Cohen, E. G. D.
2005-03-01
We briefly review some of the most relevant results that our group obtained in the past, while investigating the dynamics of the Fermi-Pasta-Ulam (FPU) models. The first result is the numerical evidence of the existence of two different kinds of transitions in the dynamics of the FPU models: (i) A stochasticity threshold (ST), characterized by a value of the energy per degree of freedom below which the overwhelming majority of the phase space trajectories are regular (vanishing Lyapunov exponents). It tends to vanish as the number N of degrees of freedom is increased. (ii) A strong stochasticity threshold (SST), characterized by a value of the energy per degree of freedom at which a crossover appears between two different power laws of the energy dependence of the largest Lyapunov exponent, which phenomenologically corresponds to the transition between weak and strong chaotic regimes. It is stable with N. The second result is the development of a Riemannian geometric theory to explain the origin of Hamiltonian chaos. Starting this theory has been motivated by the inadequacy of the approach based on homoclinic intersections to explain the origin of chaos in systems of arbitrarily large N, or arbitrarily far from quasi-integrability, or displaying a transition between weak and strong chaos. Finally, the third result stems from the search for the transition between weak and strong chaos in systems other than FPU. Actually, we found that a very sharp SST appears as the dynamical counterpart of a thermodynamic phase transition, which in turn has led, in the light of the Riemannian theory of chaos, to the development of a topological theory of phase transitions.
Detecting Chaos from Agricultural Product Price Time Series
Directory of Open Access Journals (Sweden)
Xin Su
2014-12-01
Full Text Available Analysis of the characteristics of agricultural product price volatility and trend forecasting are necessary to formulate and implement agricultural price control policies. Taking wholesale cabbage prices as an example, a multiple test methodology has been adopted to identify the nonlinearity, fractality, and chaos of the data. The approaches used include the R/S analysis, the BDS test, the power spectra, the recurrence plot, the largest Lyapunov exponent, the Kolmogorov entropy, and the correlation dimension. The results show that there is chaos in agricultural wholesale price data, which provides a good theoretical basis for selecting reasonable forecasting models as prediction techniques based on chaos theory can be applied to forecasting agricultural prices.
Chaos, scaling and existence of a continuum limit in classical non-Abelian lattice gauge theory
International Nuclear Information System (INIS)
Nielsen, H.B.; Rugh, H.H.; Rugh, S.E.
1996-01-01
We discuss space-time chaos and scaling properties for classical non-Abelian gauge fields discretized on a spatial lattice. We emphasize that there is a open-quote no goclose quotes for simulating the original continuum classical gauge fields over a long time span since there is a never ending dynamical cascading towards the ultraviolet. We note that the temporal chaotic properties of the original continuum gauge fields and the lattice gauge system have entirely different scaling properties thereby emphasizing that they are entirely different dynamical systems which have only very little in common. Considered as a statistical system in its own right the lattice gauge system in a situation where it has reached equilibrium comes closest to what could be termed a open-quotes continuum limitclose quotes in the limit of very small energies (weak non-linearities). We discuss the lattice system both in the limit for small energies and in the limit of high energies where we show that there is a saturation of the temporal chaos as a pure lattice artifact. Our discussion focuses not only on the temporal correlations but to a large extent also on the spatial correlations in the lattice system. We argue that various conclusions of physics have been based on monitoring the non-Abelian lattice system in regimes where the fields are correlated over few lattice units only. This is further evidenced by comparison with results for Abelian lattice gauge theory. How the real time simulations of the classical lattice gauge theory may reach contact with the real time evolution of (semi-classical aspects of) the quantum gauge theory (e.g. Q.C.D.) is left an important question to be further examined
Role of nonlinear dynamics and chaos in applied sciences
International Nuclear Information System (INIS)
Lawande, Quissan V.; Maiti, Nirupam
2000-02-01
Nonlinear dynamics manifests itself in a number of phenomena in both laboratory and day to day dealings. However, little attention was being paid to this dynamically rich field. With the advent of high speed computers with visual graphics, the field has proliferated over past few years. One of the most rewarding realization from nonlinear dynamics is the universally acclaimed field of chaos. Chaos has brought in order and has broken the disciplinary boundaries that existed until recently. With its universal phenomena, almost all disciplines following an evolutionary character can be treated on same footing. Chaotic dynamics has its grounding in the multidisciplinary field of synergetics founded by Professor Hermann Haken. In this report, we address some of the basics related to the field of chaos. We have discussed simple mechanisms for generating chaotic trajectories, ways and means of characterizing such systems and the manifestation of their signatures in the evolutions. We have mentioned the links of this field with other existing theories. We have outlined the topics on bifurcation and stability of dynamical systems. Information theoretic aspects and notions on fractal geometry are reviewed in the light of dynamical characterization of chaotic systems. Application oriented views of this novel dynamical phenomena are discussed through examples on simple nonlinear electronic circuits and a BWR reactor. Some ideas relating to control and synchronization in chaotic systems also addressed. In conclusion, we have explored the possibilities of exploiting nonlinear dynamics and chaos in the context of multidisciplinary character of BARC. (author)
International Nuclear Information System (INIS)
Bick, Christian; Kolodziejski, Christoph; Timme, Marc
2014-01-01
Predictive feedback control is an easy-to-implement method to stabilize unknown unstable periodic orbits in chaotic dynamical systems. Predictive feedback control is severely limited because asymptotic convergence speed decreases with stronger instabilities which in turn are typical for larger target periods, rendering it harder to effectively stabilize periodic orbits of large period. Here, we study stalled chaos control, where the application of control is stalled to make use of the chaotic, uncontrolled dynamics, and introduce an adaptation paradigm to overcome this limitation and speed up convergence. This modified control scheme is not only capable of stabilizing more periodic orbits than the original predictive feedback control but also speeds up convergence for typical chaotic maps, as illustrated in both theory and application. The proposed adaptation scheme provides a way to tune parameters online, yielding a broadly applicable, fast chaos control that converges reliably, even for periodic orbits of large period
Bick, Christian; Kolodziejski, Christoph; Timme, Marc
2014-09-01
Predictive feedback control is an easy-to-implement method to stabilize unknown unstable periodic orbits in chaotic dynamical systems. Predictive feedback control is severely limited because asymptotic convergence speed decreases with stronger instabilities which in turn are typical for larger target periods, rendering it harder to effectively stabilize periodic orbits of large period. Here, we study stalled chaos control, where the application of control is stalled to make use of the chaotic, uncontrolled dynamics, and introduce an adaptation paradigm to overcome this limitation and speed up convergence. This modified control scheme is not only capable of stabilizing more periodic orbits than the original predictive feedback control but also speeds up convergence for typical chaotic maps, as illustrated in both theory and application. The proposed adaptation scheme provides a way to tune parameters online, yielding a broadly applicable, fast chaos control that converges reliably, even for periodic orbits of large period.
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Bick, Christian [Network Dynamics, Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen (Germany); Bernstein Center for Computational Neuroscience (BCCN), 37077 Göttingen (Germany); Institute for Mathematics, Georg–August–Universität Göttingen, 37073 Göttingen (Germany); Kolodziejski, Christoph [Network Dynamics, Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen (Germany); III. Physical Institute—Biophysics, Georg–August–Universität Göttingen, 37077 Göttingen (Germany); Timme, Marc [Network Dynamics, Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen (Germany); Institute for Nonlinear Dynamics, Georg–August–Universität Göttingen, 37077 Göttingen (Germany)
2014-09-01
Predictive feedback control is an easy-to-implement method to stabilize unknown unstable periodic orbits in chaotic dynamical systems. Predictive feedback control is severely limited because asymptotic convergence speed decreases with stronger instabilities which in turn are typical for larger target periods, rendering it harder to effectively stabilize periodic orbits of large period. Here, we study stalled chaos control, where the application of control is stalled to make use of the chaotic, uncontrolled dynamics, and introduce an adaptation paradigm to overcome this limitation and speed up convergence. This modified control scheme is not only capable of stabilizing more periodic orbits than the original predictive feedback control but also speeds up convergence for typical chaotic maps, as illustrated in both theory and application. The proposed adaptation scheme provides a way to tune parameters online, yielding a broadly applicable, fast chaos control that converges reliably, even for periodic orbits of large period.
Interactions between neural networks: a mechanism for tuning chaos and oscillations.
Wang, Lipo
2007-06-01
We show that chaos and oscillations in a higher-order binary neural network can be tuned effectively using interactions between neural networks. Our results suggest that network interactions may be useful as a means of adjusting the level of dynamic activities in systems that employ chaos and oscillations for information processing, or as a means of suppressing oscillatory behaviors in systems that require stability.
Directory of Open Access Journals (Sweden)
Jian Liu
2014-11-01
Full Text Available This paper introduces a type of modified hybrid projective synchronization with complex transformationmatrix (CMHPS for different dimensional fractional-order complex chaos and fractional-order real hyper-chaos. The transformationmatrix in this type of chaotic synchronization is a non-square matrix, and its elements are complex numbers. Based on the stability theory of fractional-order systems, by employing the feedback control technique, necessary and sufficient criteria on CMHPS are derived. Furthermore, CMHPS between fractional-order real hyper-chaotic Rössler system and other two different dimensional fractional-order complex Lorenz-like chaotic systems is provided as two examples to discuss reduced order and increased order synchronization, respectively.
Forgotten and neglected theories of Poincare
International Nuclear Information System (INIS)
Arnol'd, Vladimir I
2006-01-01
This paper describes a number of published and unpublished works of Henri Poincare that await continuation by the next generations of mathematicians: works on celestial mechanics, on topology, on the theory of chaos and dynamical systems, and on homology, intersections and links. Also discussed are the history of the theory of relativity and the theory of generalized functions (distributions) and the connection between the Poincare conjecture and the theory of knot invariants.
Elimination of spiral chaos by periodic force for the Aliev-Panfilov model
Sakaguchi, Hidetsugu; Fujimoto, Takefumi
2003-01-01
Spiral chaos appears in the two dimensional Aliev-Panfilov model. The generation mechanism of the spiral chaos is related to the breathing instability of pulse trains. The spiral chaos can be eliminated by applying periodic force uniformly. The elimination of spiral chaos is most effective, when the frequency of the periodic force is close to that of the breathing motion.
Extension of spatiotemporal chaos in glow discharge-semiconductor systems.
Akhmet, Marat; Rafatov, Ismail; Fen, Mehmet Onur
2014-12-01
Generation of chaos in response systems is discovered numerically through specially designed unidirectional coupling of two glow discharge-semiconductor systems. By utilizing the auxiliary system approach, [H. D. I. Abarbanel, N. F. Rulkov, and M. M. Sushchik, Phys. Rev. E 53, 4528-4535 (1996)] it is verified that the phenomenon is not a chaos synchronization. Simulations demonstrate various aspects of the chaos appearance in both drive and response systems. Chaotic control is through the external circuit equation and governs the electrical potential on the boundary. The expandability of the theory to collectives of glow discharge systems is discussed, and this increases the potential of applications of the results. Moreover, the research completes the previous discussion of the chaos appearance in a glow discharge-semiconductor system [D. D. Šijačić U. Ebert, and I. Rafatov, Phys. Rev. E 70, 056220 (2004).].
Many-body quantum chaos: Recent developments and applications to nuclei
International Nuclear Information System (INIS)
Gomez, J.M.G.; Kar, K.; Kota, V.K.B.; Molina, R.A.; Relano, A.; Retamosa, J.
2011-01-01
In the last decade, there has been an increasing interest in the analysis of energy level spectra and wave functions of nuclei, particles, atoms and other quantum many-body systems by means of statistical methods and random matrix ensembles. The concept of quantum chaos plays a central role for understanding the universal properties of the energy spectrum of quantum systems. Since these properties concern the whole spectrum, statistical methods become an essential tool. Besides random matrix theory, new theoretical developments making use of information theory, time series analysis, and the merging of thermodynamics and the semiclassical approximation are emphasized. Applications of these methods to quantum systems, especially to atomic nuclei, are reviewed. We focus on recent developments like the study of 'imperfect spectra' to estimate the degree of symmetry breaking or the fraction of missing levels, the existence of chaos remnants in nuclear masses, the onset of chaos in nuclei, and advances in the comprehension of the Hamiltonian structure in many-body systems. Finally, some applications of statistical spectroscopy methods generated by many-body chaos and two-body random matrix ensembles are described, with emphasis on Gamow-Teller strength sums and beta decay rates for stellar evolution and supernovae.
Origin of chaos in 3-d Bohmian trajectories
International Nuclear Information System (INIS)
Tzemos, Athanasios C.; Contopoulos, George; Efthymiopoulos, Christos
2016-01-01
We study the 3-d Bohmian trajectories of a quantum system of three harmonic oscillators. We focus on the mechanism responsible for the generation of chaotic trajectories. We demonstrate the existence of a 3-d analogue of the mechanism found in earlier studies of 2-d systems [1,2], based on moving 2-d ‘nodal point–X-point complexes’. In the 3-d case, we observe a foliation of nodal point–X-point complexes, forming a ‘3-d structure of nodal and X-points’. Chaos is generated when the Bohmian trajectories are scattered at one or more close encounters with such a structure. - Highlights: • A mechanism for the emergence of 3-d Bohmian chaos is proposed. • We demonstrate the existence of a 3-d structure of nodal and X-points. • Chaos is generated when the trajectories are scattered by the X-points.
Origin of chaos in 3-d Bohmian trajectories
Energy Technology Data Exchange (ETDEWEB)
Tzemos, Athanasios C., E-mail: thanasistzemos@gmail.com; Contopoulos, George, E-mail: gcontop@academyofathens.gr; Efthymiopoulos, Christos, E-mail: cefthim@academyofathens.gr
2016-11-25
We study the 3-d Bohmian trajectories of a quantum system of three harmonic oscillators. We focus on the mechanism responsible for the generation of chaotic trajectories. We demonstrate the existence of a 3-d analogue of the mechanism found in earlier studies of 2-d systems [1,2], based on moving 2-d ‘nodal point–X-point complexes’. In the 3-d case, we observe a foliation of nodal point–X-point complexes, forming a ‘3-d structure of nodal and X-points’. Chaos is generated when the Bohmian trajectories are scattered at one or more close encounters with such a structure. - Highlights: • A mechanism for the emergence of 3-d Bohmian chaos is proposed. • We demonstrate the existence of a 3-d structure of nodal and X-points. • Chaos is generated when the trajectories are scattered by the X-points.
Controlling Mackey-Glass chaos
Kiss, Gábor; Röst, Gergely
2017-11-01
The Mackey-Glass equation is the representative example of delay induced chaotic behavior. Here, we propose various control mechanisms so that otherwise erratic solutions are forced to converge to the positive equilibrium or to a periodic orbit oscillating around that equilibrium. We take advantage of some recent results of the delay differential literature, when a sufficiently large domain of the phase space has been shown to be attractive and invariant, where the system is governed by monotone delayed feedback and chaos is not possible due to some Poincaré-Bendixson type results. We systematically investigate what control mechanisms are suitable to drive the system into such a situation and prove that constant perturbation, proportional feedback control, Pyragas control, and state dependent delay control can all be efficient to control Mackey-Glass chaos with properly chosen control parameters.
Controlling Mackey-Glass chaos.
Kiss, Gábor; Röst, Gergely
2017-11-01
The Mackey-Glass equation is the representative example of delay induced chaotic behavior. Here, we propose various control mechanisms so that otherwise erratic solutions are forced to converge to the positive equilibrium or to a periodic orbit oscillating around that equilibrium. We take advantage of some recent results of the delay differential literature, when a sufficiently large domain of the phase space has been shown to be attractive and invariant, where the system is governed by monotone delayed feedback and chaos is not possible due to some Poincaré-Bendixson type results. We systematically investigate what control mechanisms are suitable to drive the system into such a situation and prove that constant perturbation, proportional feedback control, Pyragas control, and state dependent delay control can all be efficient to control Mackey-Glass chaos with properly chosen control parameters.
Polynomial chaos functions and stochastic differential equations
International Nuclear Information System (INIS)
Williams, M.M.R.
2006-01-01
The Karhunen-Loeve procedure and the associated polynomial chaos expansion have been employed to solve a simple first order stochastic differential equation which is typical of transport problems. Because the equation has an analytical solution, it provides a useful test of the efficacy of polynomial chaos. We find that the convergence is very rapid in some cases but that the increased complexity associated with many random variables can lead to very long computational times. The work is illustrated by exact and approximate solutions for the mean, variance and the probability distribution itself. The usefulness of a white noise approximation is also assessed. Extensive numerical results are given which highlight the weaknesses and strengths of polynomial chaos. The general conclusion is that the method is promising but requires further detailed study by application to a practical problem in transport theory
Extension of spatiotemporal chaos in glow discharge-semiconductor systems
International Nuclear Information System (INIS)
Akhmet, Marat; Fen, Mehmet Onur; Rafatov, Ismail
2014-01-01
Generation of chaos in response systems is discovered numerically through specially designed unidirectional coupling of two glow discharge-semiconductor systems. By utilizing the auxiliary system approach, [H. D. I. Abarbanel, N. F. Rulkov, and M. M. Sushchik, Phys. Rev. E 53, 4528–4535 (1996)] it is verified that the phenomenon is not a chaos synchronization. Simulations demonstrate various aspects of the chaos appearance in both drive and response systems. Chaotic control is through the external circuit equation and governs the electrical potential on the boundary. The expandability of the theory to collectives of glow discharge systems is discussed, and this increases the potential of applications of the results. Moreover, the research completes the previous discussion of the chaos appearance in a glow discharge-semiconductor system [D. D. Šijačić U. Ebert, and I. Rafatov, Phys. Rev. E 70, 056220 (2004).
Hyperbolic Chaos A Physicist’s View
Kuznetsov, Sergey P
2012-01-01
"Hyperbolic Chaos: A Physicist’s View” presents recent progress on uniformly hyperbolic attractors in dynamical systems from a physical rather than mathematical perspective (e.g. the Plykin attractor, the Smale – Williams solenoid). The structurally stable attractors manifest strong stochastic properties, but are insensitive to variation of functions and parameters in the dynamical systems. Based on these characteristics of hyperbolic chaos, this monograph shows how to find hyperbolic chaotic attractors in physical systems and how to design a physical systems that possess hyperbolic chaos. This book is designed as a reference work for university professors and researchers in the fields of physics, mechanics, and engineering. Dr. Sergey P. Kuznetsov is a professor at the Department of Nonlinear Processes, Saratov State University, Russia.
Chaos synchronization of a chaotic system via nonlinear control
International Nuclear Information System (INIS)
Park, Ju H.
2005-01-01
In this letter, the problem of chaos synchronization of a chaotic system which is proposed by Lue et al. [Int J Bifurcat Chaos 2004;14:1507] is considered. A novel nonlinear controller is designed based on the Lyapunov stability theory. The proposed controller ensures that the states of the controlled chaotic slave system asymptotically synchronizes the states of the master system. A numerical example is given to illuminate the design procedure and advantage of the result derived
Transient chaos - a resolution of breakdown of quantum-classical correspondence in optomechanics.
Wang, Guanglei; Lai, Ying-Cheng; Grebogi, Celso
2016-10-17
Recently, the phenomenon of quantum-classical correspondence breakdown was uncovered in optomechanics, where in the classical regime the system exhibits chaos but in the corresponding quantum regime the motion is regular - there appears to be no signature of classical chaos whatsoever in the corresponding quantum system, generating a paradox. We find that transient chaos, besides being a physically meaningful phenomenon by itself, provides a resolution. Using the method of quantum state diffusion to simulate the system dynamics subject to continuous homodyne detection, we uncover transient chaos associated with quantum trajectories. The transient behavior is consistent with chaos in the classical limit, while the long term evolution of the quantum system is regular. Transient chaos thus serves as a bridge for the quantum-classical transition (QCT). Strikingly, as the system transitions from the quantum to the classical regime, the average chaotic transient lifetime increases dramatically (faster than the Ehrenfest time characterizing the QCT for isolated quantum systems). We develop a physical theory to explain the scaling law.
Early Exposure to Environmental Chaos and Children's Physical and Mental Health.
Coley, Rebekah Levine; Lynch, Alicia Doyle; Kull, Melissa
Environmental chaos has been proposed as a central influence impeding children's health and development, with the potential for particularly pernicious effects during the earliest years when children are most susceptible to environmental insults. This study evaluated a high-risk sample, following 495 low-income children living in poor urban neighborhoods from infancy to age 6. Longitudinal multilevel models tested the main tenets of the ecobiodevelopmental theory, finding that: (1) numerous distinct domains of environmental chaos were associated with children's physical and mental health outcomes, including housing disorder, neighborhood disorder, and relationship instability, with no significant results for residential instability; (2) different patterns emerged in relation to the timing of exposure to chaos, with more proximal exposure most strongly associated with children's functioning; and (3) the intensity of chaos also was a robust predictor of child functioning. Contrary to expectations, neither biological vulnerability (proxied through low birth weight status), maternal sensitivity, nor maternal distress moderated the role of chaos. Rather, maternal psychological distress functioned as a pathway through which environmental chaos was associated with children's functioning.
Wave chaos in quantum systems with point interaction
International Nuclear Information System (INIS)
Albeverio, S.; Seba, P.
1991-01-01
The authors study perturbations H of the quantized version H 0 of integrable Hamiltonian systems by point interactions. They relate the eigenvalues of H to the zeros of a certain meromorphic function ξ. Assuming the eigenvalues of H 0 are Poisson distributed, they get detailed information on the joint distribution of the zeros of ξ and give bounds on the probability density for the spacings of eigenvalues of H. Their results confirm the wave chaos phenomenon, as different from the quantum chaos phenomenon predicted by random matrix theory
Chaos control of chaotic dynamical systems using backstepping design
International Nuclear Information System (INIS)
Yassen, M.T.
2006-01-01
This work presents chaos control of chaotic dynamical systems by using backstepping design method. This technique is applied to achieve chaos control for each of the dynamical systems Lorenz, Chen and Lue systems. Based on Lyapunov stability theory, control laws are derived. We used the same technique to enable stabilization of chaotic motion to a steady state as well as tracking of any desired trajectory to be achieved in a systematic way. Numerical simulations are shown to verify the results
Whitesell, Corey J; Teti, Douglas M; Crosby, Brian; Kim, Bo-Ram
2015-04-01
Household chaos is a construct often overlooked in studies of human development, despite its theoretical links with the integrity of individual well-being, family processes, and child development. The present longitudinal study examined relations between household chaos and well-established correlates of chaos (sociodemographic risk, major life events, and personal distress) and several constructs that, to date, are theoretically linked with chaos but never before assessed as correlates (quality of coparenting and emotional availability with infants at bedtime). In addressing this aim, we introduce a new measure of household chaos (the Descriptive In-home Survey of Chaos--Observer ReporteD, or DISCORD), wholly reliant on independent observer report, which draws from household chaos theory and prior empirical work but extends the measurement of chaos to include information about families' compliance with a home visiting protocol. Household chaos was significantly associated with socioeconomic risk, negative life events, less favorable coparenting, and less emotionally available bedtime parenting, but not with personal distress. These findings emphasize the need to examine household chaos as a direct and indirect influence on child and family outcomes, as a moderator of intervention attempts to improving parenting and child development, and as a target of intervention in its own right. (c) 2015 APA, all rights reserved).
An exploration of dynamical systems and chaos
Argyris, John H; Haase, Maria; Friedrich, Rudolf
2015-01-01
This book is conceived as a comprehensive and detailed text-book on non-linear dynamical systems with particular emphasis on the exploration of chaotic phenomena. The self-contained introductory presentation is addressed both to those who wish to study the physics of chaotic systems and non-linear dynamics intensively as well as those who are curious to learn more about the fascinating world of chaotic phenomena. Basic concepts like Poincaré section, iterated mappings, Hamiltonian chaos and KAM theory, strange attractors, fractal dimensions, Lyapunov exponents, bifurcation theory, self-similarity and renormalisation and transitions to chaos are thoroughly explained. To facilitate comprehension, mathematical concepts and tools are introduced in short sub-sections. The text is supported by numerous computer experiments and a multitude of graphical illustrations and colour plates emphasising the geometrical and topological characteristics of the underlying dynamics. This volume is a completely revised and enlar...
The Limits of the Newtonian Forecast and the search of order in the chaos
Directory of Open Access Journals (Sweden)
N. Sánchez–Santillán
2008-04-01
Full Text Available Newtonian deterministic mechanichs can only describe and predict the behavior of simple natural systems with few components, which represent approximately 10% of those conforming the universal reality known until now. The remaining 90%, whose complexity and degree of uncertainty make them practically inaccessible to this approach, require a new holistic or total vision, with an approach that includes concepts of Newton's and Descartes's classical mechanics, as much as those emanated from the indeterministic stream, such as nonlinearity and aleatory sequences, calculus of probability and statistics, chaos and order, exponential instability, quantum Theory, attractors and fractals, and information theory.
Chaos, strange attractors, and fractal basin boundaries
International Nuclear Information System (INIS)
Grebogi, C.
1989-01-01
Even simple mathematical models of physical systems are often observed to exhibit rather complex time evolution. Upon observation, one often has the feeling that such complex time evolutions could, for most practical purposes, be best characterized by statistical properties rather than by detailed knowledge of the exact process. In such situations, the time evolution is often labeled chaotic or turbulent. The study of chaotic dynamics has recently undergone explosive growth. Motivation for this comes partly from the fact that chaotic dynamics is being found to be of fundamental importance in many branches of science and engineering. Examples illustrating the wide-ranging applications of chaotic dynamics to scientific and engineering problems are the following: fluid dynamics, biology, ecology, meteorology, optics, electronics, mechanical engineerings, physiology, economics, chemistry, accelerator technology, thermonuclear fusion, celestial mechanics, and oceanography. The common element in all of the above topics is that they involve nonlinearity in some way. Indeed chaos is expected to be common whenever nonlinearity plays a role. Since nonlinearity is inherent in so much of science and engineering, an understanding of chaos is essential. Given the varied nature of applications where chaos is important, it is natural that researchers in a broad range of fields have become interested in and have contributed to recent developments in chaos
Chaos-pass filtering in injection-locked semiconductor lasers
International Nuclear Information System (INIS)
Murakami, Atsushi; Shore, K. Alan
2005-01-01
Chaos-pass filtering (CPF) of semiconductor lasers has been studied theoretically. CPF is a phenomenon which occurs in laser chaos synchronization by injection locking and is a fundamental technique for the extraction of messages at the receiver laser in chaotic communications systems. We employ a simple theory based on driven damped oscillators to clarify the physical background of CPF. The receiver laser is optically driven by injection from the transmitter laser. We have numerically investigated the response characteristics of the receiver when it is driven by periodic (message) and chaotic (carrier) signals. It is thereby revealed that the response of the receiver laser in the two cases is quite different. For the periodic drive, the receiver exhibits a response depending on the signal frequency, while the chaotic drive provides a frequency-independent synchronous response to the receiver laser. We verify that the periodic and chaotic drives occur independently in the CPF response, and, consequently, CPF can be clearly understood in the difference of the two drives. Message extraction using CPF is also examined, and the validity of our theoretical explanation for the physical mechanism underlying CPF is thus verified
Advances in complexity of beam halo-chaos and its control methods for beam transport networks
International Nuclear Information System (INIS)
Fang Jinqing
2004-11-01
The complexity theory of beam halo-chaos in beam transport networks and its control methods for a new subject of high-tech field is discussed. It is pointed that in recent years, there has been growing interest in proton beams of high power linear accelerator due to its attractive features in possible breakthrough applications in national defense and industry. In particular, high-current accelerator driven clean activity nuclear power systems for various applications as energy resources has been one of the most focusing issues in the current research, because it provides a safer, cleaner and cheaper nuclear energy resource. However, halo-chaos in high-current beam transport networks become a key concerned issue because it can generate excessive radioactivity therefore significantly limits its applications. It is very important to study the complexity properties of beam halo-chaos and to understand the basic physical mechanisms for halo chaos formation as well as to develop effective control methods for its suppression. These are very challenging subjects for the current research. The main research advances in the subjects, including experimental investigation and the oretical research, especially some very efficient control methods developed through many years of efforts of authors are reviewed and summarized. Finally, some research outlooks are given. (author)
Gilstrap, Donald L.
2013-01-01
In addition to qualitative methods presented in chaos and complexity theories in educational research, this article addresses quantitative methods that may show potential for future research studies. Although much in the social and behavioral sciences literature has focused on computer simulations, this article explores current chaos and…
Controlling chaos in discontinuous dynamical systems
International Nuclear Information System (INIS)
Danca, Marius-F.
2004-01-01
In this paper we consider the possibility to implement the technique of changes in the system variables to control the chaos introduced by Gueemez and Matias for continuous dynamical systems to a class of discontinuous dynamical systems. The approach is realized via differential inclusions following the Filippov theory. Three practical examples are considered
Constrained Quantum Mechanics: Chaos in Non-Planar Billiards
Salazar, R.; Tellez, G.
2012-01-01
We illustrate some of the techniques to identify chaos signatures at the quantum level using as guiding examples some systems where a particle is constrained to move on a radial symmetric, but non-planar, surface. In particular, two systems are studied: the case of a cone with an arbitrary contour or "dunce hat billiard" and the rectangular…
High-dimensional chaos from self-sustained collisions of solitons
Energy Technology Data Exchange (ETDEWEB)
Yildirim, O. Ozgur, E-mail: donhee@seas.harvard.edu, E-mail: oozgury@gmail.com [Cavium, Inc., 600 Nickerson Rd., Marlborough, Massachusetts 01752 (United States); Ham, Donhee, E-mail: donhee@seas.harvard.edu, E-mail: oozgury@gmail.com [Harvard University, 33 Oxford St., Cambridge, Massachusetts 02138 (United States)
2014-06-16
We experimentally demonstrate chaos generation based on collisions of electrical solitons on a nonlinear transmission line. The nonlinear line creates solitons, and an amplifier connected to it provides gain to these solitons for their self-excitation and self-sustenance. Critically, the amplifier also provides a mechanism to enable and intensify collisions among solitons. These collisional interactions are of intrinsically nonlinear nature, modulating the phase and amplitude of solitons, thus causing chaos. This chaos generated by the exploitation of the nonlinear wave phenomena is inherently high-dimensional, which we also demonstrate.
Chaos and order in models of black hole pairs
International Nuclear Information System (INIS)
Levin, Janna
2006-01-01
Chaos in the orbits of black hole pairs has by now been confirmed by several independent groups. While the chaotic behavior of binary black hole orbits is no longer argued, it remains difficult to quantify the importance of chaos to the evolutionary dynamics of a pair of comparable mass black holes. None of our existing approximations are robust enough to offer convincing quantitative conclusions in the most highly nonlinear regime. It is intriguing to note that, in three different approximations to a black hole pair built of a spinning black hole and a nonspinning companion, two approximations exhibit chaos and one approximation does not. The fully relativistic scenario of a spinning test mass around a Schwarzschild black hole shows chaos, as does the post-Newtonian Lagrangian approximation. However, the approximately equivalent post-Newtonian Hamiltonian approximation does not show chaos when only one body spins. It is well known in dynamical systems theory that one system can be regular while an approximately related system is chaotic, so there is no formal conflict. However, the physical question remains: Is there chaos for comparable mass binaries when only one object spins? We are unable to answer this question given the poor convergence of the post-Newtonian approximation to the fully relativistic system. A resolution awaits better approximations that can be trusted in the highly nonlinear regime
Mathematics of statistical mechanics and the chaos theory
International Nuclear Information System (INIS)
Llave, R. de la; Haro, A.
2000-01-01
Statistical mechanics requires a language that unifies probabilistic and deterministic description of physical systems. We describe briefly some of the mathematical ideas needed for this unification. These ideas have also proved important in the study of chaotic systems. (Author) 17 refs
Preface to the Focus Issue: Chaos Detection Methods and Predictability
International Nuclear Information System (INIS)
Gottwald, Georg A.; Skokos, Charalampos
2014-01-01
This Focus Issue presents a collection of papers originating from the workshop Methods of Chaos Detection and Predictability: Theory and Applications held at the Max Planck Institute for the Physics of Complex Systems in Dresden, June 17–21, 2013. The main aim of this interdisciplinary workshop was to review comprehensively the theory and numerical implementation of the existing methods of chaos detection and predictability, as well as to report recent applications of these techniques to different scientific fields. The collection of twelve papers in this Focus Issue represents the wide range of applications, spanning mathematics, physics, astronomy, particle accelerator physics, meteorology and medical research. This Preface surveys the papers of this Issue
Preface to the Focus Issue: chaos detection methods and predictability.
Gottwald, Georg A; Skokos, Charalampos
2014-06-01
This Focus Issue presents a collection of papers originating from the workshop Methods of Chaos Detection and Predictability: Theory and Applications held at the Max Planck Institute for the Physics of Complex Systems in Dresden, June 17-21, 2013. The main aim of this interdisciplinary workshop was to review comprehensively the theory and numerical implementation of the existing methods of chaos detection and predictability, as well as to report recent applications of these techniques to different scientific fields. The collection of twelve papers in this Focus Issue represents the wide range of applications, spanning mathematics, physics, astronomy, particle accelerator physics, meteorology and medical research. This Preface surveys the papers of this Issue.
Chaos and Integrability in Ideal Body-Fluid Interactions
DEFF Research Database (Denmark)
Pedersen, Johan Rønby
2011-01-01
by generating Poincare sections from numerically obtained solutions. By identifying the chaotic solutions and studying the body and vortex orbits, we obtain a better mechanistic understanding of the causes of chaotic behavior. As is well-known from dynamical system theory, the chaos can often be traced back...... of relative equilibria, their stability, and the qualitatively dierent kinds of motion is studied analytically and numerically. We then perform small parametric perturbations destroying the symmetry or conservation law that makes the system integrable. The emergence of chaos in the system is diagnosed...... contains both regular and chaotic regions, and may be understood from KAM theory. We also discover two separate chaotic regimes in the interaction of a body and one point vortex when the body is either noncircular or has asymmetric internal mass distribution. For one of these chaotic regimes the eect...
Invoking the muse: Dada's chaos.
Rosen, Diane
2014-07-01
Dada, a self-proclaimed (anti)art (non)movement, took shape in 1916 among a group of writers and artists who rejected the traditions of a stagnating bourgeoisie. Instead, they adopted means of creative expression that embraced chaos, stoked instability and undermined logic, an outburst that overturned centuries of classical and Romantic aesthetics. Paradoxically, this insistence on disorder foreshadowed a new order in understanding creativity. Nearly one hundred years later, Nonlinear Dynamical Systems theory (NDS) gives renewed currency to Dada's visionary perspective on chance, chaos and creative cognition. This paper explores commonalities between NDS-theory and this early precursor of the nonlinear paradigm, suggesting that their conceptual synergy illuminates what it means to 'be creative' beyond the disciplinary boundaries of either. Key features are discussed within a 5P model of creativity based on Rhodes' 4P framework (Person, Process, Press, Product), to which I add Participant-Viewer for the interactivity of observer-observed. Grounded in my own art practice, several techniques are then put forward as non-methodical methods that invoke creative border zones, those regions where Dada's chance and design are wedded in a dialectical tension of opposites.
Chaos in Practice: Techniques for Career Counsellors
Pryor, Robert G. L.; Bright, Jim
2005-01-01
The chaos theory of careers emphasises continual change, the centrality and importance of chance events, the potential of minor events to have disproportionately large impacts on subsequent events, and the capacity for dramatic phase shifts in career behaviour. This approach challenges traditional approaches to career counselling, assumptions…
Anticontrol of chaos in continuous-time systems via time-delay feedback.
Wang, Xiao Fan; Chen, Guanrong; Yu, Xinghuo
2000-12-01
In this paper, a systematic design approach based on time-delay feedback is developed for anticontrol of chaos in a continuous-time system. This anticontrol method can drive a finite-dimensional, continuous-time, autonomous system from nonchaotic to chaotic, and can also enhance the existing chaos of an originally chaotic system. Asymptotic analysis is used to establish an approximate relationship between a time-delay differential equation and a discrete map. Anticontrol of chaos is then accomplished based on this relationship and the differential-geometry control theory. Several examples are given to verify the effectiveness of the methodology and to illustrate the systematic design procedure. (c) 2000 American Institute of Physics.
Melnikov's vector - a 'measure of chaos'
International Nuclear Information System (INIS)
Haidegger, W.
1990-01-01
In this paper a method of global perturbation theory, the method of Melnikov, is introduced as a way of detecting Smale horseshoe chaos near homoclinic and heteroclinic orbits. Special emphasis is put on the point that Melnikov's method is of great practical value, as it yields computable, often even analytically solvable expressions. (Author) 18 refs
Adventures in order and chaos a scientific autobiography
Contopoulos, George
2004-01-01
The field of Order and Chaos had a remarkable expansion in the last 50 years. The main reason was the use of computers, and the development of new theoretical methods that we call now 'the theory of chaos'. The author describes this fascinating period in a relaxed and sometimes humorous autobiographical way. He relates his interactions with many people in dynamical astronomy and he quotes several anecdotes from these interactions. He refers also to his experiences when he served in various international positions, such as general secretary of the IAU and chairman of the journal Astronomy and A
Early Exposure to Environmental Chaos and Children’s Physical and Mental Health
Coley, Rebekah Levine; Lynch, Alicia Doyle; Kull, Melissa
2015-01-01
Environmental chaos has been proposed as a central influence impeding children’s health and development, with the potential for particularly pernicious effects during the earliest years when children are most susceptible to environmental insults. This study evaluated a high-risk sample, following 495 low-income children living in poor urban neighborhoods from infancy to age 6. Longitudinal multilevel models tested the main tenets of the ecobiodevelopmental theory, finding that: (1) numerous distinct domains of environmental chaos were associated with children’s physical and mental health outcomes, including housing disorder, neighborhood disorder, and relationship instability, with no significant results for residential instability; (2) different patterns emerged in relation to the timing of exposure to chaos, with more proximal exposure most strongly associated with children’s functioning; and (3) the intensity of chaos also was a robust predictor of child functioning. Contrary to expectations, neither biological vulnerability (proxied through low birth weight status), maternal sensitivity, nor maternal distress moderated the role of chaos. Rather, maternal psychological distress functioned as a pathway through which environmental chaos was associated with children’s functioning. PMID:25844016
Transient chaos - a resolution of breakdown of quantum-classical correspondence in optomechanics
Wang, Guanglei; Lai, Ying-Cheng; Grebogi, Celso
2016-01-01
Recently, the phenomenon of quantum-classical correspondence breakdown was uncovered in optomechanics, where in the classical regime the system exhibits chaos but in the corresponding quantum regime the motion is regular - there appears to be no signature of classical chaos whatsoever in the corresponding quantum system, generating a paradox. We find that transient chaos, besides being a physically meaningful phenomenon by itself, provides a resolution. Using the method of quantum state diffusion to simulate the system dynamics subject to continuous homodyne detection, we uncover transient chaos associated with quantum trajectories. The transient behavior is consistent with chaos in the classical limit, while the long term evolution of the quantum system is regular. Transient chaos thus serves as a bridge for the quantum-classical transition (QCT). Strikingly, as the system transitions from the quantum to the classical regime, the average chaotic transient lifetime increases dramatically (faster than the Ehrenfest time characterizing the QCT for isolated quantum systems). We develop a physical theory to explain the scaling law. PMID:27748418
Quantum chaos: entropy signatures
International Nuclear Information System (INIS)
Miller, P.A.; Sarkar, S.; Zarum, R.
1998-01-01
A definition of quantum chaos is given in terms of entropy production rates for a quantum system coupled weakly to a reservoir. This allows the treatment of classical and quantum chaos on the same footing. In the quantum theory the entropy considered is the von Neumann entropy and in classical systems it is the Gibbs entropy. The rate of change of the coarse-grained Gibbs entropy of the classical system with time is given by the Kolmogorov-Sinai (KS) entropy. The relation between KS entropy and the rate of change of von Neumann entropy is investigated for the kicked rotator. For a system which is classically chaotic there is a linear relationship between these two entropies. Moreover it is possible to construct contour plots for the local KS entropy and compare it with the corresponding plots for the rate of change of von Neumann entropy. The quantitative and qualitative similarities of these plots are discussed for the standard map (kicked rotor) and the generalised cat maps. (author)
Specifying the Links between Household Chaos and Preschool Children's Development
Martin, Anne; Razza, Rachel A.; Brooks-Gunn, Jeanne
2012-01-01
Household chaos has been linked to poorer cognitive, behavioural, and self-regulatory outcomes in young children, but the mechanisms responsible remain largely unknown. Using a diverse sample of families in Chicago, the present study tests for the independent contributions made by five indicators of household chaos: noise, crowding, family…
Effect of correction of aberration dynamics on chaos in human ocular accommodation.
Hampson, Karen M; Cufflin, Matthew P; Mallen, Edward A H
2013-11-15
We used adaptive optics to determine the effect of monochromatic aberration dynamics on the level of chaos in the accommodation control system. Four participants viewed a stationary target while the dynamics of their aberrations were either left uncorrected, defocus was corrected, or all aberrations except defocus were corrected. Chaos theory analysis was used to discern changes in the accommodative microfluctuations. We found a statistically significant reduction in the chaotic nature of the accommodation microfluctuations during correction of defocus, but not when all aberrations except defocus were corrected. The Lyapunov exponent decreased from 0.71 ± 0.07 D/s (baseline) to 0.55 ± 0.03 D/s (correction of defocus fluctuations). As the reduction of chaos in physiological signals is indicative of stress to the system, the results indicate that for the participants included in this study, fluctuations in defocus have a more profound effect than those of the other aberrations. There were no changes in the power spectrum between experimental conditions. Hence chaos theory analysis is a more subtle marker of changes in the accommodation control system and will be of value in the study of myopia onset and progression.
The Capabilities of Chaos and Complexity
Directory of Open Access Journals (Sweden)
David L. Abel
2009-01-01
Full Text Available To what degree could chaos and complexity have organized a Peptide or RNA World of crude yet necessarily integrated protometabolism? How far could such protolife evolve in the absence of a heritable linear digital symbol system that could mutate, instruct, regulate, optimize and maintain metabolic homeostasis? To address these questions, chaos, complexity, self-ordered states, and organization must all be carefully defined and distinguished. In addition their cause-and-effect relationships and mechanisms of action must be delineated. Are there any formal (non physical, abstract, conceptual, algorithmic components to chaos, complexity, self-ordering and organization, or are they entirely physicodynamic (physical, mass/energy interaction alone? Chaos and complexity can produce some fascinating self-ordered phenomena. But can spontaneous chaos and complexity steer events and processes toward pragmatic benefit, select function over non function, optimize algorithms, integrate circuits, produce computational halting, organize processes into formal systems, control and regulate existing systems toward greater efficiency? The question is pursued of whether there might be some yet-to-be discovered new law of biology that will elucidate the derivation of prescriptive information and control. Ã¢Â€ÂœSystemÃ¢Â€Â will be rigorously defined. Can a low-informational rapid succession of PrigogineÃ¢Â€Â™s dissipative structures self-order into bona fide organization?
'Chaos is come again': Nothingness in Shakespeare's metadramatic time and space
Oswald, John David
The extraordinary advances of twentieth-century science, which overlay, and in some cases overturn, the Newtonian precepts upon which physics was founded, have captured a share of the popular imagination. Quantum mechanics, relativity theory, and chaos theory are the stuff of science fact and science fiction, of technological innovation and artistic invention. Intricate ``fractal'' images adorn poster art, and science fiction fantasy (long a niche market for popular fiction) is the genre of the blockbuster film and the television franchise. Astronomers and physicists are writing pop-science bestsellers for the layman, making theory accessible to those who cannot do the math. This work focuses on Shakespearean notions of time and space in selected metadramatic passages from three plays that feature embattled monarchs: Richard II, King Lear, and The Winter's Tale. Shakespeare's employment of metaphors that are also ``cardinal metaphors'' of science is examined to determine how his dramatic works fare under a post-deterministic paradigm. A chaos-theory model is advanced for theatrical performance, and analogies are drawn from scientific theory to discuss dramatic language and action (e.g., ``nothingness'' in different contexts is compared variously with black holes, dark matter, vacuum genesis in a spatial void roiling with virtual particles, the empty space within matter, etc.). Of primary importance are the notions of quantum observership (the impossibility of separating observation from participation in scientific experimentation) and complementarity (Bohr's theory to account for the dual behavior of radiation as both waves and particles). Shakespeare's persistent metadramatic emphasis is seen as an effort to draw his audience (observers) into conscious participation in the imaginative act of bringing his plays into being. Complementarity relates to the promotion of multiple perspectives in all three plays and to the dramaturgical structure of The Winter's Tale.
International Nuclear Information System (INIS)
Zhao Yiguang
1991-01-01
The method of obtaining self-consistent solutions of the field equation and the rate equations of photon density and carrier concentration has been used to study frequecny locking, quasiperiodicity, subharmonic bifurcations and chaos in high frequency modulated stripe geometry DH semiconductor lasers. The results show that the chaotic behavior arises in self-pulsing stripe geometry semiconductor lasers. The route to chaos is not period-double, but quasiperiodicity to chaos. All of the results agree with the experiments. Some obscure points in previous theory about chaos have been cleared up
Schmid, Gary Bruno
Underlying idea: A new hypothesis about how the mental state of psychosis may arise in the brain as a "linear" information processing pathology is briefly introduced. This hypothesis is proposed in the context of a complementary approach to psychiatry founded in the logical paradigm of chaos theory. To best understand the relation between chaos theory and psychiatry, the semantic structure of chaos theory is analyzed with the help of six general, and six specific, fundamental characteristics which can be directly inferred from empirical observations on chaotic systems. This enables a mathematically and physically stringent perspective on psychological phenomena which until now could only be grasped intuitively: Chaotic systems are in a general sense dynamic, intrinsically coherent, deterministic, recursive, reactive and structured: in a specific sense, self-organizing, unpredictable, nonreproducible, triadic, unstable and self-similar. To a great extent, certain concepts of chaos theory can be associated with corresponding concepts in psychiatry, psychology and psychotherapy, thus enabling an understanding of the human psyche in general as a (fractal) chaotic system and an explanation of certain mental developments, such as the course of schizophrenia, the course of psychosis and psychotherapy as chaotic processes. General overview: A short comparison and contrast of classical and chaotic physical theory leads to four postulates and one hypothesis motivating a new, dynamic, nonlinear approach to classical, causal psychiatry: Process-Oriented PSYchiatry or "POPSY", for short. Four aspects of the relationship between chaos theory and POPSY are discussed: (1) The first of these, namely, Identification of Chaos / Picture of Illness involves a definition of Chaos / Psychosis and a discussion of the 6 logical characteristics of each. This leads to the concept of dynamical disease (definition, characteristics and examples) and to the idea of "psychological disturbance as
Origin of chaos near three-dimensional quantum vortices: A general Bohmian theory
Tzemos, Athanasios C.; Efthymiopoulos, Christos; Contopoulos, George
2018-04-01
We provide a general theory for the structure of the quantum flow near three-dimensional (3D) nodal lines, i.e., one-dimensional loci where the 3D wave function becomes equal to zero. In suitably defined coordinates (comoving with the nodal line) the generic structure of the flow implies the formation of 3D quantum vortices. We show that such vortices are accompanied by nearby invariant lines of the comoving quantum flow, called X lines, which are normally hyperbolic. Furthermore, the stable and unstable manifolds of the X lines produce chaotic scatterings of nearby quantum (Bohmian) trajectories, thus inducing an intricate form of the quantum current in the neighborhood of each 3D quantum vortex. Generic formulas describing the structure around 3D quantum vortices are provided, applicable to an arbitrary choice of 3D wave function. We also give specific numerical examples as well as a discussion of the physical consequences of chaos near 3D quantum vortices.
Direct generation of all-optical random numbers from optical pulse amplitude chaos.
Li, Pu; Wang, Yun-Cai; Wang, An-Bang; Yang, Ling-Zhen; Zhang, Ming-Jiang; Zhang, Jian-Zhong
2012-02-13
We propose and theoretically demonstrate an all-optical method for directly generating all-optical random numbers from pulse amplitude chaos produced by a mode-locked fiber ring laser. Under an appropriate pump intensity, the mode-locked laser can experience a quasi-periodic route to chaos. Such a chaos consists of a stream of pulses with a fixed repetition frequency but random intensities. In this method, we do not require sampling procedure and external triggered clocks but directly quantize the chaotic pulses stream into random number sequence via an all-optical flip-flop. Moreover, our simulation results show that the pulse amplitude chaos has no periodicity and possesses a highly symmetric distribution of amplitude. Thus, in theory, the obtained random number sequence without post-processing has a high-quality randomness verified by industry-standard statistical tests.
Bonilla, L L; Carretero, M; Segura, A
2017-12-01
When quantized, traces of classically chaotic single-particle systems include eigenvalue statistics and scars in eigenfuntions. Since 2001, many theoretical and experimental works have argued that classically chaotic single-electron dynamics influences and controls collective electron transport. For transport in semiconductor superlattices under tilted magnetic and electric fields, these theories rely on a reduction to a one-dimensional self-consistent drift model. A two-dimensional theory based on self-consistent Boltzmann transport does not support that single-electron chaos influences collective transport. This theory agrees with existing experimental evidence of current self-oscillations, predicts spontaneous collective chaos via a period doubling scenario, and could be tested unambiguously by measuring the electric potential inside the superlattice under a tilted magnetic field.
Bonilla, L. L.; Carretero, M.; Segura, A.
2017-12-01
When quantized, traces of classically chaotic single-particle systems include eigenvalue statistics and scars in eigenfuntions. Since 2001, many theoretical and experimental works have argued that classically chaotic single-electron dynamics influences and controls collective electron transport. For transport in semiconductor superlattices under tilted magnetic and electric fields, these theories rely on a reduction to a one-dimensional self-consistent drift model. A two-dimensional theory based on self-consistent Boltzmann transport does not support that single-electron chaos influences collective transport. This theory agrees with existing experimental evidence of current self-oscillations, predicts spontaneous collective chaos via a period doubling scenario, and could be tested unambiguously by measuring the electric potential inside the superlattice under a tilted magnetic field.
Classical and quantum chaos in a circular billiard with a straight cut
International Nuclear Information System (INIS)
Ree, S.; Reichl, L.E.
1999-01-01
We study classical and quantum dynamics of a particle in a circular billiard with a straight cut. Classically, this system can be integrable, nonintegrable with soft chaos, or nonintegrable with hard chaos as we vary the size of the cut. We plot Poincaracute e surfaces of section to study chaos. Quantum mechanically, we look at Husimi plots, and also use the quantum web, the technique primarily used in spin systems so far, to try to see differences in quantum manifestations of soft and hard chaos. copyright 1999 The American Physical Society
Bifurcation and chaos in neural excitable system
International Nuclear Information System (INIS)
Jing Zhujun; Yang Jianping; Feng Wei
2006-01-01
In this paper, we investigate the dynamical behaviors of neural excitable system without periodic external current (proposed by Chialvo [Generic excitable dynamics on a two-dimensional map. Chaos, Solitons and Fractals 1995;5(3-4):461-79] and with periodic external current as system's parameters vary. The existence and stability of three fixed points, bifurcation of fixed points, the conditions of existences of fold bifurcation, flip bifurcation and Hopf bifurcation are derived by using bifurcation theory and center manifold theorem. The chaotic existence in the sense of Marotto's definition of chaos is proved. We then give the numerical simulated results (using bifurcation diagrams, computations of Maximum Lyapunov exponent and phase portraits), which not only show the consistence with the analytic results but also display new and interesting dynamical behaviors, including the complete period-doubling and inverse period-doubling bifurcation, symmetry period-doubling bifurcations of period-3 orbit, simultaneous occurrence of two different routes (invariant cycle and period-doubling bifurcations) to chaos for a given bifurcation parameter, sudden disappearance of chaos at one critical point, a great abundance of period windows (period 2 to 10, 12, 19, 20 orbits, and so on) in transient chaotic regions with interior crises, strange chaotic attractors and strange non-chaotic attractor. In particular, the parameter k plays a important role in the system, which can leave the chaotic behavior or the quasi-periodic behavior to period-1 orbit as k varies, and it can be considered as an control strategy of chaos by adjusting the parameter k. Combining the existing results in [Generic excitable dynamics on a two-dimensional map. Chaos, Solitons and Fractals 1995;5(3-4):461-79] with the new results reported in this paper, a more complete description of the system is now obtained
Huwe, Terence K.
2009-01-01
"Embracing the chaos" is an ongoing challenge for librarians. Embracing the chaos means librarians must have a plan for responding to the flood of new products, widgets, web tools, and gizmos that students use daily. In this article, the author argues that library instruction and access services have been grappling with that chaos with…
Poincaré chaos and unpredictable functions
Akhmet, Marat; Fen, Mehmet Onur
2017-07-01
The results of this study are continuation of the research of Poincaré chaos initiated in the papers (M. Akhmet and M.O. Fen, Commun Nonlinear Sci Numer Simulat 40 (2016) 1-5; M. Akhmet and M.O. Fen, Turk J Math, doi:10.3906/mat-1603-51, in press). We focus on the construction of an unpredictable function, continuous on the real axis. As auxiliary results, unpredictable orbits for the symbolic dynamics and the logistic map are obtained. By shaping the unpredictable function as well as Poisson function we have performed the first step in the development of the theory of unpredictable solutions for differential and discrete equations. The results are preliminary ones for deep analysis of chaos existence in differential and hybrid systems. Illustrative examples concerning unpredictable solutions of differential equations are provided.
Chaos in neurons and its application: perspective of chaos engineering.
Hirata, Yoshito; Oku, Makito; Aihara, Kazuyuki
2012-12-01
We review our recent work on chaos in neurons and its application to neural networks from perspective of chaos engineering. Especially, we analyze a dataset of a squid giant axon by newly combining our previous work of identifying Devaney's chaos with surrogate data analysis, and show that an axon can behave chaotically. Based on this knowledge, we use a chaotic neuron model to investigate possible information processing in the brain.
Chaos and The Changing Nature of Science and Medicine. Proceedings
International Nuclear Information System (INIS)
Herbert, D.E.; Croft, P.; Silver, D.S.; Williams, S.G.; Woodall, M.
1996-01-01
These proceedings represent the lectures given at the workshop on chaos and the changing nature of science and medicine. The workshop was sponsored by the University of South Alabama and the American Association of Physicists in Medicine. The topics discussed covered nonlinear dynamical systems, complexity theory, fractals, chaos in biology and medicine and in fluid dynamics. Applications of chaotic dynamics in climatology were also discussed. There were 8 lectures at the workshop and all 8 have been abstracted for the Energy Science and Technology database
Chaos synchronization of nonlinear Bloch equations
International Nuclear Information System (INIS)
Park, Ju H.
2006-01-01
In this paper, the problem of chaos synchronization of Bloch equations is considered. A novel nonlinear controller is designed based on the Lyapunov stability theory. The proposed controller ensures that the states of the controlled chaotic slave system asymptotically synchronizes the states of the master system. A numerical example is given to illuminate the design procedure and advantage of the result derived
DEFF Research Database (Denmark)
Rennison, Betina Wolfgang
of management differently. In this chaos of codes the managerial challenge is to take a second order position in order to strategically manage the communication that manages management itself. Key words: Management; personnel management; human-relations; pay-system; communication; system-theory; discursive...... of Denmark (called New Wage), this paper theorizes this complexity in terms of Niklas Luhmann's systems theory. It identifies four wholly different `codes' of communication: legal, economic, pedagogical and intimate. Each of them shapes the phenomena of `pay', the construal of the employee and the form...
Quantum signature of chaos and thermalization in the kicked Dicke model
Ray, S.; Ghosh, A.; Sinha, S.
2016-09-01
We study the quantum dynamics of the kicked Dicke model (KDM) in terms of the Floquet operator, and we analyze the connection between chaos and thermalization in this context. The Hamiltonian map is constructed by suitably taking the classical limit of the Heisenberg equation of motion to study the corresponding phase-space dynamics, which shows a crossover from regular to chaotic motion by tuning the kicking strength. The fixed-point analysis and calculation of the Lyapunov exponent (LE) provide us with a complete picture of the onset of chaos in phase-space dynamics. We carry out a spectral analysis of the Floquet operator, which includes a calculation of the quasienergy spacing distribution and structural entropy to show the correspondence to the random matrix theory in the chaotic regime. Finally, we analyze the thermodynamics and statistical properties of the bosonic sector as well as the spin sector, and we discuss how such a periodically kicked system relaxes to a thermalized state in accordance with the laws of statistical mechanics.
Quantifying chaos for ecological stoichiometry.
Duarte, Jorge; Januário, Cristina; Martins, Nuno; Sardanyés, Josep
2010-09-01
The theory of ecological stoichiometry considers ecological interactions among species with different chemical compositions. Both experimental and theoretical investigations have shown the importance of species composition in the outcome of the population dynamics. A recent study of a theoretical three-species food chain model considering stoichiometry [B. Deng and I. Loladze, Chaos 17, 033108 (2007)] shows that coexistence between two consumers predating on the same prey is possible via chaos. In this work we study the topological and dynamical measures of the chaotic attractors found in such a model under ecological relevant parameters. By using the theory of symbolic dynamics, we first compute the topological entropy associated with unimodal Poincaré return maps obtained by Deng and Loladze from a dimension reduction. With this measure we numerically prove chaotic competitive coexistence, which is characterized by positive topological entropy and positive Lyapunov exponents, achieved when the first predator reduces its maximum growth rate, as happens at increasing δ1. However, for higher values of δ1 the dynamics become again stable due to an asymmetric bubble-like bifurcation scenario. We also show that a decrease in the efficiency of the predator sensitive to prey's quality (increasing parameter ζ) stabilizes the dynamics. Finally, we estimate the fractal dimension of the chaotic attractors for the stoichiometric ecological model.
Chaos Concepts, Control and Constructive Use
Bolotin, Yurii; Yanovsky, Vladimir
2009-01-01
The study of chaotic behaviour in nonlinear, dynamical systems is now a well established research domain with ramifications into all fields of sciences, spanning a vast range of applications, from celestial mechanics, via climate change, to the functioning of brownian motors in cells. A more recent discovery is that chaos can be controlled and, under appropriate conditions, can actually be constructive in the sense of becoming a control parameter itself for the system under investigation, stochastic resonance being a prime example. The present work is putting emphasis on the latter aspects, and after recalling the paradigm changes introduced by the concept of chaos, leads the reader skillfully through the basics of chaos control by detailing relevant algorithms for both Hamiltonian and dissipative systems amongst others. The main part of the book is then devoted to the issue of synchronization in chaotic systems, an introduction to stochastic resonance and a survey of ratchet models. This short and concise pr...
In the Wake of Chaos Unpredictable Order in Dynamical Systems
Kellert, Stephen H
1993-01-01
Chaos theory has captured scientific and popular attention. What began as the discovery of randomness in simple physical systems has become a widespread fascination with "chaotic" models of everything from business cycles to brainwaves to heart attacks. But what exactly does this explosion of new research into chaotic phenomena mean for our understanding of the world? In this timely book, Stephen Kellert takes the first sustained look at the broad intellectual and philosophical questions raised by recent advances in chaos theory—its implications for science as a source of knowledge a
Martinez-Lavin, Manuel; Infante, Oscar; Lerma, Claudia
2008-02-01
Modern clinicians are often frustrated by their inability to understand fibromyalgia and similar maladies since these illnesses cannot be explained by the prevailing linear-reductionist medical paradigm. This article proposes that new concepts derived from the Complexity Theory may help understand the pathogenesis of fibromyalgia, chronic fatigue syndrome, and Gulf War syndrome. This hypothesis is based on the recent recognition of chaos fractals and complex systems in human physiology. These nonlinear dynamics concepts offer a different perspective to the notion of homeostasis and disease. They propose that the essence of disease is dysfunction and not structural damage. Studies using novel nonlinear instruments have shown that fibromyalgia and similar maladies may be caused by the degraded performance of our main complex adaptive system. This dysfunction explains the multifaceted manifestations of these entities. To understand and alleviate the suffering associated with these complex illnesses, a paradigm shift from reductionism to holism based on the Complexity Theory is suggested. This shift perceives health as resilient adaptation and some chronic illnesses as rigid dysfunction.
Time reversibility, computer simulation, algorithms, chaos
Hoover, William Graham
2012-01-01
A small army of physicists, chemists, mathematicians, and engineers has joined forces to attack a classic problem, the "reversibility paradox", with modern tools. This book describes their work from the perspective of computer simulation, emphasizing the author's approach to the problem of understanding the compatibility, and even inevitability, of the irreversible second law of thermodynamics with an underlying time-reversible mechanics. Computer simulation has made it possible to probe reversibility from a variety of directions and "chaos theory" or "nonlinear dynamics" has supplied a useful vocabulary and a set of concepts, which allow a fuller explanation of irreversibility than that available to Boltzmann or to Green, Kubo and Onsager. Clear illustration of concepts is emphasized throughout, and reinforced with a glossary of technical terms from the specialized fields which have been combined here to focus on a common theme. The book begins with a discussion, contrasting the idealized reversibility of ba...
Finding equilibrium in the spatiotemporal chaos of the complex Ginzburg-Landau equation
Ballard, Christopher C.; Esty, C. Clark; Egolf, David A.
2016-11-01
Equilibrium statistical mechanics allows the prediction of collective behaviors of large numbers of interacting objects from just a few system-wide properties; however, a similar theory does not exist for far-from-equilibrium systems exhibiting complex spatial and temporal behavior. We propose a method for predicting behaviors in a broad class of such systems and apply these ideas to an archetypal example, the spatiotemporal chaotic 1D complex Ginzburg-Landau equation in the defect chaos regime. Building on the ideas of Ruelle and of Cross and Hohenberg that a spatiotemporal chaotic system can be considered a collection of weakly interacting dynamical units of a characteristic size, the chaotic length scale, we identify underlying, mesoscale, chaotic units and effective interaction potentials between them. We find that the resulting equilibrium Takahashi model accurately predicts distributions of particle numbers. These results suggest the intriguing possibility that a class of far-from-equilibrium systems may be well described at coarse-grained scales by the well-established theory of equilibrium statistical mechanics.
Exploring chaos a guide to the new science of disorder
1994-01-01
Chaos Theory is giving scientists fresh insights into all sorts of unruly phenomena--from dripping faucets to swinging pendulums, from the vagaries of the weather to the movements of the planets, from heart rhythms to gold futures.
Hunt, Brian R; Ott, Edward
2015-09-01
In this paper, we propose, discuss, and illustrate a computationally feasible definition of chaos which can be applied very generally to situations that are commonly encountered, including attractors, repellers, and non-periodically forced systems. This definition is based on an entropy-like quantity, which we call "expansion entropy," and we define chaos as occurring when this quantity is positive. We relate and compare expansion entropy to the well-known concept of topological entropy to which it is equivalent under appropriate conditions. We also present example illustrations, discuss computational implementations, and point out issues arising from attempts at giving definitions of chaos that are not entropy-based.
Covert Binary Communications through the Application of Chaos Theory: Three Novel Approaches
Directory of Open Access Journals (Sweden)
Kyle J. Bradbury
2008-06-01
Full Text Available Today, most covert communications systems use a spreadspectrum approach to ensure that transmissions remain clandestine. This paper expands beyond traditional spreadspectrum schemes and into chaos theory in communications by presenting a novel design for a covert noncoherent binary communication system that uses chaotic signals. Three techniques are developed, with varying performance. Each system uses two chaotic signals with antipodal attractors as the information carriers. Although the two chaotic signals used are continuously generated from random starting values without containing repetitious patterns, the receiver requires neither those initial values nor does it require synchronization with the transmitter. The chaotic signals used are both spreadspectrum in the frequency domain and undetectable using matched-filter receivers, thereby achieving a level of covertness. The signal-to-noise ratio performance is presented through simulated receiver operating characteristic (ROC curves for a comparison to binary phase shift keying. This system provides a binary communication scheme which is not detectable by standard matched filtering techniques and has noise-like spectra, requiring a new receiver configuration and yielding security.
1st National Mechanics Congress
Nieuwstadt, F
1990-01-01
The Department of Applied Mechanics of the Royal Institution of Engineers in the Netherlands (Koninklijk Instituut van Ingenieurs) organised on April 2-4, 1990 the first National Applied Mechanics Congress about the theme: "Integration of Theory and Applications in Applied Mechanics" The idea behind this initiative was to bring together the Applied Mechanics communities in The Netherlands and Belgium and to create an environment in which new developments in the field could be discussed and in which connections to other disciplines could be established. Among an extensive list of possible subjects the following were selected as congress topics: - non-linear material behaviour, - chaos, - mechatronics, - liquid-solid interactions, - mathematics and applied mechanics, - integration of Applied Mechanics and other disciplines. Applied Mechanics comprises both solid mechanics and fluid mechanics. These can be subdivided further into: rheology, plasticity, theory of plates and shells, theory of elasticity, multibody...
Chaotic behaviour and controlling chaos in free electron lasers
International Nuclear Information System (INIS)
Wang Wenjie; Chen Shigang; Du Xiangwan; Wang Guangrui
1995-01-01
Chaos in free electron lasers (FEL) is reviewed. Special attention has been paid to the chaotic behaviour of the electrons and the laser field. The problem of controlling and utilizing chaotic motion of the electrons and the laser field has also been discussed. In order to find out the rules of instability and chaos in FEL, some typical methods of the chaotic theory are used. These methods include making the Poincare surface of section, drawing the phase space diagrams of the electron orbits, calculating the Liapunov exponents, and computing the power spectrum, etc. Finally, some problems in FEL research are discussed (103 refs., 54 figs.)
Li-Yorke chaos and synchronous chaos in a globally nonlocal coupled map lattice
International Nuclear Information System (INIS)
Khellat, Farhad; Ghaderi, Akashe; Vasegh, Nastaran
2011-01-01
Highlights: → A globally nonlocal coupled map lattice is introduced. → A sufficient condition for the existence of Li-Yorke chaos is determined. → A sufficient condition for synchronous behaviors is obtained. - Abstract: This paper investigates a globally nonlocal coupled map lattice. A rigorous proof to the existence of chaos in the scene of Li-Yorke in that system is presented in terms of the Marotto theorem. Analytical sufficient conditions under which the system is chaotic, and has synchronous behaviors are determined, respectively. The wider regions associated with chaos and synchronous behaviors are shown by simulations. Spatiotemporal chaos, synchronous chaos and some other synchronous behaviors such as fixed points, 2-cycles and 2 2 -cycles are also shown by simulations for some values of the parameters.
Cryptology transmitted message protection from deterministic chaos up to optical vortices
Izmailov, Igor; Romanov, Ilia; Smolskiy, Sergey
2016-01-01
This book presents methods to improve information security for protected communication. It combines and applies interdisciplinary scientific engineering concepts, including cryptography, chaos theory, nonlinear and singular optics, radio-electronics and self-changing artificial systems. It also introduces additional ways to improve information security using optical vortices as information carriers and self-controlled nonlinearity, with nonlinearity playing a key "evolving" role. The proposed solutions allow the universal phenomenon of deterministic chaos to be discussed in the context of information security problems on the basis of examples of both electronic and optical systems. Further, the book presents the vortex detector and communication systems and describes mathematical models of the chaos oscillator as a coder in the synchronous chaotic communication and appropriate decoders, demonstrating their efficiency both analytically and experimentally. Lastly it discusses the cryptologic features of analyze...
Controlling chaos in the current-driven ion acoustic instability
International Nuclear Information System (INIS)
Fukuyama, T.; Taniguchi, K.; Kawai, Y.
2002-01-01
Control of intermittent chaos caused by the current-driven ion acoustic instability is attempted and the controlling mechanism is investigated. When a small negative dc voltage is applied to the chaotic system as a perturbation, the system changes from a chaotic state to a periodic state while maintaining the instability, indicating that the chaotic state caused by the ion acoustic instability is well controlled by applying a small negative dc voltage. A hysteresis structure is observed on the V-I curve of the mesh grid to which the negative dc voltage to control is applied. Furthermore, when a negative dc voltage is applied to the state which shows a laminar structure existing under same experimental conditions, the system becomes chaotic via a bifurcation. Driven-chaos is excited when a negative dc voltage is applied to the laminar state. Applying a small negative dc voltage leads to controlling intermittent chaos while exciting driven-chaos
Controlling chaos through compactification in cosmological models with a collapsing phase
International Nuclear Information System (INIS)
Wesley, Daniel H.; Steinhardt, Paul J.; Turok, Neil
2005-01-01
We consider the effect of compactification of extra dimensions on the onset of classical chaotic mixmaster behavior during cosmic contraction. Assuming a universe that is well-approximated as a four-dimensional Friedmann-Robertson-Walker model (with negligible Kaluza-Klein excitations) when the contraction phase begins, we identify compactifications that allow a smooth contraction and delay the onset of chaos until arbitrarily close to the big crunch. These compactifications are defined by the de Rham cohomology (Betti numbers) and Killing vectors of the compactification manifold. We find compactifications that control chaos in vacuum Einstein gravity, as well as in string theories with N=1 supersymmetry and M-theory. In models where chaos is controlled in this way, the universe can remain homogeneous and flat until it enters the quantum gravity regime. At this point, the classical equations leading to chaotic behavior can no longer be trusted, and quantum effects may allow a smooth approach to the big crunch and transition into a subsequent expanding phase. Our results may be useful for constructing cosmological models with contracting phases, such as the ekpyrotic/cyclic and pre-big bang models
The edge of chaos: A nonlinear view of psychoanalytic technique.
Galatzer-Levy, Robert M
2016-04-01
The field of nonlinear dynamics (or chaos theory) provides ways to expand concepts of psychoanalytic process that have implications for the technique of psychoanalysis. This paper describes how concepts of "the edge of chaos," emergence, attractors, and coupled oscillators can help shape analytic technique resulting in an approach to doing analysis which is at the same time freer and more firmly based in an enlarged understanding of the ways in which psychoanalysis works than some current recommendation about technique. Illustrations from a lengthy analysis of an analysand with obsessive-compulsive disorder show this approach in action. Copyright © 2016 Institute of Psychoanalysis.
Pattern control and suppression of spatiotemporal chaos using geometrical resonance
International Nuclear Information System (INIS)
Gonzalez, J.A.; Bellorin, A.; Reyes, L.I.; Vasquez, C.; Guerrero, L.E.
2004-01-01
We generalize the concept of geometrical resonance to perturbed sine-Gordon, Nonlinear Schroedinger, phi (cursive,open) Greek 4 , and Complex Ginzburg-Landau equations. Using this theory we can control different dynamical patterns. For instance, we can stabilize breathers and oscillatory patterns of large amplitudes successfully avoiding chaos. On the other hand, this method can be used to suppress spatiotemporal chaos and turbulence in systems where these phenomena are already present. This method can be generalized to even more general spatiotemporal systems. A short report of some of our results has been published in [Europhys. Lett. 64 (2003) 743
Research in the theory of condensed matter and elementary particles. [Progress report
International Nuclear Information System (INIS)
1985-01-01
The proposed research is concerned with problems occupying the common ground between quantum field theory and statistical mechanics. The topics under investigation include: superconformal field theory in two dimensions, its relationship to two dimensional critical phenomena and its applications in string theory; the covariant formulation of the superstring theory; formation of large-scale structures and spatial chaos in dynamical systems; fermion-boson mass relations in BCS type theories; and properties of quantum field theories defined over galois fields. 37 refs
Specifying the Links Between Household Chaos and Preschool Children’s Development
Martin, Anne; Razza, Rachel; Brooks-Gunn, Jeanne
2011-01-01
Household chaos has been linked to poorer cognitive, behavioral, and self-regulatory outcomes in young children, but the mechanisms responsible remain largely unknown. Using a diverse sample of families in Chicago, the present study tests for the independent contributions made by five indicators of household chaos: noise, crowding, family instability, lack of routine, and television usually on. Chaos was measured at age 2; outcomes measured at age 5 tap receptive vocabulary, attention and behavior problems, and effortful control. Results show that controlling for all other measures of chaos, children with a lack of routine scored lower on receptive vocabulary and delayed gratification, while children whose television was generally on scored higher on aggression and attention problems. The provision of learning materials mediated a small part of the association between television and receptive vocabulary. Family instability, crowding, and noise did not predict any outcomes once other measures of chaos were controlled. PMID:22919120
Hutchinson, Michael; Swanson, Phillip D
2007-01-01
Refractory status epilepticus (SE) is a condition of continuous seizure activity in which there is a regular, rapid, succession of spike discharges in the brain. It is incompatible with normal consciousness and is associated with an extremely high morbidity and mortality. Prior to 1990, prevailing opinion held that a brief period of anesthesia (up to two weeks) was to be recommended, but that if SE persisted this was a sign of irreversible brain damage. Therefore support of the patient in SE was not recommended beyond two weeks. On the basis of the theoretical constructs of chaos theory we hypothesized that, for selected cases, anesthesia should be continued indefinitely until the SE resolved. This became the standard of care at the University of Washington and at other institutions. After several years, the accumulating evidence lends support for this hypothesis and we are now able to propose which patients will benefit from such therapy. It is hypothesized that only those patients for whom there is no underlying brain disease, beyond epilepsy, are likely to benefit. Secondly, chaos theory suggests that a strong perturbation will cause a rapid transition from the stable attractor of SE to the stable attractor representing normal consciousness. In certain ways, SE is analogous to ventricular tachycardia, where the cardiac muscle has an abnormally fast rhythm incompatible with proper cardiac function. Therefore the second hypothesis is that a brain perturbation, analogous to defibrillation, may be even more useful than anesthesia in refractory SE.
Krstacic, Goran; Krstacic, Antonija; Smalcelj, Anton; Milicic, Davor; Jembrek-Gostovic, Mirjana
2007-04-01
Dynamic analysis techniques may quantify abnormalities in heart rate variability (HRV) based on nonlinear and fractal analysis (chaos theory). The article emphasizes clinical and prognostic significance of dynamic changes in short-time series applied on patients with coronary heart disease (CHD) during the exercise electrocardiograph (ECG) test. The subjects were included in the series after complete cardiovascular diagnostic data. Series of R-R and ST-T intervals were obtained from exercise ECG data after sampling digitally. The range rescaled analysis method determined the fractal dimension of the intervals. To quantify fractal long-range correlation's properties of heart rate variability, the detrended fluctuation analysis technique was used. Approximate entropy (ApEn) was applied to quantify the regularity and complexity of time series, as well as unpredictability of fluctuations in time series. It was found that the short-term fractal scaling exponent (alpha(1)) is significantly lower in patients with CHD (0.93 +/- 0.07 vs 1.09 +/- 0.04; P chaos theory during the exercise ECG test point out the multifractal time series in CHD patients who loss normal fractal characteristics and regularity in HRV. Nonlinear analysis technique may complement traditional ECG analysis.
Energy Technology Data Exchange (ETDEWEB)
Cohen, E G.D.
1985-01-01
The following topics were dealt with: walks, walls and ordering in low dimensions; renormalisation of fluids; wetting transition; phases and phase transitions; liquid-vapour interface; statistical mechanics in lattice gauge theory; hydrodynamic instabilities; complex dynamics and chaos; dynamical transitions; phase separation and pattern formation; kinetic theory of clustering; localisation.
Chaos based on Riemannian geometric approach to Abelian-Higgs dynamical system
International Nuclear Information System (INIS)
Kawabe, Tetsuji
2003-01-01
Based on the Riemannian geometric approach, we study chaos of the Abelian-Higgs dynamical system derived from a classical field equation consisting of a spatially homogeneous Abelian gauge field and Higgs field. Using the global indicator of chaos formulated by the sectional curvature of the ambient manifold, we show that this approach brings the same qualitative and quantitative information about order and chaos as has been provided by the Lyapunov exponents in the conventional and phenomenological approach. We confirm that the mechanism of chaos is a parametric instability of the system. By analyzing a close relation between the sectional curvature and the Gaussian curvature, we point out that the Toda-Brumer criterion becomes a sufficient condition to the criterion based on this geometric approach as to the stability condition
Chaos as an intermittently forced linear system.
Brunton, Steven L; Brunton, Bingni W; Proctor, Joshua L; Kaiser, Eurika; Kutz, J Nathan
2017-05-30
Understanding the interplay of order and disorder in chaos is a central challenge in modern quantitative science. Approximate linear representations of nonlinear dynamics have long been sought, driving considerable interest in Koopman theory. We present a universal, data-driven decomposition of chaos as an intermittently forced linear system. This work combines delay embedding and Koopman theory to decompose chaotic dynamics into a linear model in the leading delay coordinates with forcing by low-energy delay coordinates; this is called the Hankel alternative view of Koopman (HAVOK) analysis. This analysis is applied to the Lorenz system and real-world examples including Earth's magnetic field reversal and measles outbreaks. In each case, forcing statistics are non-Gaussian, with long tails corresponding to rare intermittent forcing that precedes switching and bursting phenomena. The forcing activity demarcates coherent phase space regions where the dynamics are approximately linear from those that are strongly nonlinear.The huge amount of data generated in fields like neuroscience or finance calls for effective strategies that mine data to reveal underlying dynamics. Here Brunton et al.develop a data-driven technique to analyze chaotic systems and predict their dynamics in terms of a forced linear model.
Chaos synchronization and parameter identification of three time scales brushless DC motor system
International Nuclear Information System (INIS)
Ge, Z.-M.; Cheng, J.-W.
2005-01-01
Chaotic anticontrol and chaos synchronization of brushless DC motor system are studied in this paper. Nondimensional dynamic equations of three time scale brushless DC motor system are presented. Using numerical results, such as phase diagram, bifurcation diagram, and Lyapunov exponent, periodic and chaotic motions can be observed. Then, chaos synchronization of two identical systems via additional inputs and Lyapunov stability theory are studied. And further, the parameter of the system is traced via adaptive control and random optimization method
Directory of Open Access Journals (Sweden)
Elaine Lally
2006-01-01
Full Text Available This article explores the intersection between digital technologies and cultural planning. New information technologies ought to enable more powerful planning strategies. Yet a common seductive vision of planning is mirrored by utopian claims for cyberculture, which often fall short of the hoped-for reality. We suggest that one problem is the linear thinking common to mainstream planning and digital thinking, which leads to a cumulative lack of fit with the non-linear (chaotic world of social action. We draw on chaos and complexity theory to reframe planning problems and develop more creative digital strategies in a specific location, Western Sydney, using and adapting Geographic Information Systems.
Microscopic theory of nuclear collective dynamics
International Nuclear Information System (INIS)
Sakata, Fumihiko; Marumori, Toshio; Hashimoto, Yukio; Tsukuma, Hidehiko; Yamamoto, Yoshifumi; Iwasawa, Kazuo.
1990-10-01
A recent development of the INS-TSUKUBA joint research project on large-amplitude collective motion is summarized by putting special emphasis on an inter-relationship between quantum chaos and nuclear spectroscopy. Aiming at introducing various concepts used in this lecture, we start with recapitulating the semi-classical theory of nuclear collective dynamics formulated within the time-dependent Hartree-Fock (TDHF) theory. The central part of the semi-classical theory is provided by the self-consistent collective coordinate (SCC) method which has been developed to properly take account of the non-linear dynamics specific for the finite many-body quantum system. A decisive role of the level crossing dynamics on the order-to-chaos transition of collective motion is discussed in detail. Extending the basic idea of the semi-classical theory, we discuss a full quantum theory of nuclear collective dynamics which allows us to properly define a concept of the quantum integrability as well as the quantum chaoticity for each eigenfunction. The lecture is arranged so as to clearly show the similar structure between the semi-classical and quantum theories of nuclear collective dynamics. Using numerical calculations, we illustrate what the quantum chaos for each eigenfunction means and relate it to the usual definition of quantum chaos for nearest neighbor level spacing statistics based on the random matrix theory. (author)
Generalized Semiflows and Chaos in Multivalued Dynamical Systems
Czech Academy of Sciences Publication Activity Database
Beran, Zdeněk; Čelikovský, Sergej
2012-01-01
Roč. 26, č. 25 (2012), 1246016-1-1246016-11 ISSN 0217-9792 R&D Projects: GA ČR(CZ) GAP103/12/1794 Institutional support: RVO:67985556 Keywords : Multivalued dynamical systems * chaos * differential inclusions Subject RIV: BC - Control Systems Theory Impact factor: 0.358, year: 2012 http://library.utia.cas.cz/separaty/2012/TR/beran-0380290.pdf
Kasimov, Aslan R.; Faria, Luiz; Rosales, Rodolfo R.
2013-01-01
: steady traveling wave solutions, instability of such solutions, and the onset of chaos. Our model is the first (to our knowledge) to describe chaos in shock waves by a scalar first-order partial differential equation. The chaos arises in the equation
Chaos in complex motor networks induced by Newman—Watts small-world connections
International Nuclear Information System (INIS)
Wei Du-Qu; Luo Xiao-Shu; Zhang Bo
2011-01-01
We investigate how dynamical behaviours of complex motor networks depend on the Newman—Watts small-world (NWSW) connections. Network elements are described by the permanent magnet synchronous motor (PMSM) with the values of parameters at which each individual PMSM is stable. It is found that with the increase of connection probability p, the motor in networks becomes periodic and falls into chaotic motion as p further increases. These phenomena imply that NWSW connections can induce and enhance chaos in motor networks. The possible mechanism behind the action of NWSW connections is addressed based on stability theory. (interdisciplinary physics and related areas of science and technology)
Gravitational collapse, chaos in CFT correlators and the information paradox
Energy Technology Data Exchange (ETDEWEB)
Farahi, Arya, E-mail: aryaf@umich.edu; Pando Zayas, Leopoldo A., E-mail: lpandoz@umich.edu
2014-06-27
We consider gravitational collapse of a massless scalar field in asymptotically anti-de Sitter spacetime. Following the AdS/CFT dictionary we further study correlations in the field theory side by way of the Klein–Gordon equation of a probe scalar field in the collapsing background. We present evidence that in a certain regime the probe scalar field behaves chaotically, thus supporting Hawking's argument in the black hole information paradox proposing that although the information can be retrieved in principle, deterministic chaos impairs, in practice, the process of unitary extraction of information from a black hole. We emphasize that quantum chaos will change this picture.
Does chaos assist localization or delocalization?
Tan, Jintao; Lu, Gengbiao; Luo, Yunrong; Hai, Wenhua
2014-12-01
We aim at a long-standing contradiction between chaos-assisted tunneling and chaos-related localization study quantum transport of a single particle held in an amplitude-modulated and tilted optical lattice. We find some near-resonant regions crossing chaotic and regular regions in the parameter space, and demonstrate that chaos can heighten velocity of delocalization in the chaos-resonance overlapping regions, while chaos may aid localization in the other chaotic regions. The degree of localization enhances with increasing the distance between parameter points and near-resonant regions. The results could be useful for experimentally manipulating chaos-assisted transport of single particles in optical or solid-state lattices.
An Improved Chaos Genetic Algorithm for T-Shaped MIMO Radar Antenna Array Optimization
Directory of Open Access Journals (Sweden)
Xin Fu
2014-01-01
Full Text Available In view of the fact that the traditional genetic algorithm easily falls into local optimum in the late iterations, an improved chaos genetic algorithm employed chaos theory and genetic algorithm is presented to optimize the low side-lobe for T-shaped MIMO radar antenna array. The novel two-dimension Cat chaotic map has been put forward to produce its initial population, improving the diversity of individuals. The improved Tent map is presented for groups of individuals of a generation with chaos disturbance. Improved chaotic genetic algorithm optimization model is established. The algorithm presented in this paper not only improved the search precision, but also avoids effectively the problem of local convergence and prematurity. For MIMO radar, the improved chaos genetic algorithm proposed in this paper obtains lower side-lobe level through optimizing the exciting current amplitude. Simulation results show that the algorithm is feasible and effective. Its performance is superior to the traditional genetic algorithm.
Revisitation of chaos in Bianchi IX Universe and in generalized scalar-tensor cosmologies
International Nuclear Information System (INIS)
Lehner, Thierry; Di Menza, Laurent
2003-01-01
We show that there is a threshold for the onset of chaos in cosmology for the Universe described as a dynamical system derived from the Einstein equations of general relativity (GR). In the case of the mixmaster model (homogeneous and anisotropic cosmology with a Bianchi IX metric) the chaos occurs precisely at the prescribed necessary value H vac =0 of the GR for the energy of the Universe while the system is found regular for H vac >0 and chaotic for H vac <0 with respect to its pure vacuum part. In the case of generalized scalar tensor theories within the Bianchi IX model we show using the ADM formalism and a conformal transformation that the energy of the dynamical system as compared to vacuum lies below the threshold thus the system is not exhibiting chaos and the conclusion still holds in the presence of ordinary matter as well. The suppression of chaos occurs in a similar way for stiff matter alone
Chaos induced by quantum effect due to breakdown of the Born-Oppenheimer adiabaticity
International Nuclear Information System (INIS)
Fujisaki, Hiroshi; Takatsuka, Kazuo
2001-01-01
Chaos in the multimode nonadiabatic system constructed by Heller [J. Chem. Phys. >92, 1718 (1990)], which consists of two diabatic two-dimensional harmonic potentials with the Condon coupling, is studied. A thorough investigation is carried out by scanning the magnitudes of the Condon coupling and the Duschinsky angle. To elucidate mechanisms that can cause chaos in this quantum system, the statistical properties of the energy levels and eigenfunctions of the system are investigated. We find an evidence in terms of the nearest-neighbor spacing distribution of energy levels and other measures that a certain class of chaos is purely induced by the nonadiabatic interaction due to breakdown of the Born-Oppenheimer approximation. Since the nonadiabatic transition can induce repeated bifurcation and merging of a wave packet around the region of quasicrossing between two potential surfaces, and since this interaction does not have a counterpart in the lower adiabatic system, the present chaos deserves being called 'nonadiabatic chaos.' Another type of chaos in a nonadiabatic system was previously identified [D. M. Leitner et al., J. Chem. Phys. >104, 434 (1996)] that reflects the inherent chaos of a corresponding adiabatic potential. We present a comparative study to establish the similarity and difference between these kinds of chaos
Instabilities and chaos in a kinetic equation for active nematics
International Nuclear Information System (INIS)
Shi, Xia-qing; Ma, Yu-qiang; Chaté, Hugues
2014-01-01
We study dry active nematics at the kinetic equation level, stressing the differences with the well-known Doi theory for non-active rods near thermal equilibrium. By deriving hydrodynamic equations from the kinetic equation, we show analytically that these two description levels share the same qualitative phase diagram, as defined by the linear instability limits of spatially-homogeneous solutions. In particular, we show that the ordered, homogeneous state is unstable in a region bordering the linear onset of nematic order, and is only linearly stable deeper in the ordered phase. Direct simulations of the kinetic equation reveal that its solutions are chaotic in the region of linear instability of the ordered homogeneous state. The local mechanisms for this large-scale chaos are discussed. (paper)
Sharma, Vijay
2009-09-10
Physiological systems such as the cardiovascular system are capable of five kinds of behavior: equilibrium, periodicity, quasi-periodicity, deterministic chaos and random behavior. Systems adopt one or more these behaviors depending on the function they have evolved to perform. The emerging mathematical concepts of fractal mathematics and chaos theory are extending our ability to study physiological behavior. Fractal geometry is observed in the physical structure of pathways, networks and macroscopic structures such the vasculature and the His-Purkinje network of the heart. Fractal structure is also observed in processes in time, such as heart rate variability. Chaos theory describes the underlying dynamics of the system, and chaotic behavior is also observed at many levels, from effector molecules in the cell to heart function and blood pressure. This review discusses the role of fractal structure and chaos in the cardiovascular system at the level of the heart and blood vessels, and at the cellular level. Key functional consequences of these phenomena are highlighted, and a perspective provided on the possible evolutionary origins of chaotic behavior and fractal structure. The discussion is non-mathematical with an emphasis on the key underlying concepts.
Chaos control for a class of chaotic systems using PI-type state observer approach
International Nuclear Information System (INIS)
Jiang Guoping; Zheng Weixing
2004-01-01
In this paper, by using the PI-type state observer design approach and the characteristic of ergodicity of chaos, a new method is presented for controlling chaos, including the stabilization of unstable equilibrium points and set-point tracking, for a class of chaotic systems. Based on the theory of nonlinear ordinary differential equations, a simple criterion is derived for designing the controller gains for stabilization and tracking, in which control parameters can be selected via the pole placement technique of linear control theory. More importantly, this control method has a simple controller structure, high robustness against system parametric variations, and strong rejection of external constant disturbances. The method is applied to the chaotic Lorenz system for demonstration
Spatial interaction creates period-doubling bifurcation and chaos of urbanization
International Nuclear Information System (INIS)
Chen Yanguang
2009-01-01
This paper provides a new way of looking at complicated dynamics of simple mathematical models. The complicated behavior of simple equations is one of the headstreams of chaos theory. However, a recent study based on dynamical equations of urbanization shows that there are still some undiscovered secrets behind the simple mathematical models such as logistic equation. The rural-urban interaction model can also display varied kinds of complicated dynamics, including period-doubling bifurcation and chaos. The two-dimension map of urbanization presents the same dynamics as that from the one-dimension logistic map. In theory, the logistic equation can be derived from the two-population interaction model. This seems to suggest that the complicated behavior of simple models results from interaction rather than pure intrinsic randomicity. In light of this idea, the classical predator-prey interaction model can be revised to explain the complex dynamics of logistic equation in physical and social sciences.
Controlling chaos (OGY) implemented on a reconstructed ecological two-dimensional map
International Nuclear Information System (INIS)
Sakai, Kenshi; Noguchi, Yuko
2009-01-01
We numerically demonstrate a way to stabilize an unstable equilibrium in the ecological dynamics reconstructed from real-world time series data, namely, alternate bearing of citrus trees. The reconstruction of deterministic dynamics from short and noisy ecological time series has been a crucial issue since May's historical work [May RM. Biological populations with nonoverlapping generations: stable points, stable cycles and chaos. Science 1974;186:645-7; Hassell MP, Lawton JH, May RM. Patterns of dynamical behavior in single species populations. J Anim Ecol 1976;45:471-86]. Response surface methodology, followed by the differential equation approach is recognized as a promising method of reconstruction [Turchin P. Rarity of density dependence or population with lags? Nature 1990;344:660-3; Turchin P, Taylor AD. Complex dynamics in ecological time series. Ecology 1992;73:289-305; Ellner S, Turchin P. Chaos in a noisy world: new method and evidence from time series analysis. Am Nat 1995;145(3):343-75; Turchin P, Ellner S. Living on the edge of chaos: population dynamics of fennoscandian voles. Ecology 2000;8(11):3116]. Here, the reconstructed ecological dynamics was described by a two-dimensional map derived from the response surface created by the data. The response surface created was experimentally validated in four one-year forward predictions in 2001, 2002, 2003 and 2004. Controlling chaos is very important when applying chaos theory to solving real-world problems. The OGY method is the first and most popular methodology for controlling chaos and can be used as an algorithm to stabilize an unstable fixed point by putting the state on a stable manifold [Ott E, Grebogi C, York JA. Controlling chaos. Phys Rev Lett 1990;64:1996-9]. We applied the OGY method to our reconstructed two-dimensional map and as a result were able to control alternate bearing in numerical simulations.
Kaszás, Bálint; Feudel, Ulrike; Tél, Tamás
2016-12-01
We investigate the death and revival of chaos under the impact of a monotonous time-dependent forcing that changes its strength with a non-negligible rate. Starting on a chaotic attractor it is found that the complexity of the dynamics remains very pronounced even when the driving amplitude has decayed to rather small values. When after the death of chaos the strength of the forcing is increased again with the same rate of change, chaos is found to revive but with a different history. This leads to the appearance of a hysteresis in the complexity of the dynamics. To characterize these dynamics, the concept of snapshot attractors is used, and the corresponding ensemble approach proves to be superior to a single trajectory description, that turns out to be nonrepresentative. The death (revival) of chaos is manifested in a drop (jump) of the standard deviation of one of the phase-space coordinates of the ensemble; the details of this chaos-nonchaos transition depend on the ratio of the characteristic times of the amplitude change and of the internal dynamics. It is demonstrated that chaos cannot die out as long as underlying transient chaos is present in the parameter space. As a condition for a "quasistatically slow" switch-off, we derive an inequality which cannot be fulfilled in practice over extended parameter ranges where transient chaos is present. These observations need to be taken into account when discussing the implications of "climate change scenarios" in any nonlinear dynamical system.
DEFF Research Database (Denmark)
Lindberg, Erik
1996-01-01
The chaotic behaviour of the Colpitts oscillator reported by M.P. Kennedy is further investigated by means of PSpice simulations. Chaos is also observed with the default Ebers-Moll BJT transistor model with no memory. When the model is extended with memory and losses chaos do not occur and a 3'rd...... order limit cycle is found. If the the forward Early voltage parameter is added chaos is observed again. An examination of the eigenvalues of the oscillator with the simple memoryless Ebers-Moll BJT injection model is presented. By adding bulk resistors to the model stable limit cycles of orders 1, 2, 3...
Noise tolerant spatiotemporal chaos computing.
Kia, Behnam; Kia, Sarvenaz; Lindner, John F; Sinha, Sudeshna; Ditto, William L
2014-12-01
We introduce and design a noise tolerant chaos computing system based on a coupled map lattice (CML) and the noise reduction capabilities inherent in coupled dynamical systems. The resulting spatiotemporal chaos computing system is more robust to noise than a single map chaos computing system. In this CML based approach to computing, under the coupled dynamics, the local noise from different nodes of the lattice diffuses across the lattice, and it attenuates each other's effects, resulting in a system with less noise content and a more robust chaos computing architecture.
Samara, Ziyad; Fiamma, Marie-Noëlle; Bautin, Nathalie; Ranohavimparany, Anja; Le Coz, Patrick; Golmard, Jean-Louis; Darré, Pierre; Zelter, Marc; Poon, Chi-Sang; Similowski, Thomas
2011-01-01
Human ventilation at rest exhibits mathematical chaos-like complexity that can be described as long-term unpredictability mediated (in whole or in part) by some low-dimensional nonlinear deterministic process. Although various physiological and pathological situations can affect respiratory complexity, the underlying mechanisms remain incompletely elucidated. If such chaos-like complexity is an intrinsic property of central respiratory generators, it should appear or increase when these structures mature or are stimulated. To test this hypothesis, we employed the isolated tadpole brainstem model [Rana (Pelophylax) esculenta] and recorded the neural respiratory output (buccal and lung rhythms) of pre- (n = 8) and postmetamorphic tadpoles (n = 8), at physiologic (7.8) and acidic pH (7.4). We analyzed the root mean square of the cranial nerve V or VII neurograms. Development and acidosis had no effect on buccal period. Lung frequency increased with development (P Chaos-like complexity, assessed through the noise limit, increased from pH 7.8 to pH 7.4 (P chaos-like complexity, especially in the postmetamorphic stage and at low pH. According to the ventilatory generators homology theory, this may also be the case in mammals. PMID:21325645
Chaos and non-linear phenomena in renal vascular control
DEFF Research Database (Denmark)
Yip, K P; Holstein-Rathlou, N H
1996-01-01
are an example of deterministic chaos. Experimental studies show that the development of hypertension is associated with an increase in strength of the interaction between nephrons. Mathematical models suggest that an increased nephron-nephron interaction could cause a bifurcation in the dynamics of TGF from...... periodic oscillations to deterministic chaos. In addition to the TGF mediated oscillation, experimental studies have also demonstrated the presence of a faster oscillation, this having a frequency of 120-160 mHz. This is caused by a mechanism intrinsic to the vascular wall, and presumably represents...
Careers Education: Evolving, Adapting and Building Resilience through Chaos
Loader, Trent
2011-01-01
Career educators' ultimate goal, given the new career management paradigm, should be to ensure that students are career resilient when they leave their studies (from whatever year level). This article outlines the chaos theory of careers and resilience. It then goes on to describe a four-lesson unit of careers education work that attempts to…
Stability, bifurcation and a new chaos in the logistic differential equation with delay
International Nuclear Information System (INIS)
Jiang Minghui; Shen Yi; Jian Jigui; Liao Xiaoxin
2006-01-01
This Letter is concerned with bifurcation and chaos in the logistic delay differential equation with a parameter r. The linear stability of the logistic equation is investigated by analyzing the associated characteristic transcendental equation. Based on the normal form approach and the center manifold theory, the formula for determining the direction of Hopf bifurcation and the stability of bifurcation periodic solution in the first bifurcation values is obtained. By theoretical analysis and numerical simulation, we found a new chaos in the logistic delay differential equation
Enlightenment philosophers’ ideas about chaos
Directory of Open Access Journals (Sweden)
A. V. Kulik
2014-07-01
It is grounded that the philosopher and enlightener Johann Gottfried von Herder advanced an idea of objectivity of process of transformation chaos into order. It is shown that idea of «The law of nature» existing as for ordering chaos opened farreaching prospects for researches of interaction with chaos.
Global Complexity: Information, Chaos, and Control at ASIS 1996 Annual Meeting.
Jacob, M. E. L.
1996-01-01
Discusses proceedings of the 1996 ASIS (American Society for Information Science) annual meeting in Baltimore (Maryland), including chaos theory; electronic universities; distance education; intellectual property, including information privacy on the Internet; the need for leadership in libraries and information centers; information warfare and…
From chaos to unification: U theory vs. M theory
International Nuclear Information System (INIS)
Ye, Fred Y.
2009-01-01
A unified physical theory called U theory, that is different from M theory, is defined and characterized. U theory, which includes spinor and twistor theory, loop quantum gravity, causal dynamical triangulations, E-infinity unification theory, and Clifford-Finslerian unifications, is based on physical tradition and experimental foundations. In contrast, M theory pays more attention to mathematical forms. While M theory is characterized by supersymmetry string theory, U theory is characterized by non-supersymmetry unified field theory.
International Nuclear Information System (INIS)
Ge Zhengming; Hsu Maoyuan
2008-01-01
In this paper, chaos excited chaos synchronizations of generalized van der Pol systems with integral and fractional order are studied. Synchronizations of two identified autonomous generalized van der Pol chaotic systems are obtained by replacing their corresponding exciting terms by the same function of chaotic states of a third nonautonomous or autonomous generalized van der Pol system. Numerical simulations, such as phase portraits, Poincare maps and state error plots are given. It is found that chaos excited chaos synchronizations exist for the fractional order systems with the total fractional order both less than and more than the number of the states of the integer order generalized van der Pol system
Stochastic Estimation via Polynomial Chaos
2015-10-01
AFRL-RW-EG-TR-2015-108 Stochastic Estimation via Polynomial Chaos Douglas V. Nance Air Force Research...COVERED (From - To) 20-04-2015 – 07-08-2015 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER Stochastic Estimation via Polynomial Chaos ...This expository report discusses fundamental aspects of the polynomial chaos method for representing the properties of second order stochastic
Hybrid Chaos Synchronization of Four-Scroll Systems via Active Control
Karthikeyan, Rajagopal; Sundarapandian, Vaidyanathan
2014-03-01
This paper investigates the hybrid chaos synchronization of identical Wang four-scroll systems (Wang, 2009), identical Liu-Chen four-scroll systems (Liu and Chen, 2004) and non-identical Wang and Liu-Chen four-scroll systems. Active control method is the method adopted to achieve the hybrid chaos synchronization of the four-scroll chaotic systems addressed in this paper and our synchronization results are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the active control method is effective and convenient to hybrid synchronize identical and different Wang and Liu-Chen four-scroll chaotic systems. Numerical simulations are also shown to illustrate and validate the hybrid synchronization results derived in this paper.
Mixed-mode oscillations and chaos in a prey-predator system with dormancy of predators.
Kuwamura, Masataka; Chiba, Hayato
2009-12-01
It is shown that the dormancy of predators induces mixed-mode oscillations and chaos in the population dynamics of a prey-predator system under certain conditions. The mixed-mode oscillations and chaos are shown to bifurcate from a coexisting equilibrium by means of the theory of fast-slow systems. These results may help to find experimental conditions under which one can demonstrate chaotic population dynamics in a simple phytoplankton-zooplankton (-resting eggs) community in a microcosm with a short duration.
Nonlinear Dynamics In Quantum Physics -- Quantum Chaos and Quantum Instantons
Kröger, H.
2003-01-01
We discuss the recently proposed quantum action - its interpretation, its motivation, its mathematical properties and its use in physics: quantum mechanical tunneling, quantum instantons and quantum chaos.
Theory and Applications of Discontinuous State Feedback Generating Chaos for Linear Systems
International Nuclear Information System (INIS)
Xiao-Dan, Zhang; Zhen, Wang; Pin-Dong, Zhao
2008-01-01
We investigate a kind of chaos generating technique on a type of n-dimensional linear differential systems by adding feedback control items under a discontinuous state. This method is checked with some examples of numeric simulation. A constructive theorem is proposed for generalized synchronization related to the above chaotic system
He, Temple; Habib, Salman
2013-09-01
Simple dynamical systems--with a small number of degrees of freedom--can behave in a complex manner due to the presence of chaos. Such systems are most often (idealized) limiting cases of more realistic situations. Isolating a small number of dynamical degrees of freedom in a realistically coupled system generically yields reduced equations with terms that can have a stochastic interpretation. In situations where both noise and chaos can potentially exist, it is not immediately obvious how Lyapunov exponents, key to characterizing chaos, should be properly defined. In this paper, we show how to do this in a class of well-defined noise-driven dynamical systems, derived from an underlying Hamiltonian model.
Quantum Chaos via the Quantum Action
Kröger, H.
2002-01-01
We discuss the concept of the quantum action with the purpose to characterize and quantitatively compute quantum chaos. As an example we consider in quantum mechanics a 2-D Hamiltonian system - harmonic oscillators with anharmonic coupling - which is classically a chaotic system. We compare Poincar\\'e sections obtained from the quantum action with those from the classical action.
Complex motions and chaos in nonlinear systems
Machado, José; Zhang, Jiazhong
2016-01-01
This book brings together 10 chapters on a new stream of research examining complex phenomena in nonlinear systems—including engineering, physics, and social science. Complex Motions and Chaos in Nonlinear Systems provides readers a particular vantage of the nature and nonlinear phenomena in nonlinear dynamics that can develop the corresponding mathematical theory and apply nonlinear design to practical engineering as well as the study of other complex phenomena including those investigated within social science.
International Nuclear Information System (INIS)
Wei-Yi, Li; Qi-Chang, Zhang; Wei, Wang
2010-01-01
Based on the Silnikov criterion, this paper studies a chaotic system of cubic polynomial ordinary differential equations in three dimensions. Using the Cardano formula, it obtains the exact range of the value of the parameter corresponding to chaos by means of the centre manifold theory and the method of multiple scales combined with Floque theory. By calculating the manifold near the equilibrium point, the series expression of the homoclinic orbit is also obtained. The space trajectory and Lyapunov exponent are investigated via numerical simulation, which shows that there is a route to chaos through period-doubling bifurcation and that chaotic attractors exist in the system. The results obtained here mean that chaos occurred in the exact range given in this paper. Numerical simulations also verify the analytical results. (general)
No evidence of chaos but some evidence of dependence in the US stock market
International Nuclear Information System (INIS)
Serletis, Apostolos; Shintani, Mototsugu
2003-01-01
This paper uses recent advances in the field of applied econometrics and tools from dynamical systems theory to test for random walks and chaos in the US stock market, using daily observations on the Dow Jones Industrial Average (from January 3, 1928 to October 18, 2000 - a total of 18,490 observations). In doing so, we follow the recent contribution by Whang and Linton [J Econometr 91 (1999) 1] and construct the standard error for the Nychka et al. [J Roy Statist Soc B 54 (1992) 399] dominant Lyapunov exponent, thereby providing a statistical test of chaos. We find statistically significant evidence against low-dimensional chaos and point to the use of stochastic models and statistical inference in the modeling of asset markets
No evidence of chaos but some evidence of dependence in the US stock market
Energy Technology Data Exchange (ETDEWEB)
Serletis, Apostolos E-mail: serletis@ucalgary.ca; Shintani, Mototsugu E-mail: mototsugu.shintani@vanderbilt.edu
2003-07-01
This paper uses recent advances in the field of applied econometrics and tools from dynamical systems theory to test for random walks and chaos in the US stock market, using daily observations on the Dow Jones Industrial Average (from January 3, 1928 to October 18, 2000 - a total of 18,490 observations). In doing so, we follow the recent contribution by Whang and Linton [J Econometr 91 (1999) 1] and construct the standard error for the Nychka et al. [J Roy Statist Soc B 54 (1992) 399] dominant Lyapunov exponent, thereby providing a statistical test of chaos. We find statistically significant evidence against low-dimensional chaos and point to the use of stochastic models and statistical inference in the modeling of asset markets.
Murphy, David
2011-01-01
About 20 years ago, while lost in the midst of his PhD research, the author mused over proposed titles for his thesis. He was pretty pleased with himself when he came up with "Chaos Rules" (the implied double meaning was deliberate), or more completely, "Chaos Rules: An Exploration of the Work of Instructional Designers in Distance Education." He…
Natural hazards impact on the technosphere from the point of view of the stability and chaos theory
Kudin, Valery; Petrova, Elena
2013-04-01
Technological disasters occur when the technosphere gets into the transition interval from its stable state to the chaos. Unstable state of the system is one of the possible patterns in scenario of dynamic transition to a chaotic state through a cascade of bifurcations. According to the theory of stability, the chaotic dynamics of the state is caused due to a constant supply of energy into the system from the outside. The role of external source of energy for the man-made technosphere play environmental impacts such as natural hazards or phenomena. A qualitative change in the state of the system depends on the scale and frequency of these natural impacts. Each of the major natural-technological catastrophes is associated with a long chain of triggers and effects in the unfavorable combination of many unlikely accidental circumstances and human factors. According to the classical Gaussian distribution, large deviations are so rare that they can be ignored. However, many accidents and disasters generate statistics with an exponental distribution. In this case, rare events can not be ignored, such cases are often referred to as "heavy-tailed distributions". We should address them differently than the "usual" accidents that fit the description of normal distributions. In the case of "an exponental disaster" we should expect the worst. This is a sphere in which the elements of the stability and chaos theory are of a crucial position. Nowadays scientific research related to the forecast focus on the description and prediction of rare catastrophic events. It should be noted that the asymptotic behavior of such processes before the disaster is so-called blow-up regime, where one or more variables that characterize the system, grow to infinity in a finite time. Thus, in some cases we can reffer to some generic scenarios of disasters. In some model problems, where some value changes in chaotic regime and sometimes makes giant leaps, we can identify precursors that signal
Chaos synchronization of the energy resource system
International Nuclear Information System (INIS)
Li Xiuchun; Xu Wei; Li Ruihong
2009-01-01
This paper presents the chaos synchronization problem for new dynamical system (that is, energy resource demand-supply system), where the controller is designed using two different control methods. Firstly, based on stability criterion of linear system, chaotic synchronization is achieved with the help of the active theory, and accordingly, the simulation results are given for verifying the feasibility of the method. Secondly, based on Lyapunov stability theory, on the assumption that all the parameters of the system are unknown, adaptive control approach is proposed to make the states of two chaotic systems asymptotic synchronization. In the end, numerical simulations are used to show the effectiveness of the proposed control method.
Energy Technology Data Exchange (ETDEWEB)
Maldacena, Juan [School of Natural Sciences, Institute for Advanced Study,1 Einstein Drive, Princeton, NJ (United States); Shenker, Stephen H. [Stanford Institute for Theoretical Physics and Department of Physics, Stanford University,382 Via Pueblo Mall, Stanford, CA (United States); Stanford, Douglas [School of Natural Sciences, Institute for Advanced Study,1 Einstein Drive, Princeton, NJ (United States)
2016-08-17
We conjecture a sharp bound on the rate of growth of chaos in thermal quantum systems with a large number of degrees of freedom. Chaos can be diagnosed using an out-of-time-order correlation function closely related to the commutator of operators separated in time. We conjecture that the influence of chaos on this correlator can develop no faster than exponentially, with Lyapunov exponent λ{sub L}≤2πk{sub B}T/ℏ. We give a precise mathematical argument, based on plausible physical assumptions, establishing this conjecture.
Tachyons, Lamb Shifts and Superluminal Chaos
Tomaschitz, R
2000-01-01
An elementary account on the origins of cosmic chaos in an open and multiply connected universe is given; there is a finite region in the open 3-space in which the world-lines of galaxies are chaotic, and the mixing taking place in this chaotic nucleus of the universe provides a mechanism to create equidistribution. The galaxy background defines a distinguished frame of reference and a unique cosmic time order; in this context superluminal signal transfer is studied. Tachyons are described by a real Proca field with negative mass square, coupled to a current of subluminal matter. Estimates on tachyon mixing in the geometric optics limit are derived. The potential of a static point source in this field theory is a damped periodic function. We treat this tachyon potential as a perturbation of the Coulomb potential, and study its effects on energy levels in hydrogenic systems. By comparing the induced level shifts to high-precision Lamb shift measurements and QED calculations, we suggest a tachyon mass of 2.1 ke...
Hastily Formed Networks-Chaos to Recovery
2015-09-01
NETWORKS— CHAOS TO RECOVERY by Mark Arezzi September 2015 Thesis Co-Advisors: Douglas J. MacKinnon Brian Steckler THIS PAGE......systems to self-organize, adapt, and exert control over the chaos . Defining the role of communications requires an understanding of complexity, chaos
Pikkujamsa, S. M.; Makikallio, T. H.; Sourander, L. B.; Raiha, I. J.; Puukka, P.; Skytta, J.; Peng, C. K.; Goldberger, A. L.; Huikuri, H. V.
1999-01-01
BACKGROUND: New methods of R-R interval variability based on fractal scaling and nonlinear dynamics ("chaos theory") may give new insights into heart rate dynamics. The aims of this study were to (1) systematically characterize and quantify the effects of aging from early childhood to advanced age on 24-hour heart rate dynamics in healthy subjects; (2) compare age-related changes in conventional time- and frequency-domain measures with changes in newly derived measures based on fractal scaling and complexity (chaos) theory; and (3) further test the hypothesis that there is loss of complexity and altered fractal scaling of heart rate dynamics with advanced age. METHODS AND RESULTS: The relationship between age and cardiac interbeat (R-R) interval dynamics from childhood to senescence was studied in 114 healthy subjects (age range, 1 to 82 years) by measurement of the slope, beta, of the power-law regression line (log power-log frequency) of R-R interval variability (10(-4) to 10(-2) Hz), approximate entropy (ApEn), short-term (alpha(1)) and intermediate-term (alpha(2)) fractal scaling exponents obtained by detrended fluctuation analysis, and traditional time- and frequency-domain measures from 24-hour ECG recordings. Compared with young adults (60 years, n=29). CONCLUSIONS: Cardiac interbeat interval dynamics change markedly from childhood to old age in healthy subjects. Children show complexity and fractal correlation properties of R-R interval time series comparable to those of young adults, despite lower overall heart rate variability. Healthy aging is associated with R-R interval dynamics showing higher regularity and altered fractal scaling consistent with a loss of complex variability.
Puzzles in studies of quantum chaos
International Nuclear Information System (INIS)
Xu Gongou
1994-01-01
Puzzles in studies of quantum chaos are discussed. From the view of global properties of quantum states, it is clarified that quantum chaos originates from the break-down of invariant properties of quantum canonical transformations. There exist precise correspondences between quantum and classical chaos
Does the transition to chaos determine the dynamic aperture
International Nuclear Information System (INIS)
Jowett, J.M.
1986-06-01
We review the important notion of the dynamic aperture of a storage ring with emphasis on its relation to general ideas of dynamical instability, notably the transition to chaos. Practical approaches to the problem are compared. We suggest a somewhat novel quantitative guide to the old problem of choosing machine tunes based on a heuristic blend of KAM theory and resonance selection rules
Cheng, Chih-Hao; Chen, Chih-Ying; Chen, Jun-Da; Pan, Da-Kung; Ting, Kai-Ting; Lin, Fan-Yi
2018-04-30
We develop an unprecedented 3D pulsed chaos lidar system for potential intelligent machinery applications. Benefited from the random nature of the chaos, conventional CW chaos lidars already possess excellent anti-jamming and anti-interference capabilities and have no range ambiguity. In our system, we further employ self-homodyning and time gating to generate a pulsed homodyned chaos to boost the energy-utilization efficiency. Compared to the original chaos, we show that the pulsed homodyned chaos improves the detection SNR by more than 20 dB. With a sampling rate of just 1.25 GS/s that has a native sampling spacing of 12 cm, we successfully achieve millimeter-level accuracy and precision in ranging. Compared with two commercial lidars tested side-by-side, namely the pulsed Spectroscan and the random-modulation continuous-wave Lidar-lite, the pulsed chaos lidar that is in compliance with the class-1 eye-safe regulation shows significantly better precision and a much longer detection range up to 100 m. Moreover, by employing a 2-axis MEMS mirror for active laser scanning, we also demonstrate real-time 3D imaging with errors of less than 4 mm in depth.
Controlling DC-DC converters by chaos-based pulse width modulation to reduce EMI
International Nuclear Information System (INIS)
Li Hong; Zhang Bo; Li Zhong; Halang, Wolfgang A.; Chen Guanrong
2009-01-01
In this paper, periodic and chaotic behaviors of DC-DC converters under certain parametric conditions are simulated, experimentally verified, and analyzed. Motivated by the work of J.H.B. Deane and D.C. Hamill in 1996, where chaotic phenomena are useful in suppressing electromagnetic interference (EMI) by adjusting the parameters of the DC-DC converter and making it operate in chaos, a chaos-based pulse width modulation (CPWM) is proposed to distribute the harmonics of the DC-DC converters continuously and evenly over a wide frequency range, thereby reducing the EMI. The output waves and spectral properties of the EMI are simulated and analyzed as the carrier frequency or amplitude changes with regard to different chaotic maps. Simulation and experimental results are given to illustrate the effectiveness of the proposed CPWM, which provides a good example of applying chaos theory in engineering practice.
Good Hope in Chaos: Beyond Matching to Complexity in Career Development
Pryor, R. G. L.; Bright, J. E. H.
2009-01-01
The significance of both higher education and career counselling is outlined. The predominant matching paradigm for career development service delivery is described. Its implications for reinforcing the status quo in the South African community are identified and questioned. The Chaos Theory of Careers (CTC) is suggested as an alternative…
Fu, Yongqing; Li, Xingyuan; Li, Yanan; Yang, Wei; Song, Hailiang
2013-03-01
Chaotic communication has aroused general interests in recent years, but its communication effect is not ideal with the restriction of chaos synchronization. In this paper a new chaos M-ary digital modulation and demodulation method is proposed. By using region controllable characteristics of spatiotemporal chaos Hamilton map in phase plane and chaos unique characteristic, which is sensitive to initial value, zone mapping method is proposed. It establishes the map relationship between M-ary digital information and the region of Hamilton map phase plane, thus the M-ary information chaos modulation is realized. In addition, zone partition demodulation method is proposed based on the structure characteristic of Hamilton modulated information, which separates M-ary information from phase trajectory of chaotic Hamilton map, and the theory analysis of zone partition demodulator's boundary range is given. Finally, the communication system based on the two methods is constructed on the personal computer. The simulation shows that in high speed transmission communications and with no chaos synchronization circumstance, the proposed chaotic M-ary modulation and demodulation method has outperformed some conventional M-ary modulation methods, such as quadrature phase shift keying and M-ary pulse amplitude modulation in bit error rate. Besides, it has performance improvement in bandwidth efficiency, transmission efficiency and anti-noise performance, and the system complexity is low and chaos signal is easy to generate.
Nonlinear Spatio-Temporal Dynamics and Chaos in Semiconductors
Schöll, Eckehard
2005-08-01
Nonlinear transport phenomena are an increasingly important aspect of modern semiconductor research. This volume deals with complex nonlinear dynamics, pattern formation, and chaotic behavior in such systems. It bridges the gap between two well-established fields: the theory of dynamic systems and nonlinear charge transport in semiconductors. This unified approach helps reveal important electronic transport instabilities. The initial chapters lay a general framework for the theoretical description of nonlinear self-organized spatio-temporal patterns, such as current filaments, field domains, fronts, and analysis of their stability. Later chapters consider important model systems in detail: impact ionization induced impurity breakdown, Hall instabilities, superlattices, and low-dimensional structures. State-of-the-art results include chaos control, spatio-temporal chaos, multistability, pattern selection, activator-inhibitor kinetics, and global coupling, linking fundamental issues to electronic device applications. This book will be of great value to semiconductor physicists and nonlinear scientists alike.
Fundamental aspects of quantum theory
International Nuclear Information System (INIS)
Gorini, V.; Frigerio, A.
1986-01-01
This book presents information on the following topics: general problems and crucial experiments; the classical behavior of measuring instruments; quantum interference effect for two atoms radiating a single photon; quantization and stochastic processes; quantum Markov processes driven by Bose noise; chaotic behavior in quantum mechanics; quantum ergodicity and chaos; microscopic and macroscopic levels of description; fundamental properties of the ground state of atoms and molecules; n-level systems interacting with Bosons - semiclassical limits; general aspects of gauge theories; adiabatic phase shifts for neutrons and photons; the spins of cyons and dyons; round-table discussion the the Aharonov-Bohm effect; gravity in quantum mechanics; the gravitational phase transition; anomalies and their cancellation; a new gauge without any ghost for Yang-Mills Theory; and energy density and roughening in the 3-D Ising ferromagnet
12th International Conference of Dynamical Systems-Theory and Applications
Applied Non-Linear Dynamical Systems
2014-01-01
The book is a collection of contributions devoted to analytical, numerical and experimental techniques of dynamical systems, presented at the International Conference on Dynamical Systems: Theory and Applications, held in Łódź, Poland on December 2-5, 2013. The studies give deep insight into both the theory and applications of non-linear dynamical systems, emphasizing directions for future research. Topics covered include: constrained motion of mechanical systems and tracking control; diversities in the inverse dynamics; singularly perturbed ODEs with periodic coefficients; asymptotic solutions to the problem of vortex structure around a cylinder; investigation of the regular and chaotic dynamics; rare phenomena and chaos in power converters; non-holonomic constraints in wheeled robots; exotic bifurcations in non-smooth systems; micro-chaos; energy exchange of coupled oscillators; HIV dynamics; homogenous transformations with applications to off-shore slender structures; novel approaches to a qualitative s...
International Nuclear Information System (INIS)
Ge Zhengming; Chang Chingming; Chen Yensheng
2006-01-01
Anti-control of chaos of single time scale brushless dc motors (BLDCM) and chaos synchronization of different order systems are studied in this paper. By addition of an external nonlinear term, we can obtain anti-control of chaos. Then, by addition of the coupling terms, by the use of Lyapunov stability theorem and by the linearization of the error dynamics, chaos synchronization between a third-order BLDCM and a second-order Duffing system are presented
Train flow chaos analysis based on an improved cellular automata model
International Nuclear Information System (INIS)
Meng, Xuelei; Xiang, Wanli; Jia, Limin; Xu, Jie
2015-01-01
To control the chaos in the railway traffic flow and offer valuable information for the dispatchers of the railway system, an improved cellular model is presented to detect and analyze the chaos in the traffic flow. We first introduce the working mechanism of moving block system, analyzing the train flow movement characteristics. Then we improve the cellular model on the evolution rules to adjust the train flow movement. We give the train operation steps from three cases: the trains running on a railway section, a train will arrive in a station and a train will departure from a station. We simulate 4 trains to run on a high speed section fixed with moving block system and record the distances between the neighbor trains and draw the Poincare section to analyze the chaos in the train operation. It is concluded that there is not only chaos but order in the train operation system with moving blocking system and they can interconvert to each other. The findings have the potential value in train dispatching system construction and offer supporting information for the daily dispatching work.
Synchronization of chaos in non-identical parametrically excited systems
International Nuclear Information System (INIS)
Idowu, B.A.; Vincent, U.E.; Njah, A.N.
2009-01-01
In this paper, we investigate the synchronization of chaotic systems consisting of non-identical parametrically excited oscillators. The active control technique is employed to design control functions based on Lyapunov stability theory and Routh-Hurwitz criteria so as to achieve global chaos synchronization between a parametrically excited gyroscope and each of the parametrically excited pendulum and Duffing oscillator. Numerical simulations are implemented to verify the results.
Further discussion on chaos in duopoly games
International Nuclear Information System (INIS)
Lu, Tianxiu; Zhu, Peiyong
2013-01-01
In this paper, we study Li–Yorke chaos, distributional chaos in a sequence, Li–Yorke sensitivity, sensitivity and distributional chaos of two-dimensional dynamical system of the form Φ(x, y) = (f(y), g(x))
Chaos - a new degree of freedom in nuclear physics
International Nuclear Information System (INIS)
Besliu, Calin.; Jipa, Alexandru; Felea, Daniel
2002-01-01
Before 1985 the chaos representation and its dynamics was known as a mathematical construction generated by the solution instability for the coupled nonlinear differential equations. A number of important needs (the temporal scenarios, a stochastic time scale for nuclear processes, separation between the breakup and statistical processes, nuclear phase transitions at high and very high energies, etc.) determines a focused effort to adapt the chaos theory as a tool for the nuclear physics. In this list, essentially is the distinction between the nonequilibrium and equilibrium states and its general and local balance. The authors report an attempt to introduce the chaos representation in the first stage of the nuclear fragmentation. The trajectories lead to a chaotic behavior at the resonance regime in all cases analyzed. A number of stochastic functions (the Lyapunov exponents, the power functions, the autocorrelation coefficients and the Shannon and Kolmogorov informational entropies) verified the main conclusion. This model, usually called as the 'game of billiards', as studied in the resonance regime, is more realistic than the adiabatic case studied by the Catania-Grenoble group (Burgio, Baldo, Rapisarda, Schuck) which represents the first step for this kind of analysis. A number of properties connected to the chaotic behaviour were related, among them, the influence of the multipolarity of the nuclear barrier on the time required in order to notice the onset of the chaotic behaviour. Also, the connections between the Shannon entropy and chaos suggest the existence of a number of quasi-equilibrium states. (authors)
Asynchronous Rate Chaos in Spiking Neuronal Circuits.
Directory of Open Access Journals (Sweden)
Omri Harish
2015-07-01
Full Text Available The brain exhibits temporally complex patterns of activity with features similar to those of chaotic systems. Theoretical studies over the last twenty years have described various computational advantages for such regimes in neuronal systems. Nevertheless, it still remains unclear whether chaos requires specific cellular properties or network architectures, or whether it is a generic property of neuronal circuits. We investigate the dynamics of networks of excitatory-inhibitory (EI spiking neurons with random sparse connectivity operating in the regime of balance of excitation and inhibition. Combining Dynamical Mean-Field Theory with numerical simulations, we show that chaotic, asynchronous firing rate fluctuations emerge generically for sufficiently strong synapses. Two different mechanisms can lead to these chaotic fluctuations. One mechanism relies on slow I-I inhibition which gives rise to slow subthreshold voltage and rate fluctuations. The decorrelation time of these fluctuations is proportional to the time constant of the inhibition. The second mechanism relies on the recurrent E-I-E feedback loop. It requires slow excitation but the inhibition can be fast. In the corresponding dynamical regime all neurons exhibit rate fluctuations on the time scale of the excitation. Another feature of this regime is that the population-averaged firing rate is substantially smaller in the excitatory population than in the inhibitory population. This is not necessarily the case in the I-I mechanism. Finally, we discuss the neurophysiological and computational significance of our results.
Asynchronous Rate Chaos in Spiking Neuronal Circuits
Harish, Omri; Hansel, David
2015-01-01
The brain exhibits temporally complex patterns of activity with features similar to those of chaotic systems. Theoretical studies over the last twenty years have described various computational advantages for such regimes in neuronal systems. Nevertheless, it still remains unclear whether chaos requires specific cellular properties or network architectures, or whether it is a generic property of neuronal circuits. We investigate the dynamics of networks of excitatory-inhibitory (EI) spiking neurons with random sparse connectivity operating in the regime of balance of excitation and inhibition. Combining Dynamical Mean-Field Theory with numerical simulations, we show that chaotic, asynchronous firing rate fluctuations emerge generically for sufficiently strong synapses. Two different mechanisms can lead to these chaotic fluctuations. One mechanism relies on slow I-I inhibition which gives rise to slow subthreshold voltage and rate fluctuations. The decorrelation time of these fluctuations is proportional to the time constant of the inhibition. The second mechanism relies on the recurrent E-I-E feedback loop. It requires slow excitation but the inhibition can be fast. In the corresponding dynamical regime all neurons exhibit rate fluctuations on the time scale of the excitation. Another feature of this regime is that the population-averaged firing rate is substantially smaller in the excitatory population than in the inhibitory population. This is not necessarily the case in the I-I mechanism. Finally, we discuss the neurophysiological and computational significance of our results. PMID:26230679
The CHAOS-4 Geomagnetic Field Model
DEFF Research Database (Denmark)
Olsen, Nils; Finlay, Chris; Lühr, H.
We present CHAOS-4, a new version in the CHAOS model series, which aims at describing the Earth's magnetic field with high spatial resolution (terms up to spherical degree n=90 for the crustal field, and up to n=16 for the time-varying core field are robustly determined) and high temporal...... between the coordinate systems of the vector magnetometer and of the star sensor providing attitude information). The final CHAOS-4 model is derived by merging two sub-models: its low-degree part has been obtained using similar model parameterization and data sets as used for previous CHAOS models (but...
Nonlinear chaos control and synchronization
Huijberts, H.J.C.; Nijmeijer, H.; Schöll, E.; Schuster, H.G.
2007-01-01
This chapter contains sections titled: Introduction Nonlinear Geometric Control Some Differential Geometric Concepts Nonlinear Controllability Chaos Control Through Feedback Linearization Chaos Control Through Input-Output Linearization Lyapunov Design Lyapunov Stability and Lyapunov's First Method
Cryptography with chaos and shadowing
International Nuclear Information System (INIS)
Smaoui, Nejib; Kanso, Ali
2009-01-01
In this paper, we present a novel approach to encrypt a message (a text composed by some alphabets) using chaos and shadowing. First, we generate a numerical chaotic orbit based on the logistic map, and use the shadowing algorithm of Smaoui and Kostelich [Smaoui N, Kostelich E. Using chaos to shadow the quadratic map for all time. Int J Comput Math 1998;70:117-29] to show that there exists a finite number of true orbits that shadow the numerical orbit. Then, the finite number of maps generated is used in Baptista's algorithm [Baptista MS. Cryptography with chaos. Phys Lett A 1998;240:50-4] to encrypt each character of the message. It is shown that the use of chaos and shadowing in the encryption process enhances the security level.
Cryptography with chaos and shadowing
Energy Technology Data Exchange (ETDEWEB)
Smaoui, Nejib [Department of Mathematics and Computer Science, Kuwait University, P.O. Box 5969, Safat 13060 (Kuwait)], E-mail: nsmaoui64@yahoo.com; Kanso, Ali [Department of Mathematics and Computer Science, Kuwait University, P.O. Box 5969, Safat 13060 (Kuwait)], E-mail: akanso@hotmail.com
2009-11-30
In this paper, we present a novel approach to encrypt a message (a text composed by some alphabets) using chaos and shadowing. First, we generate a numerical chaotic orbit based on the logistic map, and use the shadowing algorithm of Smaoui and Kostelich [Smaoui N, Kostelich E. Using chaos to shadow the quadratic map for all time. Int J Comput Math 1998;70:117-29] to show that there exists a finite number of true orbits that shadow the numerical orbit. Then, the finite number of maps generated is used in Baptista's algorithm [Baptista MS. Cryptography with chaos. Phys Lett A 1998;240:50-4] to encrypt each character of the message. It is shown that the use of chaos and shadowing in the encryption process enhances the security level.
Quantum mechanics theory and experiment
Beck, Mark
2012-01-01
This textbook presents quantum mechanics at the junior/senior undergraduate level. It is unique in that it describes not only quantum theory, but also presents five laboratories that explore truly modern aspects of quantum mechanics. These laboratories include "proving" that light contains photons, single-photon interference, and tests of local realism. The text begins by presenting the classical theory of polarization, moving on to describe the quantum theory of polarization. Analogies between the two theories minimize conceptual difficulties that students typically have when first presented with quantum mechanics. Furthermore, because the laboratories involve studying photons, using photon polarization as a prototypical quantum system allows the laboratory work to be closely integrated with the coursework. Polarization represents a two-dimensional quantum system, so the introduction to quantum mechanics uses two-dimensional state vectors and operators. This allows students to become comfortable with the mat...
Chaos, patterns, coherent structures, and turbulence: Reflections on nonlinear science.
Ecke, Robert E
2015-09-01
The paradigms of nonlinear science were succinctly articulated over 25 years ago as deterministic chaos, pattern formation, coherent structures, and adaptation/evolution/learning. For chaos, the main unifying concept was universal routes to chaos in general nonlinear dynamical systems, built upon a framework of bifurcation theory. Pattern formation focused on spatially extended nonlinear systems, taking advantage of symmetry properties to develop highly quantitative amplitude equations of the Ginzburg-Landau type to describe early nonlinear phenomena in the vicinity of critical points. Solitons, mathematically precise localized nonlinear wave states, were generalized to a larger and less precise class of coherent structures such as, for example, concentrated regions of vorticity from laboratory wake flows to the Jovian Great Red Spot. The combination of these three ideas was hoped to provide the tools and concepts for the understanding and characterization of the strongly nonlinear problem of fluid turbulence. Although this early promise has been largely unfulfilled, steady progress has been made using the approaches of nonlinear science. I provide a series of examples of bifurcations and chaos, of one-dimensional and two-dimensional pattern formation, and of turbulence to illustrate both the progress and limitations of the nonlinear science approach. As experimental and computational methods continue to improve, the promise of nonlinear science to elucidate fluid turbulence continues to advance in a steady manner, indicative of the grand challenge nature of strongly nonlinear multi-scale dynamical systems.
Four dimensional chaos and intermittency in a mesoscopic model of the electroencephalogram.
Dafilis, Mathew P; Frascoli, Federico; Cadusch, Peter J; Liley, David T J
2013-06-01
The occurrence of so-called four dimensional chaos in dynamical systems represented by coupled, nonlinear, ordinary differential equations is rarely reported in the literature. In this paper, we present evidence that Liley's mesoscopic theory of the electroencephalogram (EEG), which has been used to describe brain activity in a variety of clinically relevant contexts, possesses a chaotic attractor with a Kaplan-Yorke dimension significantly larger than three. This accounts for simple, high order chaos for a physiologically admissible parameter set. Whilst the Lyapunov spectrum of the attractor has only one positive exponent, the contracting dimensions are such that the integer part of the Kaplan-Yorke dimension is three, thus giving rise to four dimensional chaos. A one-parameter bifurcation analysis with respect to the parameter corresponding to extracortical input is conducted, with results indicating that the origin of chaos is due to an inverse period doubling cascade. Hence, in the vicinity of the high order, strange attractor, the model is shown to display intermittent behavior, with random alternations between oscillatory and chaotic regimes. This phenomenon represents a possible dynamical justification of some of the typical features of clinically established EEG traces, which can arise in the case of burst suppression in anesthesia and epileptic encephalopathies in early infancy.
Quantum chaos and chiral symmetry at the QCD and QED phase transition
International Nuclear Information System (INIS)
Bittner, Elmar; Markum, Harald; Pullirsch, Rainer
2001-01-01
We investigate the eigenvalue spectrum of the staggered Dirac matrix in SU(3) gauge theory and in full QCD as well as in quenched U(1) theory. As a measure of the fluctuation properties of the eigenvalues, we consider the nearest-neighbor spacing distribution. We find that in all regions of their phase diagrams, compact lattice gauge theories have bulk spectral correlations given by random matrix theory, which is an indication for quantum chaos. In the confinement phase, the low-lying Dirac spectrum of these quantum field theories is well described by random matrix theory, exhibiting universal behavior. Related results for gauge theories with minimal coupling are now discussed also in the chirally symmetric phase
Periodic flows to chaos in time-delay systems
Luo, Albert C J
2017-01-01
This book for the first time examines periodic motions to chaos in time-delay systems, which exist extensively in engineering. For a long time, the stability of time-delay systems at equilibrium has been of great interest from the Lyapunov theory-based methods, where one cannot achieve the ideal results. Thus, time-delay discretization in time-delay systems was used for the stability of these systems. In this volume, Dr. Luo presents an accurate method based on the finite Fourier series to determine periodic motions in nonlinear time-delay systems. The stability and bifurcation of periodic motions are determined by the time-delayed system of coefficients in the Fourier series and the method for nonlinear time-delay systems is equivalent to the Laplace transformation method for linear time-delay systems. Facilitates discovery of analytical solutions of nonlinear time-delay systems; Illustrates bifurcation trees of periodic motions to chaos; Helps readers identify motion complexity and singularity; Explains pro...
International Nuclear Information System (INIS)
Sakata, F.; Marumori, T.; Hashimoto, Y.; Tsukuma, H.; Yamamoto, Y.; Terasaki, J.; Iwasawa, Y.; Itabashi, H.
1992-01-01
Since the research field of nuclear physics is expanding rapidly, it is becoming more imperative to develop the microscopie theory of nuclear matter physics which provides us with a unified understanding of diverse phenomena exhibited by nuclei. An estabishment of various stable mean-fields in nuclei allows us to develop the microscopie theory of nuclear collective dynamics within the mean-field approximation. The classical-level theory of nuclear collective dynamics is developed by exploiting the symplectic structure of the timedependent Hartree-Fock (TDHF)-manifold. The importance of exploring the single-particle dynamics, e.g. the level-crossing dynamics in connection with the classical order-to-chaos transition mechanism is pointed out. Since the classical-level theory os directly related to the full quantum mechanical boson expansion theory via the symplectic structure of the TDHF-manifold, the quantum theory of nuclear collective dynamics is developed at the dictation of what os developed on the classical-level theory. The quantum theory thus formulated enables us to introduce the quantum integrability and quantum chaoticity for individual eigenstates. The inter-relationship between the classical-level and quantum theories of nuclear collective dynamics might play a decisive role in developing the quantum theory of many-body problems. (orig.)
Torus Destruction and Chaos-Chaos Intermittency in a Commodity Distribution Chain
DEFF Research Database (Denmark)
Sosnovtseva, O.; Mosekilde, Erik
1997-01-01
The destruction of two-dimensional tori T2 and the transitions to chaos are studied in a high-dimensional model describing the decision-making behavior of human subjects in a simulated managerial environment (the beer production-distribution model). Two different routes from quasiperiodicity...... to chaos can be distinguished. Intermittency transitions between chaotic and hyperchaotic attractors are characterized, and transients in which the system "pursues the ghost" of a vanished hyperchaotic attractor are studied....
Chaos Modelling with Computers
Indian Academy of Sciences (India)
Chaos is one of the major scientific discoveries of our times. In fact many scientists ... But there are other natural phenomena that are not predictable though ... characteristics of chaos. ... The position and velocity are all that are needed to determine the motion of a .... a system of equations that modelled the earth's weather ...
Chaos resulting from nonlinear relations between different variables
International Nuclear Information System (INIS)
Dohtani, Akitaka
2011-01-01
Research highlights: → We prove a general result on the existence of chaos. → We focus on the cyclic composites of interdependent relations between different variables. → By considering several examples, we conclude that the cyclic composites play an important role in detecting chaotic dynamics. - Abstract: In this study, we further develop the perturbation method of Marotto and investigate the general mechanisms responsible for nonlinear dynamics, which are typical of multidimensional systems. We focus on the composites of interdependent relations between different variables. First, we prove a general result on chaos, which shows that the cyclic composites of nonlinear interdependent relations are sources of chaotic dynamics in multidimensional systems. By considering several examples, we conclude that the cyclic composites play an important role in detecting chaotic dynamics.
Dynamical control of chaos by slave-master feedback
International Nuclear Information System (INIS)
Behnia, S.; Akhshani, A.
2009-01-01
Techniques for stabilizing unstable state in nonlinear dynamical systems using small perturbations fall into three general categories: feedback, non-feedback schemes, and a combination of feedback and non-feedback. However, the general problem of finding conditions for creation or suppression of chaos still remains open. We describe a method for dynamical control of chaos. This method is based on a definition of the hierarchy of solvable chaotic maps with dynamical parameter as a control parameter. In order to study the new mechanism of control of chaotic process, Kolmogorov-Sinai entropy of the chaotic map with dynamical parameter based on discussion the properties of invariant measure have been calculated and confirmed by calculation of Lyapunov exponents. The introduced chaotic maps can be used as dynamical control.
Generating macroscopic chaos in a network of globally coupled phase oscillators
So, Paul; Barreto, Ernest
2011-01-01
We consider an infinite network of globally coupled phase oscillators in which the natural frequencies of the oscillators are drawn from a symmetric bimodal distribution. We demonstrate that macroscopic chaos can occur in this system when the coupling strength varies periodically in time. We identify period-doubling cascades to chaos, attractor crises, and horseshoe dynamics for the macroscopic mean field. Based on recent work that clarified the bifurcation structure of the static bimodal Kuramoto system, we qualitatively describe the mechanism for the generation of such complicated behavior in the time varying case. PMID:21974662
Quasiperiodic transition to chaos in a plasma
International Nuclear Information System (INIS)
Weixing, D.; Huang Wei; Wang Xiaodong; Yu, C.X.
1993-01-01
The quasiperiodic transition to chaos in an undriven discharge plasma has been investigated. Results from the power spectrum and Lyapunov exponents quantitatively confirm the transition to chaos through quasiperiodicity. A low-dimension strange attractor has been found for this kind of plasma chaos
The CHAOS-4 geomagnetic field model
DEFF Research Database (Denmark)
Olsen, Nils; Lühr, H.; Finlay, Chris
2014-01-01
We present CHAOS-4, a new version in the CHAOS model series, which aims to describe the Earth's magnetic field with high spatial and temporal resolution. Terms up to spherical degree of at least n = 85 for the lithospheric field, and up to n = 16 for the time-varying core field are robustly...... to the core field, but the high-degree lithospheric field is regularized for n > 85. CHAOS-4 model is derived by merging two submodels: its low-degree part has been derived using similar model parametrization and data sets as used for previous CHAOS models (but of course including more recent data), while its...
Canonical duality theory unified methodology for multidisciplinary study
Latorre, Vittorio; Ruan, Ning
2017-01-01
This book on canonical duality theory provides a comprehensive review of its philosophical origin, physics foundation, and mathematical statements in both finite- and infinite-dimensional spaces. A ground-breaking methodological theory, canonical duality theory can be used for modeling complex systems within a unified framework and for solving a large class of challenging problems in multidisciplinary fields in engineering, mathematics, and the sciences. This volume places a particular emphasis on canonical duality theory’s role in bridging the gap between non-convex analysis/mechanics and global optimization. With 18 total chapters written by experts in their fields, this volume provides a nonconventional theory for unified understanding of the fundamental difficulties in large deformation mechanics, bifurcation/chaos in nonlinear science, and the NP-hard problems in global optimization. Additionally, readers will find a unified methodology and powerful algorithms for solving challenging problems in comp...
Encounters with chaos and fractals
Gulick, Denny
2012-01-01
Periodic Points Iterates of Functions Fixed Points Periodic Points Families of Functions The Quadratic Family Bifurcations Period-3 Points The Schwarzian Derivative One-Dimensional Chaos Chaos Transitivity and Strong Chaos Conjugacy Cantor Sets Two-Dimensional Chaos Review of Matrices Dynamics of Linear FunctionsNonlinear Maps The Hénon Map The Horseshoe Map Systems of Differential Equations Review of Systems of Differential Equations Almost Linearity The Pendulum The Lorenz System Introduction to Fractals Self-Similarity The Sierpiński Gasket and Other "Monsters"Space-Filling Curves Similarity and Capacity DimensionsLyapunov Dimension Calculating Fractal Dimensions of Objects Creating Fractals Sets Metric Spaces The Hausdorff Metric Contractions and Affine Functions Iterated Function SystemsAlgorithms for Drawing Fractals Complex Fractals: Julia Sets and the Mandelbrot Set Complex Numbers and Functions Julia Sets The Mandelbrot Set Computer Programs Answers to Selected Exercises References Index.
Observation of a Pomeau-Manneville intermittent route to chaos in a nonlinear oscillator
International Nuclear Information System (INIS)
Jeffries, C.; Perez, J.
1982-01-01
For a driven nonlinear semiconductor oscillator which shows a period-doubling pitchfork bifurcation route to chaos, we report an additional route to chaos: the Pomeau-Manneville intermittency route, characterized by a periodic (laminar) phase interrupted by bursts of aperiodic behavior. This occurs near a tangent bifurcation as the system driving parameter is reduced by epsilon from the threshold value for a periodic window. Data are presented for the dependence of the average laminar length on epsilon, and also on additive random noise voltage. The results are in reasonable agreement with the intermittency theory of Hirsch, Huberman, and Scalapino. The distribution P(l) is also reported
Complexity: a new paradigm for fracture mechanics
Directory of Open Access Journals (Sweden)
S. Puzzi
2009-10-01
Full Text Available The so-called Complexity Sciences are a topic of fast growing interest inside the scientific community. Actually, researchers did not come to a definition of complexity, since it manifests itself in so many different ways [1]. This field itself is not a single discipline, but rather a heterogeneous amalgam of different techniques of mathematics and science. In fact, under the label of Complexity Sciences we comprehend a large variety of approaches: nonlinear dynamics, deterministic chaos theory, nonequilibrium thermodynamics, fractal geometry, intermediate asymptotics, complete and incomplete similarity, renormalization group theory, catastrophe theory, self-organized criticality, neural networks, cellular automata, fuzzy logic, etc. Aim of this paper is at providing insight into the role of complexity in the field of Materials Science and Fracture Mechanics [2-3]. The presented examples will be concerned with the snap-back instabilities in the structural behaviour of composite structures (Carpinteri [4-6], the occurrence of fractal patterns and selfsimilarity in material damage and deformation of heterogeneous materials, and the apparent scaling on the nominal mechanical properties of disordered materials (Carpinteri [7,8]. Further examples will deal with criticality in the acoustic emissions of damaged structures and with scaling in the time-to-failure (Carpinteri et al. [9]. Eventually, results on the transition towards chaos in the dynamics of cracked beams will be reported (Carpinteri and Pugno [10,11].
Simulation on control of beam halo-chaos by power function in the hackle periodic-focusing channel
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
The K-V beam through a hackle periodic-focusing magnetic field is studied using the particle-core model. The beam halo-chaos is found, and a power function controller is proposed based on mechanism of halo formation and strategy of controlling halo-chaos. Multiparticle simulation was performed to control the halo by using the power function control method. The results show that the halo-chaos and its regeneration can be eliminated effectively. We also find that the radial particle density evolvement is of uniformity at the beam's centre as long as appropriate paramours are chosen.
Chaos and routes to chaos in coupled Duffing oscillators with multiple degrees of freedom
International Nuclear Information System (INIS)
Musielak, D.E.; Musielak, Z.E.; Benner, J.W.
2005-01-01
New results are reported on the routes to chaos in increasingly complex Duffing oscillator systems, which are formed by coupling several oscillators, thereby increasing the number of degrees of freedom. Other forms of increasing system complexity through distributed excitation, different forcing function phasing, different excitation frequency ratios, and higher order coupling are also studied. Changes in the quantitative aspects of the chaotic regions and in the routes to chaos of complex Duffing systems are investigated by performing numerical simulations. It is shown that the number of chaotic regions in these systems is significantly reduced when compared to the original Duffing system, and that crisis replaces period doubling as the dominant route to chaos when the number of degrees of freedom is increased. A new discovered phenomenon is that chaos emerges in the symmetrically and asymmetrically coupled Duffing oscillators only after the quasi-periodic torus breaks down through a 3-periodic and 2-periodic window, respectively
A phase transition induces chaos in a predator-prey ecosystem with a dynamic fitness landscape.
Gilpin, William; Feldman, Marcus W
2017-07-01
In many ecosystems, natural selection can occur quickly enough to influence the population dynamics and thus future selection. This suggests the importance of extending classical population dynamics models to include such eco-evolutionary processes. Here, we describe a predator-prey model in which the prey population growth depends on a prey density-dependent fitness landscape. We show that this two-species ecosystem is capable of exhibiting chaos even in the absence of external environmental variation or noise, and that the onset of chaotic dynamics is the result of the fitness landscape reversibly alternating between epochs of stabilizing and disruptive selection. We draw an analogy between the fitness function and the free energy in statistical mechanics, allowing us to use the physical theory of first-order phase transitions to understand the onset of rapid cycling in the chaotic predator-prey dynamics. We use quantitative techniques to study the relevance of our model to observational studies of complex ecosystems, finding that the evolution-driven chaotic dynamics confer community stability at the "edge of chaos" while creating a wide distribution of opportunities for speciation during epochs of disruptive selection-a potential observable signature of chaotic eco-evolutionary dynamics in experimental studies.
Accessing Creativity: Jungian Night Sea Journeys, Wandering Minds, and Chaos.
Rosen, Diane
2016-01-01
NDS theory has been meaningfully applied to the dynamics of creativity and psychology. These complex systems have much in common, including a broad definition of "product" as new order emerging from disorder, a new whole (etymologically, 'health') out of disintegration or destabilization. From a nonlinear dynamical systems perspective, this paper explores the far-from-equilibrium zone of creative incubation: first in the Jungian night sea journey, a primordial myth of psychological and creative transformation; then in the neuroscience of mind wandering, the well-spring of creative ideation within the larger neural matrix. Finally, chaos theory grounds the elusive subject of creativity, modeling chaotic generation of idea elements that tend toward strange attractors, combine unpredictably, and produce change by means of tension between opposites, particularly notes consciousness (light) and the poetic unconscious (darkness). Examples from my own artwork illustrate this dialectical process. Considered together, the unconscious mythic sea journey, the unknowing wandering mind, and the generative paradigm of deterministic chaos suggest conditions that facilitate creativity across disciplines, providing fresh indications that the darkness of the unknown or irrational is, paradoxically, the illuminative source and strength of creativity.
International Nuclear Information System (INIS)
Li Qianshu; Zhu Rui
2004-01-01
A three-variable model of the Belousov-Zhabotinsky reaction system subject to external sinusoidal perturbations is investigated by means of frequency spectrum analysis. In the period-1 window of the model, the transitions from periodicity to chaos are observed; in the chaotic window, the transitions from chaos to periodicity are found. The former might be understood by the circle map of two coupled oscillators, and the latter is partly explained by the resonance between the main frequency of the chaos and the frequency of the external periodic perturbations
International Nuclear Information System (INIS)
Shayeghi, H.; Ghasemi, A.
2014-01-01
Highlights: • This paper presents a developed multi objective CIABC based on CLS theory for solving EED problem. • The EED problem is formulated as a non-convex multi objective optimization problem. • Considered three test systems to demonstrate its efficiency including practical constrains. • The significant improvement in the results comparing the reported literature. - Abstract: In this paper, a modified ABC based on chaos theory namely CIABC is comprehensively enhanced and effectively applied for solving a multi-objective EED problem to minimize three conflicting objective functions with non-smooth and non-convex generator fuel cost characteristics while satisfying the operation constraints. The proposed method uses a Chaotic Local Search (CLS) to enhance the self searching ability of the original ABC algorithm for finding feasible optimal solutions of the EED problem. Also, many linear and nonlinear constraints, such as generation limits, transmission line loss, security constraints and non-smooth cost functions are considered as dynamic operational constraints. Moreover, a method based on fuzzy set theory is employed to extract one of the Pareto-optimal solutions as the best compromise one. The proposed multi objective evolutionary method has been applied to the standard IEEE 30 bus six generators, fourteen generators and 40 thermal generating units, respectively, as small, medium and large test power system. The numerical results obtained with the proposed method based on tables and figures compared with other evolutionary algorithm of scientific literatures. The results regards that the proposed CIABC algorithm surpasses the other available methods in terms of computational efficiency and solution quality
Biological conditions for oscillations and chaos generated by multispecies competition
Huisman, J; Weissing, FJ
2001-01-01
We investigate biological mechanisms that generate oscillations and chaos in multispecies competition models. For this purpose, we use a competition model concerned with competition for abiotic essential resources. Because phytoplankton and plants consume quite a number of abiotic essential
[Dynamic paradigm in psychopathology: "chaos theory", from physics to psychiatry].
Pezard, L; Nandrino, J L
2001-01-01
For the last thirty years, progress in the field of physics, known as "Chaos theory"--or more precisely: non-linear dynamical systems theory--has increased our understanding of complex systems dynamics. This framework's formalism is general enough to be applied in other domains, such as biology or psychology, where complex systems are the rule rather than the exception. Our goal is to show here that this framework can become a valuable tool in scientific fields such as neuroscience and psychiatry where objects possess natural time dependency (i.e. dynamical properties) and non-linear characteristics. The application of non-linear dynamics concepts on these topics is more precise than a loose metaphor and can throw a new light on mental functioning and dysfunctioning. A class of neural networks (recurrent neural networks) constitutes an example of the implementation of the dynamical system concept and provides models of cognitive processes (15). The state of activity of the network is represented in its state space and the time evolution of this state is a trajectory in this space. After a period of time those networks settle on an equilibrium (a kind of attractor). The strength of connections between neurons define the number and relations between those attractors. The attractors of the network are usually interpreted as "mental representations". When an initial condition is imposed to the network, the evolution towards an attractor is considered as a model of information processing (27). This information processing is not defined in a symbolic manner but is a result of the interaction between distributed elements. Several properties of dynamical models can be used to define a way where the symbolic properties emerge from physical and dynamical properties (28) and thus they can be candidates for the definition of the emergence of mental properties on the basis of neuronal dynamics (42). Nevertheless, mental properties can also be considered as the result of an
Quantum chaos: statistical relaxation in discrete spectrum
International Nuclear Information System (INIS)
Chirikov, B.V.
1990-01-01
The controversial phenomenon of quantum chaos is discussed using the quantized standard map, or the kicked rotator, as a simple model. The relation to the classical dynamical chaos is tracked down on the basis of the correspondence principle. Several definitions of the quantum chaos are discussed. 27 refs
FROM ORDER TO CHAOS IN EARTH SATELLITE ORBITS
Energy Technology Data Exchange (ETDEWEB)
Gkolias, Ioannis; Gachet, Fabien [Department of Mathematics, University of Rome Tor Vergata, I-00133 Rome (Italy); Daquin, Jérôme [IMCCE/Observatoire de Paris, Université Lille1, F-59000 Lille (France); Rosengren, Aaron J., E-mail: gkolias@mat.uniroma2.it [IFAC-CNR, 50019 Sesto Fiorentino, Florence (Italy)
2016-11-01
We consider Earth satellite orbits in the range of semimajor axes where the perturbing effects of Earth’s oblateness and lunisolar gravity are of comparable order. This range covers the medium-Earth orbits (MEO) of the Global Navigation Satellite Systems and the geosynchronous orbits (GEO) of the communication satellites. We recall a secular and quadrupolar model, based on the Milankovitch vector formulation of perturbation theory, which governs the long-term orbital evolution subject to the predominant gravitational interactions. We study the global dynamics of this two-and-a-half degrees-of-freedom Hamiltonian system by means of the fast Lyapunov indicator (FLI), used in a statistical sense. Specifically, we characterize the degree of chaoticity of the action space using angle-averaged normalized FLI maps, thereby overcoming the angle dependencies of the conventional stability maps. Emphasis is placed upon the phase-space structures near secular resonances, which are of primary importance to the space debris community. We confirm and quantify the transition from order to chaos in MEO, stemming from the critical inclinations and find that highly inclined GEO orbits are particularly unstable. Despite their reputed normality, Earth satellite orbits can possess an extraordinarily rich spectrum of dynamical behaviors and, from a mathematical perspective, have all the complications that make them very interesting candidates for testing the modern tools of chaos theory.
International Nuclear Information System (INIS)
Mueller, B.
1997-01-01
The report contains viewgraphs on the following: ergodicity and chaos; Hamiltonian dynamics; metric properties; Lyapunov exponents; KS entropy; dynamical realization; lattice formulation; and numerical results
Energy Technology Data Exchange (ETDEWEB)
Mueller, B.
1997-09-22
The report contains viewgraphs on the following: ergodicity and chaos; Hamiltonian dynamics; metric properties; Lyapunov exponents; KS entropy; dynamical realization; lattice formulation; and numerical results.
Recent results in quantum chaos and its applications to nuclei and particles
International Nuclear Information System (INIS)
Gomez, J.M.G.; Retamosa, J.; Munoz, L.; Relano, A.; Molina, R.A.; Faleiro, E.
2013-01-01
In the last decade or so, the study of chaos in nuclei and other quantum systems has been a very active research field. Besides work based on random matrix theory, new theoretical developments making use of information theory, time series analysis, and the merging of thermodynamics and the semiclassical approximation have been published. In this talk, a survey of chaotic dynamics in atomic nuclei is presented, using on the one hand standard statistics of quantum chaos studies, as well as time series analysis methods. We emphasize the energy and isospin dependence of nuclear chaoticity, based on shell-model energy spectra fluctuations in Ca, Sc and Ti isotopes, which are analyzed using standard statistics such as the nearest level spacing distribution P(s) and the Dyson-Mehta Δ 3 statistic. We also discuss quantum chaos in general using a new approach based on the analogy between the sequence of energy levels and a discrete time series. Considering the energy spectrum fluctuations as a discrete time series, we have shown that chaotic quantum systems such as 24 Mg and 32 Na nuclei, quantum billiards, and random matrix theory (RMT) ensembles, exhibit 1/f noise in their power spectrum. Moreover, we show that the spectra of integrable quantum systems exhibit 1/f 2 noise. Therefore we suggest the following conjecture: The energy spectra of chaotic quantum systems are characterized by 1/f noise. We have also derived an analytic expression for the energy level fluctuations power spectrum of RMT ensembles, and the results confirm the above conjecture. The order to chaos transition has been studied in terms of this power spectrum for several intermediate systems, such as the Robnik billiard, the quartic oscillator or the kicked top. A power law 1/f is found at all the transition stages, and it is shown that the exponent β is related to the chaotic component of the classical phase space of the quantum system. This approach has also been applied to study the possible
Endodontic inter-appointment flare-ups: An example of chaos?
Directory of Open Access Journals (Sweden)
Poorya Jalali
2015-01-01
Full Text Available Introduction: Pain and/or swelling after instrumentation of a root canal constitute a significant complication during endodontic treatment. Despite a large number of articles discussing the causative factors behind endodontic flare-ups, the exact mechanism is still not understood. The Hypothesis: The seemingly irrational behavior of endodontic inter-appointment flare-ups may be due to sensitive dependence on initial conditions. A model based on Lorenz′ chaos theory is presented as a possible explanation for the sudden emergence and unpredictability of flare-ups. Evaluation of the Hypothesis: All studies agree on some common traits regarding inter-appointment flare-ups: Careful instrumentation can still cause flare-up; the host inflammatory response behaves as a complex nonlinear network; and also the poly-etiologic nature of this phenomenon all illustrate the sensitive dependence on initial conditions of the system. Integrating more variables (e.g., different species of bacteria into this already complex system will make it increasingly chaotic reflecting its unpredictable behavior.
Chaos in body-vortex interactions
DEFF Research Database (Denmark)
Pedersen, Johan Rønby; Aref, Hassan
2010-01-01
of a circle is integrable. As the body is made slightly elliptic, a chaotic region grows from an unstable relative equilibrium of the circle-vortex case. The case of a cylindrical body of any shape moving in fluid otherwise at rest is also integrable. A second transition to chaos arises from the limit between...... rocking and tumbling motion of the body known in this case. In both instances, the chaos may be detected both in the body motion and in the vortex motion. The effect of increasing body mass at a fixed body shape is to damp the chaos....
PHASE CHAOS IN THE DISCRETE KURAMOTO MODEL
DEFF Research Database (Denmark)
Maistrenko, V.; Vasylenko, A.; Maistrenko, Y.
2010-01-01
The paper describes the appearance of a novel, high-dimensional chaotic regime, called phase chaos, in a time-discrete Kuramoto model of globally coupled phase oscillators. This type of chaos is observed at small and intermediate values of the coupling strength. It arises from the nonlinear...... interaction among the oscillators, while the individual oscillators behave periodically when left uncoupled. For the four-dimensional time-discrete Kuramoto model, we outline the region of phase chaos in the parameter plane and determine the regions where phase chaos coexists with different periodic...
Robinson's chaos in set-valued discrete systems
International Nuclear Information System (INIS)
Roman-Flores, Heriberto; Chalco-Cano, Y.
2005-01-01
Let (X,d) be a compact metric space and f:X->X a continuous function. If we consider the space (K(X),H) of all non-empty compact subsets of X endowed with the Hausdorff metric induced by d and f-bar :K(X)->K(X), f-bar (A)={f(a)/a-bar A}, then the aim of this work is to show that Robinson's chaos in f-bar implies Robinson's chaos in f. Also, we give an example showing that R-chaos in f does not implies R-chaos in f-bar
The chaos cookbook a practical programming guide
Pritchard, Joe
2014-01-01
The Chaos Cookbook: A Practical Programming Guide discusses the use of chaos in computer programming. The book is comprised of 11 chapters that tackle various topics relevant to chaos and programming. Chapter 1 reviews the concept of chaos, and Chapter 2 discusses the iterative functions. Chapters 3 and 4 cover differential and Lorenz equations. Chapter 5 talks about strange attractors, while Chapter 6 deals with the fractal link. The book also discusses the Mandelbrot set, and then covers the Julia sets. The other fractal systems and the cellular automata are also explained. The last chapter
How to test for partially predictable chaos.
Wernecke, Hendrik; Sándor, Bulcsú; Gros, Claudius
2017-04-24
For a chaotic system pairs of initially close-by trajectories become eventually fully uncorrelated on the attracting set. This process of decorrelation can split into an initial exponential decrease and a subsequent diffusive process on the chaotic attractor causing the final loss of predictability. Both processes can be either of the same or of very different time scales. In the latter case the two trajectories linger within a finite but small distance (with respect to the overall extent of the attractor) for exceedingly long times and remain partially predictable. Standard tests for chaos widely use inter-orbital correlations as an indicator. However, testing partially predictable chaos yields mostly ambiguous results, as this type of chaos is characterized by attractors of fractally broadened braids. For a resolution we introduce a novel 0-1 indicator for chaos based on the cross-distance scaling of pairs of initially close trajectories. This test robustly discriminates chaos, including partially predictable chaos, from laminar flow. Additionally using the finite time cross-correlation of pairs of initially close trajectories, we are able to identify laminar flow as well as strong and partially predictable chaos in a 0-1 manner solely from the properties of pairs of trajectories.
Energy Technology Data Exchange (ETDEWEB)
Bolotin, IU L; Gonchar, V IU; Truten, V I; Shulga, N F
1986-01-01
It is shown that axial channeling of relativistic electrons can give rise to the effect of dynamic chaos which involves essentially chaotic motion of a particle in the channel. The conditions leading to the effect of dynamic chaos and the manifestations of this effect in physical processes associated with the passage of particles through a crystal are examined using a silicon crystal as an example. 7 references.
Deterministic chaos in entangled eigenstates
Schlegel, K. G.; Förster, S.
2008-05-01
We investigate the problem of deterministic chaos in connection with entangled states using the Bohmian formulation of quantum mechanics. We show for a two particle system in a harmonic oscillator potential, that in a case of entanglement and three energy eigen-values the maximum Lyapunov-parameters of a representative ensemble of trajectories for large times develops to a narrow positive distribution, which indicates nearly complete chaotic dynamics. We also present in short results from two time-dependent systems, the anisotropic and the Rabi oscillator.
Deterministic chaos in entangled eigenstates
Energy Technology Data Exchange (ETDEWEB)
Schlegel, K.G. [Fakultaet fuer Physik, Universitaet Bielefeld, Postfach 100131, D-33501 Bielefeld (Germany)], E-mail: guenter.schlegel@arcor.de; Foerster, S. [Fakultaet fuer Physik, Universitaet Bielefeld, Postfach 100131, D-33501 Bielefeld (Germany)
2008-05-12
We investigate the problem of deterministic chaos in connection with entangled states using the Bohmian formulation of quantum mechanics. We show for a two particle system in a harmonic oscillator potential, that in a case of entanglement and three energy eigen-values the maximum Lyapunov-parameters of a representative ensemble of trajectories for large times develops to a narrow positive distribution, which indicates nearly complete chaotic dynamics. We also present in short results from two time-dependent systems, the anisotropic and the Rabi oscillator.
Deterministic chaos in entangled eigenstates
International Nuclear Information System (INIS)
Schlegel, K.G.; Foerster, S.
2008-01-01
We investigate the problem of deterministic chaos in connection with entangled states using the Bohmian formulation of quantum mechanics. We show for a two particle system in a harmonic oscillator potential, that in a case of entanglement and three energy eigen-values the maximum Lyapunov-parameters of a representative ensemble of trajectories for large times develops to a narrow positive distribution, which indicates nearly complete chaotic dynamics. We also present in short results from two time-dependent systems, the anisotropic and the Rabi oscillator
Homoclinic tubes and chaos in perturbed sine-Gordon equation
International Nuclear Information System (INIS)
Li, Y. Charles
2004-01-01
Sine-Gordon equation under a quasi-periodic perturbation or a chaotic perturbation is studied. Existence of a homoclinic tube is proved. Established are chaos associated with the homoclinic tube, and 'chaos cascade' referring to the embeddings of smaller scale chaos in larger scale chaos
Coherence and chaos in extended dynamical systems
International Nuclear Information System (INIS)
Bishop, A.R.
1994-01-01
Coherence, chaos, and pattern formation are characteristic elements of the nonequilibrium statistical mechanics controlling mesoscopic order and disorder in many-degree-of-freedom nonlinear dynamical systems. Competing length scales and/or time scales are the underlying microscopic driving forces for many of these aspects of ''complexity.'' We illustrate the basic concepts with some model examples of classical and quantum, ordered and disordered, nonlinear systems
Chaos and complexity by design
Energy Technology Data Exchange (ETDEWEB)
Roberts, Daniel A. [Center for Theoretical Physics and Department of Physics,Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States); School of Natural Sciences, Institute for Advanced Study,Princeton, NJ 08540 (United States); Yoshida, Beni [Perimeter Institute for Theoretical Physics,Waterloo, Ontario N2L 2Y5 (Canada)
2017-04-20
We study the relationship between quantum chaos and pseudorandomness by developing probes of unitary design. A natural probe of randomness is the “frame potential,” which is minimized by unitary k-designs and measures the 2-norm distance between the Haar random unitary ensemble and another ensemble. A natural probe of quantum chaos is out-of-time-order (OTO) four-point correlation functions. We show that the norm squared of a generalization of out-of-time-order 2k-point correlators is proportional to the kth frame potential, providing a quantitative connection between chaos and pseudorandomness. Additionally, we prove that these 2k-point correlators for Pauli operators completely determine the k-fold channel of an ensemble of unitary operators. Finally, we use a counting argument to obtain a lower bound on the quantum circuit complexity in terms of the frame potential. This provides a direct link between chaos, complexity, and randomness.
Chaos and complexity by design
International Nuclear Information System (INIS)
Roberts, Daniel A.; Yoshida, Beni
2017-01-01
We study the relationship between quantum chaos and pseudorandomness by developing probes of unitary design. A natural probe of randomness is the “frame potential,” which is minimized by unitary k-designs and measures the 2-norm distance between the Haar random unitary ensemble and another ensemble. A natural probe of quantum chaos is out-of-time-order (OTO) four-point correlation functions. We show that the norm squared of a generalization of out-of-time-order 2k-point correlators is proportional to the kth frame potential, providing a quantitative connection between chaos and pseudorandomness. Additionally, we prove that these 2k-point correlators for Pauli operators completely determine the k-fold channel of an ensemble of unitary operators. Finally, we use a counting argument to obtain a lower bound on the quantum circuit complexity in terms of the frame potential. This provides a direct link between chaos, complexity, and randomness.
Quantum chaos: diffusion photoeffect in hydrogen
Energy Technology Data Exchange (ETDEWEB)
Shepelyanskij, D L
1987-05-01
Ionization process in highly excited hydrogen atom in electromagnetic field is presented in the form of an extraordinary photoeffect, in which ionization at the frequency, being much lower than ionization energy, occurs much quicker than single-photon one. Such a quick ionization is explained by dynamic chaos occurence. Question, related to quantum effect influence on chaotic movement of the electron (quantum chaos) is considered. Electron excitation in the chaos area is described by a diffusional equation.
Chaos for cardiac arrhythmias through a one-dimensional modulation equation for alternans
Dai, Shu; Schaeffer, David G.
2010-01-01
Instabilities in cardiac dynamics have been widely investigated in recent years. One facet of this work has studied chaotic behavior, especially possible correlations with fatal arrhythmias. Previously chaotic behavior was observed in various models, specifically in the breakup of spiral and scroll waves. In this paper we study cardiac dynamics and find spatiotemporal chaotic behavior through the Echebarria–Karma modulation equation for alternans in one dimension. Although extreme parameter values are required to produce chaos in this model, it seems significant mathematically that chaos may occur by a different mechanism from previous observations. PMID:20590327
Straus, Christian; Samara, Ziyad; Fiamma, Marie-Noëlle; Bautin, Nathalie; Ranohavimparany, Anja; Le Coz, Patrick; Golmard, Jean-Louis; Darré, Pierre; Zelter, Marc; Poon, Chi-Sang; Similowski, Thomas
2011-05-01
Human ventilation at rest exhibits mathematical chaos-like complexity that can be described as long-term unpredictability mediated (in whole or in part) by some low-dimensional nonlinear deterministic process. Although various physiological and pathological situations can affect respiratory complexity, the underlying mechanisms remain incompletely elucidated. If such chaos-like complexity is an intrinsic property of central respiratory generators, it should appear or increase when these structures mature or are stimulated. To test this hypothesis, we employed the isolated tadpole brainstem model [Rana (Pelophylax) esculenta] and recorded the neural respiratory output (buccal and lung rhythms) of pre- (n = 8) and postmetamorphic tadpoles (n = 8), at physiologic (7.8) and acidic pH (7.4). We analyzed the root mean square of the cranial nerve V or VII neurograms. Development and acidosis had no effect on buccal period. Lung frequency increased with development (P acidosis, but in postmetamorphic tadpoles only (P respiratory central rhythm generator accounts for ventilatory chaos-like complexity, especially in the postmetamorphic stage and at low pH. According to the ventilatory generators homology theory, this may also be the case in mammals.
Measurement theory in quantum mechanics
International Nuclear Information System (INIS)
Klein, G.
1980-01-01
It is assumed that consciousness, memory and liberty (within the limits of the quantum mechanics indeterminism) are fundamental properties of elementary particles. Then, using this assumption it is shown how measurements and observers may be introduced in a natural way in the quantum mechanics theory. There are no longer fundamental differences between macroscopic and microscopic objects, between classical and quantum objects, between observer and object. Thus, discrepancies and paradoxes have disappeared from the conventional quantum mechanics theory. One consequence of the cumulative memory of the particles is that the sum of negentropy plus information is a constant. Using this theory it is also possible to explain the 'paranormal' phenomena and what is their difference from the 'normal' ones [fr
Navigating Through Chaos: Charge Nurses and Patient Safety.
Cathro, Heather
2016-04-01
The aim of this study was to explore actions and the processes charge nurses (CNs) implement to keep patients safe and generate an emerging theory to inform CN job descriptions, orientation, and training to promote patient safety in practice. Healthcare workers must provide a safe environment for patients. CNs are the frontline leaders on most hospital units and can function as gatekeepers for safe patient care. This grounded theory study utilized purposive sampling of CNs on medical-surgical units in a 400-bed metropolitan hospital. Data collection consisted of 11 interviews and 6 observations. The emerging theory was navigating through chaos: CNs balancing multiple roles, maintaining a watchful eye, and working with and leading the healthcare team to keep patients safe. CNs have knowledge of patients, staff, and complex healthcare environments, putting them in opportune positions to influence patient safety.
Chaos and bifurcations in periodic windows observed in plasmas
International Nuclear Information System (INIS)
Qin, J.; Wang, L.; Yuan, D.P.; Gao, P.; Zhang, B.Z.
1989-01-01
We report the experimental observations of deterministic chaos in a steady-state plasma which is not driven by any extra periodic forces. Two routes to chaos have been found, period-doubling and intermittent chaos. The fine structures in chaos such as periodic windows and bifurcations in windows have also been observed
International Nuclear Information System (INIS)
Soloviev, V.G.
1995-01-01
Order and chaos and order-to-chaos transition are treated in terms of nuclear wave functions. A quasiparticle-phonon interaction is responsible for the fragmentation of one- and many-quasiparticle and phonon states and for the mixing of closely spaced states. Complete damping of one-quasiparticle states cannot be considered as a transition to chaos due to large many-quasiparticle or quasiparticle-phonon terms in their wave functions. An experimental investigation of the strength distribution of many-quasiparticle and quasiparticle-phonon states should uncover a new region of a regularity in nuclei at intermediate excitation energy. A chaotic behaviour of nuclear states can be shifted to higher excitation energies. ((orig.))
Universal signatures of quantum chaos
International Nuclear Information System (INIS)
Aurich, R.; Bolte, J.; Steiner, F.
1994-02-01
We discuss fingerprints of classical chaos in spectra of the corresponding bound quantum systems. A novel quantity to measure quantum chaos in spectra is proposed and a conjecture about its universal statistical behaviour is put forward. Numerical as well as theoretical evidence is provided in favour of the conjecture. (orig.)
Order out of chaos in atomic nuclei
Energy Technology Data Exchange (ETDEWEB)
Rotter, I
1988-07-01
The transition from the resonance reaction mechanism at low level density to the direct reaction mechanism at high level density is investigated by means of numerical results obtained from microscopic calculations for nucleon-induced reactions. The transition takes place rather sharply at GAMMA approx. = D-bar. Here, two types of motion of the nucleons exist simultaneously: a motion in long-living states which are near equilibrium and a motion in short-living states which are far from equilibrium. A formation of order out of chaos takes place only in the open quantum mechanical nuclear system. It is caused by quantum fluctuations via the continuum.
Household chaos and family sleep during infants' first year.
Whitesell, Corey J; Crosby, Brian; Anders, Thomas F; Teti, Douglas M
2018-05-21
Household chaos has been linked with dysregulated family and individual processes. The present study investigated linkages between household chaos and infant and parent sleep, a self-regulated process impacted by individual, social, and environmental factors. Studies of relations between household chaos and child sleep have focused on older children and teenagers, with little attention given to infants or parent sleep. This study examines these relationships using objective measures of household chaos and sleep while controlling for, respectively, maternal emotional availability at bedtime and martial adjustment, in infant and parent sleep. Multilevel modeling examined mean and variability of sleep duration and fragmentation for infants, mothers, and fathers when infants were 1, 3, 6, 9, and 12 months (N = 167). Results indicated infants in higher chaos homes experienced delays in sleep consolidation patterns, with longer and more variable sleep duration, and greater fragmentation. Parent sleep was also associated with household chaos such that in higher chaos homes, mothers and fathers experienced greater variability in sleep duration, which paralleled infant findings. In lower chaos homes, parents' sleep fragmentation mirrored infants' decreasingly fragmented sleep across the first year and remained lower at all timepoints compared to parents and infants in high chaos homes. Collectively, these findings indicate that after controlling for maternal emotional availability and marital adjustment (respectively) household chaos has a dysregulatory impact on infant and parent sleep. Results are discussed in terms of the potential for chaos-induced poor sleep to dysregulate daytime functioning and, in turn, place parent-infant relationships at risk. (PsycINFO Database Record (c) 2018 APA, all rights reserved).
Resurvey of order and chaos in spinning compact binaries
International Nuclear Information System (INIS)
Wu Xin; Xie Yi
2008-01-01
This paper is mainly devoted to applying the invariant, fast, Lyapunov indicator to clarify some doubt regarding the apparently conflicting results of chaos in spinning compact binaries at the second-order post-Newtonian approximation of general relativity from previous literatures. It is shown with a number of examples that no single physical parameter or initial condition can be described as responsible for causing chaos, but a complicated combination of all parameters and initial conditions is responsible. In other words, a universal rule for the dependence of chaos on each parameter or initial condition cannot be found in general. Chaos does not depend only on the mass ratio, and the maximal spins do not necessarily bring the strongest effect of chaos. Additionally, chaos does not always become drastic when the initial spin vectors are nearly perpendicular to the orbital plane, and the alignment of spins cannot trigger chaos by itself
Chaotic behavior of seismic mechanisms: experiment and observation
Directory of Open Access Journals (Sweden)
Mourad Bezzeghoud
2012-04-01
Full Text Available
To simulate the dynamics of earthquakes, a mechanical prototype was constructed that was inspired by the Burridge-Knopoff model and equipped with accurate instrumental devices. The data obtained by the prototype appeared to be consistent with seismic data from the San Andreas Fault, California, USA, which were analyzed using two different methodologies: seismology and modern developments of chaos theory. Perspectives for future work are also presented.
The three versions of distributional chaos
International Nuclear Information System (INIS)
Balibrea, F.; Smital, J.; Stefankova, M.
2005-01-01
The notion of distributional chaos was introduced by Schweizer and Smital [Trans. Amer. Math. Soc. 344 (1994) 737] for continuous maps of the interval. However, it turns out that, for continuous maps of a compact metric space three mutually nonequivalent versions of distributional chaos, DC1-DC3, can be considered. In this paper we consider the weakest one, DC3. We show that DC3 does not imply chaos in the sense of Li and Yorke. We also show that DC3 is not invariant with respect to topological conjugacy. In other words, there are lower and upper distribution functions Φ xy and Φxy* generated by a continuous map f of a compact metric space (M, ρ) such that Φxy*(t)>Φxy(t) for all t in an interval. However, f on the same space M, but with a metric ρ' generating the same topology as ρ is no more DC3.Recall that, contrary to this, either DC1 or DC2 is topological conjugacy invariant and implies Li and Yorke chaos (cf. [Chaos, Solitons and Fractals 21 (2004) 1125])
Chaotic dynamics and chaos control in nonlinear laser systems
International Nuclear Information System (INIS)
Fang Jinqing; Yao Weiguang
2001-01-01
Chaotic dynamics and chaos control have become a great challenge in nonlinear laser systems and its advances are reviewed mainly based on the ring cavity laser systems. The principle and stability conditions for time-delay feedback control are analyzed and applied to chaos control in the laser systems. Other advanced methods of chaos control, such as weak spatial perturbation and occasional proportional feedback technique, are discussed. Prospects of chaos control for application (such as improvement of laser power and performance, synchronized chaos secure communication and information processing) are pointed out finally
Angius, S.; Bisegni, C.; Ciuffetti, P.; Di Pirro, G.; Foggetta, L. G.; Galletti, F.; Gargana, R.; Gioscio, E.; Maselli, D.; Mazzitelli, G.; Michelotti, A.; Orrù, R.; Pistoni, M.; Spagnoli, F.; Spigone, D.; Stecchi, A.; Tonto, T.; Tota, M. A.; Catani, L.; Di Giulio, C.; Salina, G.; Buzzi, P.; Checcucci, B.; Lubrano, P.; Piccini, M.; Fattibene, E.; Michelotto, M.; Cavallaro, S. R.; Diana, B. F.; Enrico, F.; Pulvirenti, S.
2016-01-01
The paper is aimed to present the !CHAOS open source project aimed to develop a prototype of a national private Cloud Computing infrastructure, devoted to accelerator control systems and large experiments of High Energy Physics (HEP). The !CHAOS project has been financed by MIUR (Italian Ministry of Research and Education) and aims to develop a new concept of control system and data acquisition framework by providing, with a high level of aaabstraction, all the services needed for controlling and managing a large scientific, or non-scientific, infrastructure. A beta version of the !CHAOS infrastructure will be released at the end of December 2015 and will run on private Cloud infrastructures based on OpenStack.
International Nuclear Information System (INIS)
Angius, S.; Bisegni, C.; Ciuffetti, P.
2016-01-01
The paper is aimed to present the !CHAOS open source project aimed to develop a prototype of a national private Cloud Computing infrastructure, devoted to accelerator control systems and large experiments of High Energy Physics (HEP). The !CHAOS project has been financed by MIUR (Italian Ministry of Research and Education) and aims to develop a new concept of control system and data acquisition framework by providing, with a high level of abstraction, all the services needed for controlling and managing a large scientific, or non-scientific, infrastructure. A beta version of the !CHAOS infrastructure will be released at the end of December 2015 and will run on private Cloud infrastructures based on OpenStack.
International Nuclear Information System (INIS)
Turiaci, Gustavo J.; Verlinde, Herman
2016-01-01
We make three observations that help clarify the relation between CFT and quantum chaos. We show that any 1+1-D system in which conformal symmetry is non-linearly realized exhibits two main characteristics of chaos: maximal Lyapunov behavior and a spectrum of Ruelle resonances. We use this insight to identify a lattice model for quantum chaos, built from parafermionic spin variables with an equation of motion given by a Y-system. Finally we point to a relation between the spectrum of Ruelle resonances of a CFT and the analytic properties of OPE coefficients between light and heavy operators. In our model, this spectrum agrees with the quasi-normal modes of the BTZ black hole.
Energy Technology Data Exchange (ETDEWEB)
Turiaci, Gustavo J. [Physics Department, Princeton University,Princeton NJ 08544 (United States); Verlinde, Herman [Physics Department, Princeton University,Princeton NJ 08544 (United States); Princeton Center for Theoretical Science, Princeton University,Princeton NJ 08544 (United States)
2016-12-21
We make three observations that help clarify the relation between CFT and quantum chaos. We show that any 1+1-D system in which conformal symmetry is non-linearly realized exhibits two main characteristics of chaos: maximal Lyapunov behavior and a spectrum of Ruelle resonances. We use this insight to identify a lattice model for quantum chaos, built from parafermionic spin variables with an equation of motion given by a Y-system. Finally we point to a relation between the spectrum of Ruelle resonances of a CFT and the analytic properties of OPE coefficients between light and heavy operators. In our model, this spectrum agrees with the quasi-normal modes of the BTZ black hole.
Homoclinic chaos and energy condition violation
International Nuclear Information System (INIS)
Heinzle, J. Mark; Roehr, Niklas; Uggla, Claes
2006-01-01
In this letter we discuss the connection between so-called homoclinic chaos and the violation of energy conditions in locally rotationally symmetric Bianchi type IX models, where the matter is assumed to be nontilted dust and a positive cosmological constant. We show that homoclinic chaos in these models is an artifact of unphysical assumptions: it requires that there exist solutions with positive matter energy density ρ>0 that evolve through the singularity and beyond as solutions with negative matter energy density ρ<0. Homoclinic chaos is absent when it is assumed that the dust particles always retain their positive mass. In addition, we discuss more general models: for solutions that are not locally rotationally symmetric we demonstrate that the construction of extensions through the singularity, which is required for homoclinic chaos, is not possible in general
International Nuclear Information System (INIS)
Scheck, Florian
2010-01-01
Stringent presentation of field theory, mediates the connection from the classicalelectrodynamics up to modern gauge theories. The compact presentation is ideal for the bachelor study. New chapter on general relativity theory. Deepens the learned by numerous application from laser physic, metamaterials and different more. Theoretical physics 3. Classical field theory. On electrodynamics, non-Abelian, and gravitation is the third of five volumes on theoretical physics by professor Scheck. The cycle theoretical physics comprehends: Volume 1: Mechanics. From Newtons law to the deterministic chaos. Volume 2: Nonrelativistic quantum theory. From the hydrogen atom to the many-particle systems. Volume 3: Classical field theory. From the electrodynamics to the gauge theories. Volume 5: From the laws of thermodynamics to the quantum statistics. This textbook mediates modern theoretical physics in string presentation illustrated by many examples. It contains numerous problems with solution hints ore exemplary, complete solutions. The third edition was revised in many single topics, especially the chapter on general relativity theory was supplemented by an extensive analysis of the Schwarzschild solution. [de
2005-01-01
[figure removed for brevity, see original site] Context image for PIA03200 Iani Chaos This VIS image of Iani Chaos shows the layered deposit that occurs on the floor. It appears that the layers were deposited after the chaos was formed. Image information: VIS instrument. Latitude 2.3S, Longitude 342.3E. 17 meter/pixel resolution. Note: this THEMIS visual image has not been radiometrically nor geometrically calibrated for this preliminary release. An empirical correction has been performed to remove instrumental effects. A linear shift has been applied in the cross-track and down-track direction to approximate spacecraft and planetary motion. Fully calibrated and geometrically projected images will be released through the Planetary Data System in accordance with Project policies at a later time. NASA's Jet Propulsion Laboratory manages the 2001 Mars Odyssey mission for NASA's Office of Space Science, Washington, D.C. The Thermal Emission Imaging System (THEMIS) was developed by Arizona State University, Tempe, in collaboration with Raytheon Santa Barbara Remote Sensing. The THEMIS investigation is led by Dr. Philip Christensen at Arizona State University. Lockheed Martin Astronautics, Denver, is the prime contractor for the Odyssey project, and developed and built the orbiter. Mission operations are conducted jointly from Lockheed Martin and from JPL, a division of the California Institute of Technology in Pasadena.
Semiconductor Lasers Stability, Instability and Chaos
Ohtsubo, Junji
2008-01-01
This monograph describes fascinating recent progress in the field of chaos, stability and instability of semiconductor lasers. Applications and future prospects are discussed in detail. The book emphasizes the various dynamics induced in semiconductor lasers by optical and electronic feedback, optical injection, and injection current modulation. Recent results of both theoretical and experimental investigations are presented. Demonstrating applications of semiconductor laser chaos, control and noise, Semiconductor Lasers describes suppression and chaotic secure communications. For those who are interested in optics but not familiar with nonlinear systems, a brief introduction to chaos analysis is presented.
Chua's circuit a paradigm for chaos
1993-01-01
For uninitiated researchers, engineers, and scientists interested in a quick entry into the subject of chaos, this book offers a timely collection of 55 carefully selected papers covering almost every aspect of this subject. Because Chua's circuit is endowed with virtually every bifurcation phenomena reported in the extensive literature on chaos, and because it is the only chaotic system which can be easily built by a novice, simulated in a personal computer, and tractable mathematically, it has become a paradigm for chaos, and a vehicle for illustrating this ubiquitous phenomenon. Its supreme
2017-01-20
AFRL-AFOSR-JP-TR-2017-0012 The Strength of Chaos : accurate simulation of resonant electron scattering by many-electron ions and atoms in the presence...of quantum chaos Igor Bray CURTIN UNIVERSITY OF TECHNOLOGY Final Report 01/20/2017 DISTRIBUTION A: Distribution approved for public release. AF...SUBTITLE The Strength of Chaos : accurate simulation of resonant electron scattering by many- electron ions and atoms in the presence of quantum chaos
Integrability and chaos in body-vortex interactions
DEFF Research Database (Denmark)
Pedersen, Johan Rønby; Aref, Hassan
2009-01-01
. The equations of motion may be cast in Hamiltonian form. We analyze the equations of motion using techniques from the theory of dynamical systems. The simplest such system, a single point vortex and a circular body, is integrable. As we add vortices, or change other features of the system such as the body shape......, the motion may become chaotic. Numerical solutions are shown and analyzed with an emphasis on the transition to chaos and its physical meaning. This class of systems provides a rich family of few-degree-of-freedom systems that capture essential fluid-body interaction physics....
Geometry in the large and hyperbolic chaos
Energy Technology Data Exchange (ETDEWEB)
Hasslacher, B.; Mainieri, R.
1998-11-01
This is the final report of a three-year, Laboratory Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). The authors calculated observables in strongly chaotic systems. This is difficult to do because of a lack of a workable orbit classification for such systems. This is due to global geometrical information from the original dynamical system being entangled in an unknown way throughout the orbit sequence. They used geometrical methods from modern mathematics and recent connections between global geometry and modern quantum field theory to study the natural geometrical objects belonging to hard chaos-hyperbolic manifolds.
CHAOS-BASED ADVANCED ENCRYPTION STANDARD
Abdulwahed, Naif B.
2013-05-01
This thesis introduces a new chaos-based Advanced Encryption Standard (AES). The AES is a well-known encryption algorithm that was standardized by U.S National Institute of Standard and Technology (NIST) in 2001. The thesis investigates and explores the behavior of the AES algorithm by replacing two of its original modules, namely the S-Box and the Key Schedule, with two other chaos- based modules. Three chaos systems are considered in designing the new modules which are Lorenz system with multiplication nonlinearity, Chen system with sign modules nonlinearity, and 1D multiscroll system with stair case nonlinearity. The three systems are evaluated on their sensitivity to initial conditions and as Pseudo Random Number Generators (PRNG) after applying a post-processing technique to their output then performing NIST SP. 800-22 statistical tests. The thesis presents a hardware implementation of dynamic S-Boxes for AES that are populated using the three chaos systems. Moreover, a full MATLAB package to analyze the chaos generated S-Boxes based on graphical analysis, Walsh-Hadamard spectrum analysis, and image encryption analysis is developed. Although these S-Boxes are dynamic, meaning they are regenerated whenever the encryption key is changed, the analysis results show that such S-Boxes exhibit good properties like the Strict Avalanche Criterion (SAC) and the nonlinearity and in the application of image encryption. Furthermore, the thesis presents a new Lorenz-chaos-based key expansion for the AES. Many researchers have pointed out that there are some defects in the original key expansion of AES and thus have motivated such chaos-based key expansion proposal. The new proposed key schedule is analyzed and assessed in terms of confusion and diffusion by performing the frequency and SAC test respectively. The obtained results show that the new proposed design is more secure than the original AES key schedule and other proposed designs in the literature. The proposed
A Heuristic Approach to Intra-Brain Communications Using Chaos in a Recurrent Neural Network Model
Soma, Ken-ichiro; Mori, Ryota; Sato, Ryuichi; Nara, Shigetoshi
2011-09-01
To approach functional roles of chaos in brain, a heuristic model to consider mechanisms of intra-brain communications is proposed. The key idea is to use chaos in firing pattern dynamics of a recurrent neural network consisting of birary state neurons, as propagation medium of pulse signals. Computer experiments and numerical methods are introduced to evaluate signal transport characteristics by calculating correlation functions between sending neurons and receiving neurons of pulse signals.
How Complex, Probable, and Predictable is Genetically Driven Red Queen Chaos?
Duarte, Jorge; Rodrigues, Carla; Januário, Cristina; Martins, Nuno; Sardanyés, Josep
2015-12-01
Coevolution between two antagonistic species has been widely studied theoretically for both ecologically- and genetically-driven Red Queen dynamics. A typical outcome of these systems is an oscillatory behavior causing an endless series of one species adaptation and others counter-adaptation. More recently, a mathematical model combining a three-species food chain system with an adaptive dynamics approach revealed genetically driven chaotic Red Queen coevolution. In the present article, we analyze this mathematical model mainly focusing on the impact of species rates of evolution (mutation rates) in the dynamics. Firstly, we analytically proof the boundedness of the trajectories of the chaotic attractor. The complexity of the coupling between the dynamical variables is quantified using observability indices. By using symbolic dynamics theory, we quantify the complexity of genetically driven Red Queen chaos computing the topological entropy of existing one-dimensional iterated maps using Markov partitions. Co-dimensional two bifurcation diagrams are also built from the period ordering of the orbits of the maps. Then, we study the predictability of the Red Queen chaos, found in narrow regions of mutation rates. To extend the previous analyses, we also computed the likeliness of finding chaos in a given region of the parameter space varying other model parameters simultaneously. Such analyses allowed us to compute a mean predictability measure for the system in the explored region of the parameter space. We found that genetically driven Red Queen chaos, although being restricted to small regions of the analyzed parameter space, might be highly unpredictable.
A novel chaos-based image encryption scheme with an efficient permutation-diffusion mechanism
Ye, Ruisong
2011-10-01
This paper proposes a novel chaos-based image encryption scheme with an efficient permutation-diffusion mechanism, in which permuting the positions of image pixels incorporates with changing the gray values of image pixels to confuse the relationship between cipher-image and plain-image. In the permutation process, a generalized Arnold map is utilized to generate one chaotic orbit used to get two index order sequences for the permutation of image pixel positions; in the diffusion process, a generalized Arnold map and a generalized Bernoulli shift map are employed to yield two pseudo-random gray value sequences for a two-way diffusion of gray values. The yielded gray value sequences are not only sensitive to the control parameters and initial conditions of the considered chaotic maps, but also strongly depend on the plain-image processed, therefore the proposed scheme can resist statistical attack, differential attack, known-plaintext as well as chosen-plaintext attack. Experimental results are carried out with detailed analysis to demonstrate that the proposed image encryption scheme possesses large key space to resist brute-force attack as well.
Deterministic chaos in the pitting phenomena of passivable alloys
International Nuclear Information System (INIS)
Hoerle, Stephane
1998-01-01
It was shown that electrochemical noise recorded in stable pitting conditions exhibits deterministic (even chaotic) features. The occurrence of deterministic behaviors depend on the material/solution severity. Thus, electrolyte composition ([Cl - ]/[NO 3 - ] ratio, pH), passive film thickness or alloy composition can change the deterministic features. Only one pit is sufficient to observe deterministic behaviors. The electrochemical noise signals are non-stationary, which is a hint of a change with time in the pit behavior (propagation speed or mean). Modifications of electrolyte composition reveals transitions between random and deterministic behaviors. Spontaneous transitions between deterministic behaviors of different features (bifurcation) are also evidenced. Such bifurcations enlighten various routes to chaos. The routes to chaos and the features of chaotic signals allow to suggest the modeling (continuous and discontinuous models are proposed) of the electrochemical mechanisms inside a pit, that describe quite well the experimental behaviors and the effect of the various parameters. The analysis of the chaotic behaviors of a pit leads to a better understanding of propagation mechanisms and give tools for pit monitoring. (author) [fr
Catastrophe theory with application in nuclear technology
International Nuclear Information System (INIS)
Valeca, Serban Constantin
2002-01-01
The monograph is structured on the following seven chapters: 1. Correlation of risk, catastrophe and chaos at the level of polyfunctional systems with nuclear injection; 1.1 Approaching the risk at the level of power systems; 1.2 Modelling the chaos-catastrophe-risk correlation in the structure of integrated classical and nuclear processes; 2. Catastrophe theory applied in ecosystems models and applications; 2.1 Posing the problems in catastrophe theory; 2.2 Application of catastrophe theory in the engineering of the power ecosystems with nuclear injection; 4.. Decision of abatement of the catastrophic risk based on minimal costs; 4.1 The nuclear power systems sensitive to risk-catastrophe-chaos in the structure of minimal costs; 4.2 Evaluating the market structure on the basis of power minimal costs; 4.3 Decisions in power systems built on minimal costs; 5. Models of computing the minimal costs in classical and nuclear power systems; 5.1 Calculation methodologies of power minimal cost; 5.2 Calculation methods of minimal costs in nuclear power sector; 6. Expert and neuro expert systems for supervising the risk-catastrophe-chaos correlation; 6.1 The structure of expert systems; 6.2 Application of the neuro expert program; 7. Conclusions and operational proposals; 7.1 A synthesis of the problems presented in this work; 7.2 Highlighting the novel aspects applicable in the power systems with nuclear injection
Prediction based chaos control via a new neural network
International Nuclear Information System (INIS)
Shen Liqun; Wang Mao; Liu Wanyu; Sun Guanghui
2008-01-01
In this Letter, a new chaos control scheme based on chaos prediction is proposed. To perform chaos prediction, a new neural network architecture for complex nonlinear approximation is proposed. And the difficulty in building and training the neural network is also reduced. Simulation results of Logistic map and Lorenz system show the effectiveness of the proposed chaos control scheme and the proposed neural network
Lee, William H K.
2016-01-01
A complex system consists of many interacting parts, generates new collective behavior through self organization, and adaptively evolves through time. Many theories have been developed to study complex systems, including chaos, fractals, cellular automata, self organization, stochastic processes, turbulence, and genetic algorithms.
Data protection by using the «Сhua’s circuit » chaos generator
Directory of Open Access Journals (Sweden)
Тетяна Олександрівна Левицька
2017-07-01
Full Text Available This article focuses on the justification of the use of cryptosystems based on a mathematical model of the chaos generator (an electric circuit, showing modes of chaotic oscillations, proposed by Leon Chua in 1983. This article also describes the principles of implementation of cryptographic algorithm and its application prospects. Reviewed the next questions: the problems of widespread cryptosystems, the theory of cryptographically strong algorithms, absolutely and computationally secure ciphers, particular theoretical method for solving the problem of increasing the reliability of hybrid computational proof systems by inclusion of a mathematical model of chaos as a generator to encrypt transmitted data key. Here described the recommendations on the implementation of cryptographic system and requirements on the Chua’s circuit generator ch
Discursive Maps at the Edge of Chaos
2017-05-25
Discursive Maps at the Edge of Chaos A Monograph by Major Mathieu Primeau Canadian Army, Royal Canadian Engineer School of Advanced Military...Master’s Thesis 3. DATES COVERED (From - To) JUN 2016 – MAY 2017 4. TITLE AND SUBTITLE Discursive Maps at the Edge of Chaos 5a. CONTRACT NUMBER 5b...meaning of boundaries and polarize conflict towards violence. The edge of chaos is the fine line between disorder and coherence. Discursive maps
Exploiting chaos for applications.
Ditto, William L; Sinha, Sudeshna
2015-09-01
We discuss how understanding the nature of chaotic dynamics allows us to control these systems. A controlled chaotic system can then serve as a versatile pattern generator that can be used for a range of application. Specifically, we will discuss the application of controlled chaos to the design of novel computational paradigms. Thus, we present an illustrative research arc, starting with ideas of control, based on the general understanding of chaos, moving over to applications that influence the course of building better devices.
Exploiting chaos for applications
Energy Technology Data Exchange (ETDEWEB)
Ditto, William L., E-mail: wditto@hawaii.edu [Department of Physics and Astronomy, University of Hawaii at Mānoa, Honolulu, Hawaii 96822 (United States); Sinha, Sudeshna, E-mail: sudeshna@iisermohali.ac.in [Indian Institute of Science Education and Research (IISER), Mohali, Knowledge City, Sector 81, SAS Nagar, PO Manauli 140306, Punjab (India)
2015-09-15
We discuss how understanding the nature of chaotic dynamics allows us to control these systems. A controlled chaotic system can then serve as a versatile pattern generator that can be used for a range of application. Specifically, we will discuss the application of controlled chaos to the design of novel computational paradigms. Thus, we present an illustrative research arc, starting with ideas of control, based on the general understanding of chaos, moving over to applications that influence the course of building better devices.
Experimental verification of rank 1 chaos in switch-controlled Chua circuit.
Oksasoglu, Ali; Ozoguz, Serdar; Demirkol, Ahmet S; Akgul, Tayfun; Wang, Qiudong
2009-03-01
In this paper, we provide the first experimental proof for the existence of rank 1 chaos in the switch-controlled Chua circuit by following a step-by-step procedure given by the theory of rank 1 maps. At the center of this procedure is a periodically kicked limit cycle obtained from the unforced system. Then, this limit cycle is subjected to periodic kicks by adding externally controlled switches to the original circuit. Both the smooth nonlinearity and the piecewise linear cases are considered in this experimental investigation. Experimental results are found to be in concordance with the conclusions of the theory.
Chaos, Chaos Control and Synchronization of a Gyrostat System
GE, Z.-M.; LIN, T.-N.
2002-03-01
The dynamic behavior of a gyrostat system subjected to external disturbance is studied in this paper. By applying numerical results, phase diagrams, power spectrum, period-T maps, and Lyapunov exponents are presented to observe periodic and choatic motions. The effect of the parameters changed in the system can be found in the bifurcation and parametric diagrams. For global analysis, the basins of attraction of each attractor of the system are located by employing the modified interpolated cell mapping (MICM) method. Several methods, the delayed feedback control, the addition of constant torque, the addition of periodic force, the addition of periodic impulse torque, injection of dither signal control, adaptive control algorithm (ACA) control and bang-bang control are used to control chaos effectively. Finally, synchronization of chaos in the gyrostat system is studied.
Chaos and its Role in Design and Simulation of Railway Vehicles
DEFF Research Database (Denmark)
True, Hans
1996-01-01
First certain important properties of nonlinear problems are discussed. Thenthe concept of chaos is described. It can only appear in nonlinear systemsand it is very common in the real world. Certain characteristic features ofdeterministic chaos and in relation hereto tests for the existence...... of chaos indynamical systems are presented.\\ Next the relevance of chaos for railwaydynamics is discussed and examples of chaotic oscillations in railwaydynamical model are shown, whereby the distinction between a chaoticattractor and transient chaos is introduces. Some causes of chaos in railwaytechnology...... are discussed. Finally the effects of chaos on field tests andnumerical simulations are discussed....
Dynamical chaos of plasma ions in electrostatic waves
International Nuclear Information System (INIS)
Fasoli, A.; Kleiber, R.; Tran, M.Q.; Paris, P.J.; Skiff, F.
1992-09-01
Chaos generated by the interaction between charged particles and electrostatic plasma waves has been observed in a linear magnetized plasma. The macroscopic wave properties, the kinetic ion dielectric response and the microscopic heating mechanisms have been investigated via optical diagnostic techniques based on laser induced fluorescence. Observations of test-particle dynamical evolution indicate an exponential separation of initially close ion trajectories. (author) 5 figs., 20 refs
Computational complexity of symbolic dynamics at the onset of chaos
Lakdawala, Porus
1996-05-01
In a variety of studies of dynamical systems, the edge of order and chaos has been singled out as a region of complexity. It was suggested by Wolfram, on the basis of qualitative behavior of cellular automata, that the computational basis for modeling this region is the universal Turing machine. In this paper, following a suggestion of Crutchfield, we try to show that the Turing machine model may often be too powerful as a computational model to describe the boundary of order and chaos. In particular we study the region of the first accumulation of period doubling in unimodal and bimodal maps of the interval, from the point of view of language theory. We show that in relation to the ``extended'' Chomsky hierarchy, the relevant computational model in the unimodal case is the nested stack automaton or the related indexed languages, while the bimodal case is modeled by the linear bounded automaton or the related context-sensitive languages.
A-coupled-expanding and distributional chaos
International Nuclear Information System (INIS)
Kim, Cholsan; Ju, Hyonhui; Chen, Minghao; Raith, Peter
2015-01-01
The concept of A-coupled-expanding maps is one of the more natural and useful ideas generalized from the horseshoe map which is commonly known as a criterion of chaos. It is well known that distributional chaos is one of the concepts which reflect strong chaotic behavior. In this paper, we focus on the relationship between A-coupled-expanding and distributional chaos. We prove two theorems which give sufficient conditions for a strictly A-coupled-expanding map to be distributionally chaotic in the senses of two kinds, where A is an m × m irreducible transition matrix
Ruette, Sylvie
2017-01-01
The aim of this book is to survey the relations between the various kinds of chaos and related notions for continuous interval maps from a topological point of view. The papers on this topic are numerous and widely scattered in the literature; some of them are little known, difficult to find, or originally published in Russian, Ukrainian, or Chinese. Dynamical systems given by the iteration of a continuous map on an interval have been broadly studied because they are simple but nevertheless exhibit complex behaviors. They also allow numerical simulations, which enabled the discovery of some chaotic phenomena. Moreover, the "most interesting" part of some higher-dimensional systems can be of lower dimension, which allows, in some cases, boiling it down to systems in dimension one. Some of the more recent developments such as distributional chaos, the relation between entropy and Li-Yorke chaos, sequence entropy, and maps with infinitely many branches are presented in book form for the first time. The author gi...
Deterministic Chaos: Proposal of an Informal Educational Activity Aimed at High School Students
Greco, Valeria; Spagnolo, Salvatore
2016-01-01
Chaos theory is not present in the Italian school curricula and textbooks in spite of being present in many topics of classical physics and in everyday life. Chaotic dynamics, in fact, are involved in phenomena easily accessible to everyone or in events experienced by most people in their lives (the dripping of a faucet which keeps people awoken…
Phase Chaos and Multistability in the Discrete Kuramoto Model
DEFF Research Database (Denmark)
Maistrenko, V. L.; Vasylenko, A. A.; Maistrenko, Y. L.
2008-01-01
The paper describes the appearance of a novel high-dimensional chaotic regime, called phase chaos, in the discrete Kuramoto model of globally coupled phase oscillators. This type of chaos is observed at small and intermediate values of the coupling strength. It is caused by the nonlinear interact......The paper describes the appearance of a novel high-dimensional chaotic regime, called phase chaos, in the discrete Kuramoto model of globally coupled phase oscillators. This type of chaos is observed at small and intermediate values of the coupling strength. It is caused by the nonlinear...... interaction of the oscillators, while the individual oscillators behave periodically when left uncoupled. For the four-dimensional discrete Kuramoto model, we outline the region of phase chaos in the parameter plane, distinguish the region where the phase chaos coexists with other periodic attractors...
Deterministic Chaos - Complex Chance out of Simple Necessity ...
Indian Academy of Sciences (India)
This is a very lucid and lively book on deterministic chaos. Chaos is very common in nature. However, the understanding and realisation of its potential applications is very recent. Thus this book is a timely addition to the subject. There are several books on chaos and several more are being added every day. In spite of this ...
Chaos analysis of the electrical signal time series evoked by acupuncture
International Nuclear Information System (INIS)
Wang Jiang; Sun Li; Fei Xiangyang; Zhu Bing
2007-01-01
This paper employs chaos theory to analyze the time series of electrical signal which are evoked by different acupuncture methods applied to the Zusanli point. The phase space is reconstructed and the embedding parameters are obtained by the mutual information and Cao's methods. Subsequently, the largest Lyapunov exponent is calculated. From the analyses we can conclude that the time series are chaotic. In addition, differences between various acupuncture methods are discussed
Decoherence, determinism and chaos revisited
International Nuclear Information System (INIS)
Noyes, H.P.
1994-01-01
We suggest that the derivation of the free space Maxwell Equations for classical electromagnetism, using a discrete ordered calculus developed by L.H. Kauffman and T. Etter, necessarily pushes the discussion of determinism in natural science down to the level of relativistic quantum mechanics and hence renders the mathematical phenomena studied in deterministic chaos research irrelevant to the question of whether the world investigated by physics is deterministic. We believe that this argument reinforces Suppes' contention that the issue of determinism versus indeterminism should be viewed as a Kantian antinomy incapable of investigation using currently available scientific tools
Decoherence, determinism and chaos revisited
Energy Technology Data Exchange (ETDEWEB)
Noyes, H.P.
1994-11-15
We suggest that the derivation of the free space Maxwell Equations for classical electromagnetism, using a discrete ordered calculus developed by L.H. Kauffman and T. Etter, necessarily pushes the discussion of determinism in natural science down to the level of relativistic quantum mechanics and hence renders the mathematical phenomena studied in deterministic chaos research irrelevant to the question of whether the world investigated by physics is deterministic. We believe that this argument reinforces Suppes` contention that the issue of determinism versus indeterminism should be viewed as a Kantian antinomy incapable of investigation using currently available scientific tools.
Chaos of discrete dynamical systems in complete metric spaces
International Nuclear Information System (INIS)
Shi Yuming; Chen Guanrong
2004-01-01
This paper is concerned with chaos of discrete dynamical systems in complete metric spaces. Discrete dynamical systems governed by continuous maps in general complete metric spaces are first discussed, and two criteria of chaos are then established. As a special case, two corresponding criteria of chaos for discrete dynamical systems in compact subsets of metric spaces are obtained. These results have extended and improved the existing relevant results of chaos in finite-dimensional Euclidean spaces
Many-Body Quantum Chaos: Analytic Connection to Random Matrix Theory
Kos, Pavel; Ljubotina, Marko; Prosen, Tomaž
2018-04-01
A key goal of quantum chaos is to establish a relationship between widely observed universal spectral fluctuations of clean quantum systems and random matrix theory (RMT). Most prominent features of such RMT behavior with respect to a random spectrum, both encompassed in the spectral pair correlation function, are statistical suppression of small level spacings (correlation hole) and enhanced stiffness of the spectrum at large spectral ranges. For single-particle systems with fully chaotic classical counterparts, the problem has been partly solved by Berry [Proc. R. Soc. A 400, 229 (1985), 10.1098/rspa.1985.0078] within the so-called diagonal approximation of semiclassical periodic-orbit sums, while the derivation of the full RMT spectral form factor K (t ) (Fourier transform of the spectral pair correlation function) from semiclassics has been completed by Müller et al. [Phys. Rev. Lett. 93, 014103 (2004), 10.1103/PhysRevLett.93.014103]. In recent years, the questions of long-time dynamics at high energies, for which the full many-body energy spectrum becomes relevant, are coming to the forefront even for simple many-body quantum systems, such as locally interacting spin chains. Such systems display two universal types of behaviour which are termed the "many-body localized phase" and "ergodic phase." In the ergodic phase, the spectral fluctuations are excellently described by RMT, even for very simple interactions and in the absence of any external source of disorder. Here we provide a clear theoretical explanation for these observations. We compute K (t ) in the leading two orders in t and show its agreement with RMT for nonintegrable, time-reversal invariant many-body systems without classical counterparts, a generic example of which are Ising spin-1 /2 models in a periodically kicking transverse field. In particular, we relate K (t ) to partition functions of a class of twisted classical Ising models on a ring of size t ; hence, the leading-order RMT behavior
Gain control through divisive inhibition prevents abrupt transition to chaos in a neural mass model.
Papasavvas, Christoforos A; Wang, Yujiang; Trevelyan, Andrew J; Kaiser, Marcus
2015-09-01
Experimental results suggest that there are two distinct mechanisms of inhibition in cortical neuronal networks: subtractive and divisive inhibition. They modulate the input-output function of their target neurons either by increasing the input that is needed to reach maximum output or by reducing the gain and the value of maximum output itself, respectively. However, the role of these mechanisms on the dynamics of the network is poorly understood. We introduce a novel population model and numerically investigate the influence of divisive inhibition on network dynamics. Specifically, we focus on the transitions from a state of regular oscillations to a state of chaotic dynamics via period-doubling bifurcations. The model with divisive inhibition exhibits a universal transition rate to chaos (Feigenbaum behavior). In contrast, in an equivalent model without divisive inhibition, transition rates to chaos are not bounded by the universal constant (non-Feigenbaum behavior). This non-Feigenbaum behavior, when only subtractive inhibition is present, is linked to the interaction of bifurcation curves in the parameter space. Indeed, searching the parameter space showed that such interactions are impossible when divisive inhibition is included. Therefore, divisive inhibition prevents non-Feigenbaum behavior and, consequently, any abrupt transition to chaos. The results suggest that the divisive inhibition in neuronal networks could play a crucial role in keeping the states of order and chaos well separated and in preventing the onset of pathological neural dynamics.
Can chaos be observed in quantum gravity?
International Nuclear Information System (INIS)
Dittrich, Bianca; Höhn, Philipp A.; Koslowski, Tim A.; Nelson, Mike I.
2017-01-01
Full general relativity is almost certainly ‘chaotic’. We argue that this entails a notion of non-integrability: a generic general relativistic model, at least when coupled to cosmologically interesting matter, likely possesses neither differentiable Dirac observables nor a reduced phase space. It follows that the standard notion of observable has to be extended to include non-differentiable or even discontinuous generalized observables. These cannot carry Poisson-algebraic structures and do not admit a standard quantization; one thus faces a quantum representation problem of gravitational observables. This has deep consequences for a quantum theory of gravity, which we investigate in a simple model for a system with Hamiltonian constraint that fails to be completely integrable. We show that basing the quantization on standard topology precludes a semiclassical limit and can even prohibit any solutions to the quantum constraints. Our proposed solution to this problem is to refine topology such that a complete set of Dirac observables becomes continuous. In the toy model, it turns out that a refinement to a polymer-type topology, as e.g. used in loop gravity, is sufficient. Basing quantization of the toy model on this finer topology, we find a complete set of quantum Dirac observables and a suitable semiclassical limit. This strategy is applicable to realistic candidate theories of quantum gravity and thereby suggests a solution to a long-standing problem which implies ramifications for the very concept of quantization. Our work reveals a qualitatively novel facet of chaos in physics and opens up a new avenue of research on chaos in gravity which hints at deep insights into the structure of quantum gravity.
Can chaos be observed in quantum gravity?
Energy Technology Data Exchange (ETDEWEB)
Dittrich, Bianca, E-mail: bdittrich@perimeterinstitute.ca [Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, ON N2L 2Y5 (Canada); Höhn, Philipp A., E-mail: p.hoehn@univie.ac.at [Vienna Center for Quantum Science and Technology, and Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna (Austria); Koslowski, Tim A., E-mail: koslowski@nucleares.unam.mx [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apartado Postal 70-543, México D.F. 04510 (Mexico); Nelson, Mike I., E-mail: mike@aims.edu.gh [African Institute for Mathematical Sciences, P.O Box LG 197, Legon, Accra (Ghana)
2017-06-10
Full general relativity is almost certainly ‘chaotic’. We argue that this entails a notion of non-integrability: a generic general relativistic model, at least when coupled to cosmologically interesting matter, likely possesses neither differentiable Dirac observables nor a reduced phase space. It follows that the standard notion of observable has to be extended to include non-differentiable or even discontinuous generalized observables. These cannot carry Poisson-algebraic structures and do not admit a standard quantization; one thus faces a quantum representation problem of gravitational observables. This has deep consequences for a quantum theory of gravity, which we investigate in a simple model for a system with Hamiltonian constraint that fails to be completely integrable. We show that basing the quantization on standard topology precludes a semiclassical limit and can even prohibit any solutions to the quantum constraints. Our proposed solution to this problem is to refine topology such that a complete set of Dirac observables becomes continuous. In the toy model, it turns out that a refinement to a polymer-type topology, as e.g. used in loop gravity, is sufficient. Basing quantization of the toy model on this finer topology, we find a complete set of quantum Dirac observables and a suitable semiclassical limit. This strategy is applicable to realistic candidate theories of quantum gravity and thereby suggests a solution to a long-standing problem which implies ramifications for the very concept of quantization. Our work reveals a qualitatively novel facet of chaos in physics and opens up a new avenue of research on chaos in gravity which hints at deep insights into the structure of quantum gravity.
Global chaos synchronization with channel time-delay
International Nuclear Information System (INIS)
Jiang Guoping; Zheng Weixing; Chen Guanrong
2004-01-01
This paper addresses a practical issue in chaos synchronization where there is a time-delay in the receiver as compared with the transmitter. A new synchronization scheme and a general criterion for global chaos synchronization are proposed and developed from the approach of unidirectional linear error feedback coupling with time-delay. The chaotic Chua's circuit is used for illustration, where the coupling parameters are determined according to the criterion under which the global chaos synchronization of the time-delay coupled systems is achieved
Hueso, Miguel; Cruzado, Josep M; Torras, Joan; Navarro, Estanislao
2018-06-12
Atherosclerosis (ATH) and coronary artery disease (CAD) are chronic inflammatory diseases with an important genetic background; they derive from the cumulative effect of multiple common risk alleles, most of which are located in genomic noncoding regions. These complex diseases behave as nonlinear dynamical systems that show a high dependence on their initial conditions; thus, long-term predictions of disease progression are unreliable. One likely possibility is that the nonlinear nature of ATH could be dependent on nonlinear correlations in the structure of the human genome. In this review, we show how chaos theory analysis has highlighted genomic regions that have shared specific structural constraints, which could have a role in ATH progression. These regions were shown to be enriched with repetitive sequences of the Alu family, genomic parasites that have colonized the human genome, which show a particular secondary structure and are involved in the regulation of gene expression. Here, we show the impact of Alu elements on the mechanisms that regulate gene expression, especially highlighting the molecular mechanisms via which the Alu elements alter the inflammatory response. We devote special attention to their relationship with the long noncoding RNA (lncRNA); antisense noncoding RNA in the INK4 locus ( ANRIL ), a risk factor for ATH; their role as microRNA (miRNA) sponges; and their ability to interfere with the regulatory circuitry of the (nuclear factor kappa B) NF-κB response. We aim to characterize ATH as a nonlinear dynamic system, in which small initial alterations in the expression of a number of repetitive elements are somehow amplified to reach phenotypic significance.
1989-01-01
Le mouvement brownien ; la mémoire des atomes ; le chaos ; déterminisme et prédictabilité ; déterminisme et chaos ; les phénomènes de physique et les échelles de longueur ; un ordre caché dans la matière désordonnée ; les verres de spin et l'étude des milieux désordonnés ; la convection ; la croissance fractale ; la physique de la matière hétérogène ; la matière ultradivisée.
A new approach for realizing electronic chaos generators
International Nuclear Information System (INIS)
Elwakeel, A.E.
1997-01-01
A dictionary definition of chaos is a 'formless primordial matter, utter confusion' [1]. The study of chaos is part of a larger program of study of so-called strongly nonlinear systems. No strict definition of chaos yet exists, however, nonrandom complicated motions that exhibit a very rapid growth of errors and that, despite perfect determinism, inhibit any ability to render accurate long-term prediction are usually termed chaotic. In other words, chaos may be referred to as deterministic randomness since it is the phenomenon where deterministic laws, are sometimes extremely simple, show random (or random-like) behaviours while random (or random-like) motions happen to follow strict deterministic laws. The sense of order in chaos can be usually observed in the space of dimensions where time is not a dimension, while the sense of randomness is usually evident when time is incorporated. 10 refs., 29 figs
Route to broadband chaos in a chaotic laser diode subject to optical injection.
Wang, An-Bang; Wang, Yun-Cai; Wang, Juan-Fen
2009-04-15
We experimentally and numerically demonstrate a route to bandwidth-enhanced chaos that is induced by an additional optical injection for a chaotic laser diode with optical feedback. The measured and calculated optical spectra consistently reveal that the mechanism of bandwidth enhancement is the interaction between the injection and chaotic laser field via beating. The bandwidth can be maximized only when the injected light is detuned into the edge of the optical spectrum of the chaotic laser field and the beating frequency exceeds the original bandwidth. The simulated dynamics maps indicate that 20 GHz broadband chaos can be obtained by commonly used laser diodes.
Particle ratios, quarks, and Chao-Yang statistics
Energy Technology Data Exchange (ETDEWEB)
Chew, C K; Low, G B; Lo, S Y [Nanyang Univ. (Singapore). Dept. of Physics; Phua, K K [Argonne National Lab., IL (USA)
1980-01-01
By introducing quarks into Chao-Yang statistics for 'violent' collisions, particle ratios are obtained which are consistent with the Chao-Yang results. The present method can also be extended to baryon-meson and baryon-antibaryon ratios.
Pulsating instabilities and chaos in lasers
Energy Technology Data Exchange (ETDEWEB)
Harrison, R G; Biswas, D J
1985-01-01
A detailed state of the art survey of deterministic chaos in laser systems is presented. The mechanism of single mode instability is discussed, including spontaneous and induced mode splitting and the threshold for laser instabilities. Single mode homogeneously broadened systems are addressed, including optically pumped far infrared lasers and near-resonantly pumped midinfrared systems. Single mode inhomogeneously broadened systems are considered, including the He-Xe laser and the He-Ne laser at 3.39 microns. Single mode lasers with external control parameter are discussed, as is the multimode laser. 297 references.
On Nonextensive Statistics, Chaos and Fractal Strings
Castro, C
2004-01-01
Motivated by the growing evidence of universality and chaos in QFT and string theory, we study the Tsallis non-extensive statistics ( with a non-additive $ q$-entropy ) of an ensemble of fractal strings and branes of different dimensionalities. Non-equilibrium systems with complex dynamics in stationary states may exhibit large fluctuations of intensive quantities which are described in terms of generalized statistics. Tsallis statistics is a particular representative of such class. The non-extensive entropy and probability distribution of a canonical ensemble of fractal strings and branes is studied in terms of their dimensional spectrum which leads to a natural upper cutoff in energy and establishes a direct correlation among dimensions, energy and temperature. The absolute zero temperature ( Kelvin ) corresponds to zero dimensions (energy ) and an infinite temperature corresponds to infinite dimensions. In the concluding remarks some applications of fractal statistics, quasi-particles, knot theory, quantum...
Operational Shock Complexity Theory
2005-05-26
Theory : Recommendations For The National Strategy To Defeat Terrorism.” Student Issue Paper, Center for Strategic Leadership , US Army War College, July...Lens of Complexity Theory : Recommendations For The National Strategy To Defeat Terrorism.” (Student Issue Paper, Center for Strategic Leadership , US...planners managed to cause confusion in the enemy’s internal model by operating in an unexpected manner. 140 Glenn E. James, “Chaos Theory : The
Chaos analysis of the electrical signal time series evoked by acupuncture
Energy Technology Data Exchange (ETDEWEB)
Wang Jiang [School of Electrical Engineering, Tianjin University, Tianjin 300072 (China)]. E-mail: jiangwang@tju.edu.cn; Sun Li [School of Electrical Engineering, Tianjin University, Tianjin 300072 (China); Fei Xiangyang [School of Electrical Engineering, Tianjin University, Tianjin 300072 (China); Zhu Bing [Institute of Acupuncture and Moxibustion, China Academy of Traditional Chinese Medicine, Beijing 100700 (China)
2007-08-15
This paper employs chaos theory to analyze the time series of electrical signal which are evoked by different acupuncture methods applied to the Zusanli point. The phase space is reconstructed and the embedding parameters are obtained by the mutual information and Cao's methods. Subsequently, the largest Lyapunov exponent is calculated. From the analyses we can conclude that the time series are chaotic. In addition, differences between various acupuncture methods are discussed.
Lost in the chaos: Flawed literature should not generate new disorders
Van Rooij, Antonius J.; Kardefelt-Winther, Daniel
2017-01-01
The paper by Kuss, Griffiths, and Pontes (2016) titled ?Chaos and confusion in DSM-5 diagnosis of Internet Gaming Disorder: Issues, concerns, and recommendations for clarity in the field? examines issues relating to the concept of Internet Gaming Disorder. We agree that there are serious issues and extend their arguments by suggesting that the field lacks basic theory, definitions, patient research, and properly validated and standardized assessment tools. As most studies derive data from sur...
Improvement and empirical research on chaos control by theory of "chaos + chaos = order".
Fulai, Wang
2012-12-01
This paper focuses on advancing the understanding of Parrondian effects and their paradoxical behavior in nonlinear dynamical systems. Some examples are given to show that a dynamics combined by more than two discrete chaotic dynamics in deterministic manners can give rise to order when combined. The chaotic maps in our study are more general than those in the current literatures as far as "chaos + chaos = order" is concerned. Some problems left over in the current literatures are solved. It is proved both theoretically and numerically that, given any m chaotic dynamics generated by the one-dimensional real Mandelbrot maps, it is no possible to get a periodic system when all the m chaotic dynamics are alternated in random manner, but for any integer m(m ≥ 2) a dynamics combined in deterministic manner by m Mandelbrot chaotic dynamics can be found to give rise to a periodic dynamics of m periods. Numerical and mathematical analysis prove that the paradoxical phenomenon of "chaos + chaos = order" also exist in the dynamics generated by non-Mandelbrot maps.
Chaos based encryption system for encrypting electroencephalogram signals.
Lin, Chin-Feng; Shih, Shun-Han; Zhu, Jin-De
2014-05-01
In the paper, we use the Microsoft Visual Studio Development Kit and C# programming language to implement a chaos-based electroencephalogram (EEG) encryption system involving three encryption levels. A chaos logic map, initial value, and bifurcation parameter for the map were used to generate Level I chaos-based EEG encryption bit streams. Two encryption-level parameters were added to these elements to generate Level II chaos-based EEG encryption bit streams. An additional chaotic map and chaotic address index assignment process was used to implement the Level III chaos-based EEG encryption system. Eight 16-channel EEG Vue signals were tested using the encryption system. The encryption was the most rapid and robust in the Level III system. The test yielded superior encryption results, and when the correct deciphering parameter was applied, the EEG signals were completely recovered. However, an input parameter error (e.g., a 0.00001 % initial point error) causes chaotic encryption bit streams, preventing the recovery of 16-channel EEG Vue signals.
Chaos from simple models to complex systems
Cencini, Massimo; Vulpiani, Angelo
2010-01-01
Chaos: from simple models to complex systems aims to guide science and engineering students through chaos and nonlinear dynamics from classical examples to the most recent fields of research. The first part, intended for undergraduate and graduate students, is a gentle and self-contained introduction to the concepts and main tools for the characterization of deterministic chaotic systems, with emphasis to statistical approaches. The second part can be used as a reference by researchers as it focuses on more advanced topics including the characterization of chaos with tools of information theor
Towards CHAOS-5 - How can Swarm contribute?
DEFF Research Database (Denmark)
Finlay, Chris; Olsen, Nils; Tøffner-Clausen, Lars
2014-01-01
The launch of ESA's satellite trio Swarm in November 2013 opens an exciting new chapter in the observation and monitoring of Earth's magnetic field from space. We report preliminary results from an extension of the CHAOS series of geomagnetic field models to include both scalar and vector field...... observations from the three Swarm satellites, along with the most recent quasi-definitive ground observatory data. The fit of this new update CHAOS field model to the Swarm observations will be presented in detail providing useful insight the initial Swarm data. Enhancements of the CHAOS modelling scheme...
Reconstruction of chaotic signals with applications to chaos-based communications
Feng, Jiu Chao
2008-01-01
This book provides a systematic review of the fundamental theory of signal reconstruction and the practical techniques used in reconstructing chaotic signals. Specific applications of signal reconstruction methods in chaos-based communications are expounded in full detail, along with examples illustrating the various problems associated with such applications.The book serves as an advanced textbook for undergraduate and graduate courses in electronic and information engineering, automatic control, physics and applied mathematics. It is also highly suited for general nonlinear scientists who wi
Controlling chaos in a pendulum equation with ultra-subharmonic resonances
International Nuclear Information System (INIS)
Yang Jianping; Jing Zhujun
2009-01-01
Analytical and numerical results concerning control of chaos in a pendulum equation with parametric and external excitations are given by using Melnikov methods. We give the necessary conditions of chaos control with ultra-subharmonic resonances (i.e. Ω/ω=p/q,q>1,p,q are prime), where homoclinic chaos or heteroclinic chaos can be inhibited. Numerical simulations show that chaotic behavior can be converted to period-nq (n element of Z + ) orbits by adjusting amplitude and phase-difference of parametric excitation, and the distribution of maximum Lyapunov exponents in parameter-plane (Ψ,β) gives the regions in which chaos can be controlled.
An adaptive chaos synchronization scheme applied to secure communication
International Nuclear Information System (INIS)
Feki, Moez
2003-01-01
This paper deals with the problem of synchronization of a class of continuous-time chaotic systems using the drive-response concept. An adaptive observer-based response system is designed to synchronize with a given chaotic drive system whose dynamical model is subjected to unknown parameters. Using the Lyapunov stability theory an adaptation law is derived to estimate the unknown parameters. We show that synchronization is achieved asymptotically. The approach is next applied to chaos-based secure communication. To demonstrate the efficiency of the proposed scheme numerical simulations are presented
Chaos desynchronization in strongly coupled systems
International Nuclear Information System (INIS)
Wu Ye; Liu Weiqing; Xiao, Jinghua; Zhan Meng
2007-01-01
The dynamics of chaos desynchronization in strongly coupled oscillator systems is studied. We find a new bifurcation from synchronous chaotic state, chaotic short wave bifurcation, i.e. a chaotic desynchronization attractor is new born in the systems due to chaos desynchronization. In comparison with the usual periodic short wave bifurcation, very rich but distinct phenomena are observed
Galloping instability to chaos of cables
Luo, Albert C J
2017-01-01
This book provides students and researchers with a systematic solution for fluid-induced structural vibrations, galloping instability and the chaos of cables. They will also gain a better understanding of stable and unstable periodic motions and chaos in fluid-induced structural vibrations. Further, the results presented here will help engineers effectively design and analyze fluid-induced vibrations.
Probing the quantum analog of chaos with atoms in external fields
Energy Technology Data Exchange (ETDEWEB)
Gay, J C; Delande, D
1987-01-01
For a few years, considerable interest arose in the problem of the quantum analog of classical chaos for hamiltonian system. Among several other simple atomic physics systems, the atom in a magnetic field turns out to be the most promising prototype for tackling such questions. The classical and quantum motions are now well understood. The experimental study is possible in high Rydberg states of atoms. Throughout the study of some aspects of this problem, the authors demonstrate that the quantum analog of chaos presents a two-fold aspect. While the spectral properties at short range are conveniently described by Random matrix theories, a long-range order still exist in the quantum dynamics which indicates the existence of scars of symmetries. This in turn is quite clearly exhibited in the experimental data on Rydberg atoms. Finally the authors indicate how to generalize the notions to any situation involving the Coulomb field and perturbing potentials. 21 refs.; 8 figs.
Control of chaos in a three-well duffing system
International Nuclear Information System (INIS)
Yang Jianping; Jing Zhujun
2009-01-01
Analytical and numerical results concerning control of chaos in a three-well duffing system with two external excitations are given by using the Melnikov methods proposed by Chacon et al. [Chacon R. General results on chaos suppression for biharmonically driven dissipative systems. Phys Lett A 1999;257:293-300, Chacon R, Palmero F, Balibrea F. Taming chaos in a driven Josephson Junction. Int J Bifurc Chaos 2001;11(7):1897-909, Chacon R. Role of ultrasubharmonic resonances in taming chaos by weak harmonic perturbations. Europhys Lett 2001;54(2):148C153]. We theoretically give the parameter-space region and intervals of initial phase difference for primary and subharmonic resonance and the necessary condition for the superharmonic and supersubharmonic resonance, where homoclinic chaos or heteroclinic chaos can be suppressed. Numerical simulations show the consistency and difference with theoretical analysis and the chaotic behavior can be converted to periodic orbits by adjusting amplitude and phase-difference of inhibiting excitation. Moreover, we consider the influence of parametric frequency on maximum Lyapunov exponent (LE) for different phase-differences, and give the distribution of maximum Lyapunov exponents in parameter-plane, which indicates the regions of non-chaotic states (non-positive LE) and chaotic states (positive LE).
CHAOS: An SDN-Based Moving Target Defense System
Directory of Open Access Journals (Sweden)
Yuan Shi
2017-01-01
Full Text Available Moving target defense (MTD has provided a dynamic and proactive network defense to reduce or move the attack surface that is available for exploitation. However, traditional network is difficult to realize dynamic and active security defense effectively and comprehensively. Software-defined networking (SDN points out a brand-new path for building dynamic and proactive defense system. In this paper, we propose CHAOS, an SDN-based MTD system. Utilizing the programmability and flexibility of SDN, CHAOS obfuscates the attack surface including host mutation obfuscation, ports obfuscation, and obfuscation based on decoy servers, thereby enhancing the unpredictability of the networking environment. We propose the Chaos Tower Obfuscation (CTO method, which uses the Chaos Tower Structure (CTS to depict the hierarchy of all the hosts in an intranet and define expected connection and unexpected connection. Moreover, we develop fast CTO algorithms to achieve a different degree of obfuscation for the hosts in each layer. We design and implement CHAOS as an application of SDN controller. Our approach makes it very easy to realize moving target defense in networks. Our experimental results show that a network protected by CHAOS is capable of decreasing the percentage of information disclosure effectively to guarantee the normal flow of traffic.
Chaos in blood flow control in genetic and renovascular hypertensive rats
DEFF Research Database (Denmark)
Yip, K P; Holstein-Rathlou, N H; Marsh, D J
1991-01-01
Hydrostatic pressure and flow in renal proximal tubules oscillate at 30-40 mHz in normotensive rats anesthetized with halothane. The oscillations originate in tubuloglomerular feedback, a mechanism that provides local blood flow regulation. Instead of oscillations, spontaneously hypertensive rats...... (SHR) have aperiodic tubular pressure fluctuations; the pattern is suggestive of deterministic chaos. Normal rats made hypertensive by clipping one renal artery had similar aperiodic tubular pressure fluctuations in the unclipped kidney, and the fraction of rats with irregular fluctuations increased...... with time after the application of the renal artery clip. Statistical measures of deterministic chaos were applied to tubular pressure data. The correlation dimension, a measure of the dimension of the phase space attractor generating the time series, indicated the presence of a low-dimension strange...
International Nuclear Information System (INIS)
Remler, E.A.
1977-01-01
A gauge-invariant version of the Wigner representation is used to relate relativistic mechanics, statistical mechanics, and quantum field theory in the context of the electrodynamics of scalar particles. A unified formulation of quantum field theory and statistical mechanics is developed which clarifies the physics interpretation of the single-particle Wigner function. A covariant form of Ehrenfest's theorem is derived. Classical electrodynamics is derived from quantum field theory after making a random-phase approximation. The validity of this approximation is discussed
Gain control through divisive inhibition prevents abrupt transition to chaos in a neural mass model
Papasavvas, Christoforos A.; Wang, Yujiang; Trevelyan, Andrew J.; Kaiser, Marcus
2016-01-01
Experimental results suggest that there are two distinct mechanisms of inhibition in cortical neuronal networks: subtractive and divisive inhibition. They modulate the input-output function of their target neurons either by increasing the input that is needed to reach maximum output or by reducing the gain and the value of maximum output itself, respectively. However, the role of these mechanisms on the dynamics of the network is poorly understood. We introduce a novel population model and numerically investigate the influence of divisive inhibition on network dynamics. Specifically, we focus on the transitions from a state of regular oscillations to a state of chaotic dynamics via period-doubling bifurcations. The model with divisive inhibition exhibits a universal transition rate to chaos (Feigenbaum behavior). In contrast, in an equivalent model without divisive inhibition, transition rates to chaos are not bounded by the universal constant (non-Feigenbaum behavior). This non-Feigenbaum behavior, when only subtractive inhibition is present, is linked to the interaction of bifurcation curves in the parameter space. Indeed, searching the parameter space showed that such interactions are impossible when divisive inhibition is included. Therefore, divisive inhibition prevents non-Feigenbaum behavior and, consequently, any abrupt transition to chaos. The results suggest that the divisive inhibition in neuronal networks could play a crucial role in keeping the states of order and chaos well separated and in preventing the onset of pathological neural dynamics. PMID:26465514
Path and semimartingale properties of chaos processes
DEFF Research Database (Denmark)
Basse-O'Connor, Andreas; Graversen, Svend-Erik
2010-01-01
The present paper characterizes various properties of chaos processes which in particular include processes where all time variables admit a Wiener chaos expansion of a fixed finite order. The main focus is on the semimartingale property, p-variation and continuity. The general results obtained...
Exact Solution of a Strongly Coupled Gauge Theory in 0 +1 Dimensions
Krishnan, Chethan; Kumar, K. V. Pavan
2018-05-01
Gauged tensor models are a class of strongly coupled quantum mechanical theories. We present the exact analytic solution of a specific example of such a theory: namely, the smallest colored tensor model due to Gurau and Witten that exhibits nonlinearities. We find explicit analytic expressions for the eigenvalues and eigenstates, and the former agree precisely with previous numerical results on (a subset of) eigenvalues of the ungauged theory. The physics of the spectrum, despite the smallness of N , exhibits rudimentary signatures of chaos. This Letter is a summary of our main results: the technical details will appear in companion paper [C. Krishnan and K. V. Pavan Kumar, Complete solution of a gauged tensor model, arXiv:1804.10103].
Controlling beam halo-chaos via backstepping design
International Nuclear Information System (INIS)
Gao Yuan; Kong Feng
2008-01-01
A backstepping control method is proposed for controlling beam halo-chaos in the periodic focusing channels (PFCs) of high-current ion accelerator. The analysis and numerical results show that the method, via adjusting an exterior magnetic field, is effective to control beam halo chaos with five types of initial distribution ion beams, all statistical quantities of the beam halo-chaos are largely reduced, and the uniformity of ion beam is improved. This control method has an important value of application, for the exterior magnetic field can be easily adjusted in the periodical magnetic focusing channels in experiment
Lecar, Myron; Franklin, Fred A.; Holman, Matthew J.; Murray, Norman J.
2001-01-01
The physical basis of chaos in the solar system is now better understood: In all cases investigated so far, chaotic orbits result from overlapping resonances. Perhaps the clearest examples are found in the asteroid belt. Overlapping resonances account for its kirkwood gaps and were used to predict and find evidence for very narrow gaps in the outer belt. Further afield, about one new "short-peroid" comet is discovered each year. They are believed to come from the "Kuiper Belt" (at 40 AU or more) via chaotic orbits produced by mean-motion and secular resonances with Neptune. Finally, the planetary system itself is not immune from chaos. In the inner solar system, overlapping secular resonances have been identified as the possible source of chaos. For example, Mercury in 1012 years, may suffer a close encounter with Venus or plunge into the Sun. In the outer solar system, three-body resonances have been identified as a source of chaos, but on an even longer time scale of 109 times the age of the solar system. On the human time scale, the planets do follow their orbits in a stately procession, and we can predict their trajectories for hundreds of thousands of years. That is because the mavericks, with shorter instability times, have long since been ejected. The solar system is not stable; it is just old!
Symbolic dynamics of noisy chaos
Energy Technology Data Exchange (ETDEWEB)
Crutchfield, J P; Packard, N H
1983-05-01
One model of randomness observed in physical systems is that low-dimensional deterministic chaotic attractors underly the observations. A phenomenological theory of chaotic dynamics requires an accounting of the information flow fromthe observed system to the observer, the amount of information available in observations, and just how this information affects predictions of the system's future behavior. In an effort to develop such a description, the information theory of highly discretized observations of random behavior is discussed. Metric entropy and topological entropy are well-defined invariant measures of such an attractor's level of chaos, and are computable using symbolic dynamics. Real physical systems that display low dimensional dynamics are, however, inevitably coupled to high-dimensional randomness, e.g. thermal noise. We investigate the effects of such fluctuations coupled to deterministic chaotic systems, in particular, the metric entropy's response to the fluctuations. It is found that the entropy increases with a power law in the noise level, and that the convergence of the entropy and the effect of fluctuations can be cast as a scaling theory. It is also argued that in addition to the metric entropy, there is a second scaling invariant quantity that characterizes a deterministic system with added fluctuations: I/sub 0/, the maximum average information obtainable about the initial condition that produces a particular sequence of measurements (or symbols). 46 references, 14 figures, 1 table.
Induced fission of nuclei: dynamical chaos and lifetime of compound nucleus
Energy Technology Data Exchange (ETDEWEB)
Krivoshej, I V
1987-01-01
A semi-phenomenological theory is proposed to describe the induced fission of heavy nuclei at low and intermediate excitation energies. The theory is based on the concept of the dynamical chaos, arising because of a negative curvature of the n-dimensional potential energy surface (PES). The nuclear fission is treated as a diffusion of the representing point across a vicinity of the saddle point in PES. The diffusion coefficient is calculated for various metrics in PES as an explicit function of the two-dimensional curvatures at the saddle point of PES. The present theory suggests an estimate for the fission time, tau/sub f/approx.10/sup -14/ s. Coefficients of nuclear friction and viscosity are also calculated in general, and the resulting numerical estimates are in agreement with the experimental data.
Energy Technology Data Exchange (ETDEWEB)
Clausse, A; Delmastro, D F
1991-12-31
This work presents a description of the research lines carried out by the authors on chaos and fractal theories, oriented to the nuclear field. The possibilities that appear in the nuclear security branch where the information deriving from chaos and fractal techniques may help to the development of better criteria and more reliable designs, are of special importance. (Author). [Espanol] En este trabajo se presenta una descripcion de las lineas de investigacion que los autores estan llevando a cabo en teoria de caos y fractales orientadas al campo nuclear. Es de especial importancia las posibilidades que se abren en el area de la seguridad nuclear, en donde la informacion proveniente de las tecnicas de caos y fractales pueden ayudar al desarrollo de mejores criterios y disenos mas confiables. (Autor).
Effortful control and school adjustment: The moderating role of classroom chaos.
Berger, Rebecca H; Valiente, Carlos; Eisenberg, Nancy; Hernandez, Maciel M; Thompson, Marilyn; Spinrad, Tracy; VanSchyndel, Sarah; Silva, Kassondra; Southworth, Jody
2017-11-01
Guided by the person by environment framework, the primary goal of this study was to determine whether classroom chaos moderated the relation between effortful control and kindergarteners' school adjustment. Classroom observers reported on children's ( N = 301) effortful control in the fall. In the spring, teachers reported on classroom chaos and school adjustment outcomes (teacher-student relationship closeness and conflict, and school liking and avoidance). Cross-level interactions between effortful control and classroom chaos predicting school adjustment outcomes were assessed. A consistent pattern of interactions between effortful control and classroom chaos indicated that the relations between effortful control and the school adjustment outcomes were strongest in high chaos classrooms. Post-hoc analyses indicated that classroom chaos was associated with poor school adjustment when effortful control was low, suggesting that the combination of high chaos and low effortful control was associated with the poorest school outcomes.
Wang, Zhe; Deater-Deckard, Kirby; Petrill, Stephen A; Thompson, Lee A
2012-08-01
Previous research documented a robust link between difficulties in self-regulation and development of externalizing problems (i.e., aggression and delinquency). In this study, we examined the longitudinal additive and interactive genetic and environmental covariation underlying this well-established link using a twin design. The sample included 131 pairs of monozygotic twins and 173 pairs of same-sex dizygotic twins who participated in three waves of annual assessment. Mothers and fathers provided reports of externalizing problems. Teacher report and observer rating were used to assess twin's attention regulation. The etiology underlying the link between externalizing problems and attention regulation shifted from a common genetic mechanism to a common environmental mechanism in the transition across middle childhood. Household chaos moderated the genetic variance of and covariance between externalizing problems and attention regulation. The genetic influence on individual differences in both externalizing problems and attention regulation was stronger in more chaotic households. However, higher levels of household chaos attenuated the genetic link between externalizing problems and attention regulation.
Chaos synchronization based on intermittent state observer
Institute of Scientific and Technical Information of China (English)
Li Guo-Hui; Zhou Shi-Ping; Xu De-Ming
2004-01-01
This paper describes the method of synchronizing slave to the master trajectory using an intermittent state observer by constructing a synchronizer which drives the response system globally tracing the driving system asymptotically. It has been shown from the theory of synchronization error-analysis that a satisfactory result of chaos synchronization is expected under an appropriate intermittent period and state observer. Compared with continuous control method,the proposed intermittent method can target the desired orbit more efficiently. The application of the method is demonstrated on the hyperchaotic Rossler systems. Numerical simulations show that the length of the synchronization interval rs is of crucial importance for our scheme, and the method is robust with respect to parameter mismatch.
Chaos as a Social Determinant of Child Health: Reciprocal Associations?
Schmeer, Kammi K.; Taylor, Miles
2013-01-01
This study informs the social determinants of child health by exploring an understudied aspect of children’s social contexts: chaos. Chaos has been conceptualized as crowded, noisy, disorganized, unpredictable settings for child development (Evans et al., 2010). We measure chaos at two levels of children’s ecological environment - the microsystem (household) and the mesosystem (work-family-child care nexus) – and at two points in early childhood (ages 3 and 5). Using data from the Fragile Families and Child Wellbeing Study (N=3288), a study of predominantly low-income women and their partners in large US cities, we develop structural equation models that assess how maternal-rated child health (also assessed at ages 3 and 5) is associated with latent constructs of chaos, and whether there are important reciprocal effects. Autoregressive crosslagged path analysis suggest that increasing chaos (at both the household and maternal work levels) is associated with worse child health, controlling for key confounders like household economic status, family structure, and maternal health status. Child health has little effect on chaos, providing further support for the hypothesis that chaos is an important social determinant of child health in this sample of relatively disadvantaged children. This suggests child health may be improved by supporting families in ways that reduce chaos in their home and work/family environments, and that as researchers move beyond SES, race, and family structure to explore other sources of health inequalities, chaos and its proximate determinants may be a promising avenue for future research. PMID:23541250
Campbell, David
1987-11-01
I provide a brief overview of the current status of the field of deterministic "chaos" stressing its interrelations and applications to other fields and suggesting a number of important open problems for future study.
Chaos in plasma simulation and experiment
International Nuclear Information System (INIS)
Watts, C.; Sprott, J.C.
1993-09-01
We investigate the possibility that chaos and simple determinism are governing the dynamics of reversed field pinch (RFP) plasmas using data from both numerical simulations and experiment. A large repertoire of nonlinear analysis techniques is used to identify low dimensional chaos. These tools include phase portraits and Poincard sections, correlation dimension, the spectrum of Lyapunov exponents and short term predictability. In addition, nonlinear noise reduction techniques are applied to the experimental data in an attempt to extract any underlying deterministic dynamics. Two model systems are used to simulate the plasma dynamics. These are -the DEBS code, which models global RFP dynamics, and the dissipative trapped electron mode (DTEM) model, which models drift wave turbulence. Data from both simulations show strong indications of low,dimensional chaos and simple determinism. Experimental data were obtained from the Madison Symmetric Torus RFP and consist of a wide array of both global and local diagnostic signals. None of the signals shows any indication of low dimensional chaos or other simple determinism. Moreover, most of the analysis tools indicate the experimental system is very high dimensional with properties similar to noise. Nonlinear noise reduction is unsuccessful at extracting an underlying deterministic system