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 for the biomedical engineer.
Eberhart, R C
1989-01-01
A brief introduction to chaos theory is provided. Definitions of chaos and attributes of chaos and fractals are discussed. Several general examples are examined, and fractals are introduced with a brief look at the Mandelbrot and Julia sets. Biomedical examples of chaotic behaviour and fractals are presented.
Ergodic theory, randomness, and "chaos".
Ornstein, D S
1989-01-13
Ergodic theory is the theory of the long-term statistical behavior of dynamical systems. The baker's transformation is an object of ergodic theory that provides a paradigm for the possibility of deterministic chaos. It can now be shown that this connection is more than an analogy and that at some level of abstraction a large number of systems governed by Newton's laws are the same as the baker's transformation. Going to this level of abstraction helps to organize the possible kinds of random behavior. The theory also gives new concrete results. For example, one can show that the same process could be produced by a mechanism governed by Newton's laws or by a mechanism governed by coin tossing. It also gives a statistical analog of structural stability.
"Chaos" Theory: Implications for Educational Research.
Lindsay, Jean S.
"Chaos" theory is a revolutionary new paradigm developed by scientists to study the behavior of natural systems. "Chaos" refers to the tendency of dynamic non-linear systems toward irregular, sometimes unpredictable, yet deterministic behavior. Major tenets of the theory are presented. The precedent for use of models developed in the natural…
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...
Legal System and Legal Chaos Theory
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Amir Syarifudin
2015-08-01
Full Text Available Order of the universe and other objects can be described either by cosmology and physics. But from of the regularity of the object there in terms or aspect of irregularity or fractal (broken that difficult to describe by Auklides and Calculus mathematical models. Benoit Medelbrot tried to explain the chaotic objects with fractal theory which basically a branch of mathematics. The fractal theory affect the view of the law that inspired Charles Sampford which then sparked a legal chaos theory. The core of legal chaos theory is (1 social relationships , including the relationship established based on the relationship of forces (power relation, (2 the parties who make that relationship does not have the same strength or balance, and (3 at the time of execution of the respective relations based on their subjective opinions. Those three thing that is causing chaos. But the atmosphere of chaos that would eventually return to the regularity, because of the strength towing (strange attractor that in the area of law is the law and the power of the state. Chaos basically contained in the freedom -based relationship beyond the confines of order. When the towing force managed to recover the chaos so as to create harmony between order and freedom, the peace that one of the legal goal is achieved.
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,…
Wang, Frank Y
2009-01-01
The general public has been made aware of the research field of "chaos" by the book of that title by James Gleick. This paper will focus on the achievements of Sonya Kovalevskaya, Mary Cartwright, and Mary Tsingou, whose pioneer works were not mentioned in Gleick's book.
Legal System and Legal Chaos Theory
Amir Syarifudin; Indah Febriani
2015-01-01
Order of the universe and other objects can be described either by cosmology and physics. But from of the regularity of the object there in terms or aspect of irregularity or fractal (broken) that difficult to describe by Auklides and Calculus mathematical models. Benoit Medelbrot tried to explain the chaotic objects with fractal theory which basically a branch of mathematics. The fractal theory affect the view of the law that inspired Charles Sampford which then sparked a legal chaos theory....
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.
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
CHAOS THEORY: A CONTRIBUTION TO THE FORMATION OF STRATEGIES
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Marcio Luiz Marietto
2011-12-01
Full Text Available It is our intention, through this work, to contribute to the understanding of the influence of chaos theory on the formation of organizational strategies in the dynamic and complex environment in which organizations are embedded. In this sense, we present a theoretical review, leveraged by a dialectical epistemology, in which we propose to show some attributes of chaos theory and theoretical assumptions to be considered in the context of different areas of organizational strategy, with the goal of trying to elucidate and approximate the analytical characteristics of both theories and make evident how chaos theory can contribute to and/or influence the formation of business strategies.
Major open problems in chaos theory and nonlinear dynamics
Li, Y Charles
2013-01-01
Nowadays, chaos theory and nonlinear dynamics lack research focuses. Here we mention a few major open problems: 1. an effective description of chaos and turbulence, 2. rough dependence on initial data, 3. arrow of time, 4. the paradox of enrichment, 5. the paradox of pesticides, 6. the paradox of plankton.
The "Chaos" Pattern in Piaget's Theory of Cognitive Development.
Lindsay, Jean S.
Piaget's theory of the cognitive development of the child is related to the recently developed non-linear "chaos" model. The term "chaos" refers to the tendency of dynamical, non-linear systems toward irregular, sometimes unpredictable, deterministic behavior. Piaget identified this same pattern in his model of cognitive development in children.…
Strategic leadership: a view from quantum and chaos theories.
McDaniel, R R
1997-01-01
Viewing health care from the perspective of chaos and quantum theories offers new insights into management techniques for effective and efficient delivery of health care services. This article introduces these concepts and gives specific prescriptions for managerial action. PMID:9058085
THEORY OF SECULAR CHAOS AND MERCURY'S ORBIT
International Nuclear Information System (INIS)
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.
A NOVEL APPROACH TO GENERATE FRACTAL IMAGES USING CHAOS THEORY
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K. Thamizhchelvy
2014-08-01
Full Text Available We propose the fractal generation method to generate the different types of fractals using chaos theory. The fractals are generated by Iterated Function System (IFS technique. The chaos theory is an unpredictable behavior arises in the dynamical system. Chaos in turns explains the nonlinearity and randomness. Chaotic behavior depends upon the initial condition called as “seed” or “key”. Pseudo Random Number Generator (PRNG fixes the initial condition from the difference equations. The system uses the PRNG value and it generates the fractals, also it is hard to break. We apply the rules to generate the fractals. The different types of fractals are generated for the same data, because of the great sensitivity to the initial condition. It can be used as a digital signature in online applications such as e-Banking and online shopping.
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…
Predicting vibration signals of automobile engine using chaos theory
Institute of Scientific and Technical Information of China (English)
LIU Chun; ZHANG Laibin; WANG Zhaohui
2004-01-01
Condition monitoring and life prediction of the vehicle engine is an important and urgent problem during the vehicle development process. The vibration signals that are closely associated with the engine running condition and its development trend are complex and nonlinear. The chaos theory is used to treat the nonlinear dynamical system recently. A novel chaos method in conjunction with SVD (singular value decomposition)denoising skill are used to predict the vibration time series. Two types of time series and their prediction errors are provided to illustrate the practical utility of the method.
The butterfly and the tornado: chaos theory and climate change
International Nuclear Information System (INIS)
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 CO2 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
Understanding of Arab Spring with Chaos Theory - Uprising or Revolution
Açıkalın, Şuay Nilhan; Bölücek, Cemal Alpgiray
`Arab Spring' can be considered as one of the most remarkable events in the history of world politics. On December 18, 2010, a Tunisian young protestor burned himself in a public square of the city. This event triggered probably one of the most chaotic and long term uprisings in the Middle East. From the day of its initiation until the present, `Arab Spring' in the Middle East created unstable political situation and several uprisings. In this chapter, we will first give general information about chaos theory, and then we will examine the `butterfly effect' created by the Tunisian young protestor and process of Arab Spring in the Middle East regarding its extend and form in those countries within the framework of chaos theory. For the first part of this chapter, the spark created by the Tunisian young protestor and its effects can be analyzed under `butterfly effect' perspective within chaos theory, arguing whether the events followed each other consecutively or randomly. The question is whether the incidents following each other have reasonable links of causality to one another, or the events defining the phenomena known as `Arab Spring' have no predictable reasons and outcomes regardless of the regional, social and political differences. The events caused the collapse of the regimes in Tunisia, Egypt and Libya; they had very serious outcomes.
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
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.
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.
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
Drinkard, Lynne Bradford
1995-01-01
Early systems theory was a precursor of complexity theory, a global theory that suggests that the universe is an open system interacting on many dimensions. Chaos theory, a subset of complexity theory, states that in seeming chaos there is an underlying order. Between chaos and order lies emergence, from which healthy growth and change occur. Twenty years ago, chaos theory did not have a name and dissociative disorders were largely written off as rare or more imaginative than real. After physicists and mathematicians explained chaos and complexity in language understood by those outside their fields, scientists and practitioners from disparate disciplines were struck by the potential for applying the theories to their respective fields. Complexity and chaos theory combine reductionistic and holistic approaches to explain phenomena. Many mental health practitioners have suggested that a systems framework based in complexity theory may lead to greater understanding of human nature and ultimately toward more effective treatment of different disorders. This paper proposes that complexity and chaos theories may offer insight into the efficacy of various treatments for dissociative disorders.
Polynomial chaos theory for performance evaluation of ATR systems
DeVore, Michael D.; Bateman, Alec J.
2010-04-01
The development of a more unified theory of automatic target recognition (ATR) has received considerable attention over the last several years from individual researchers, working groups, and workshops. One of the major benefits expected to accrue from such a theory is an ability to analytically derive performance metrics that accurately predict real-world behavior. Numerous sources of uncertainty affect the actual performance of an ATR system, so direct calculation has been limited in practice to a few special cases because of the practical difficulties of manipulating arbitrary probability distributions over high dimensional spaces. This paper introduces an alternative approach for evaluating ATR performance based on a generalization of NorbertWiener's polynomial chaos theory. Through this theory, random quantities are expressed not in terms of joint distribution functions but as convergent orthogonal series over a shared random basis. This form can be used to represent any finite-variance distribution and can greatly simplify the propagation of uncertainties through complex systems and algorithms. The paper presents an overview of the relevant theory and, as an example application, a discussion of how it can be applied to model the distribution of position errors from target tracking algorithms.
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…
Chaos and transformation: implications of nonequilibrium theory for social science and society.
Loye, D; Eisler, R
1987-01-01
This article deals with all levels of both living (biological, psychological, sociological, and cultural) and nonliving (physical, chemical, and mathematical) systems. The idea of applying the natural scientific self-organizing, evolutionary, and non-equilibrium or "chaos" theory associated with the names of Prigogine and others to world problems of impending social, political, economic, and ecological "chaos" is gaining ground. The leap from natural science to social action, however, is impossible without considerable attention to the main intervening step: the development of "chaos"-equivalent, evolution-, systems-, and action-oriented social theory. Construction of such theory requires understanding by social scientists of natural scientific "chaos" theory as well as their own "chaos" theoretical heritage, of natural scientists of the now seemingly far distant social problem-solving potential of their nonequilibrium and self-organizing theories, and of both natural and social scientists of how advancement at both levels could help gain a peaceful as well as humanistic "order out of chaos" in this troubled world of ours. This paper surveys relevant concepts, problems, theorists, research, and works in progress within a perspective of the challenge of survival at a critical juncture in the evolution of our species. PMID:3689300
Application of Theories of Complexity and Chaos to Economic Misgovernance
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Partha Gangopadhyay
2011-01-01
Full Text Available Problem statement: In this study we develop a comprehensive model involving local taxes, intergovernmental transfers and bureaucratic corruption to characterize a fiscal equilibrium in order to explain the provision of local (public expenditure in developing nations. The main goal of the research is to explain economic misgovernance as an equilibrium phenomenon, which is therefore expected to persist over time despite serious economic and social costs. Approach: We develop an interactive model of fiscal gaming to understand economic misgovernance in the context of game theory. Resutls: It is constructively argued that the proposed fiscal game is beset with multiple equilibria and the consequent indeterminacy. The possibility of unstable equilibria, or an absence of pure-strategy equilibrium renders the system highly fragile. We also demonstrate the possibility of serious bifurcations of a stable fiscal equilibrium that loses stability with changes in values of relevant parameters. We extend this model further to argue how the chaotic behavior and complexities can characterize the dynamics of decision-making in this present context. Conclusion: The emergence of chaos can undermine the efficiency and predictability of the equilibrium of the proposed fiscal game, which can in turn seriously impinge on the quality of local goods in developing nations. We argue that an understanding of the fragility and complexity of local government system is essential for policy makers for achieving a sustainable local government system in developing nations.
Controlling Chaos in permanent magnet synchronous motor based on finite-time stability theory
Institute of Scientific and Technical Information of China (English)
Wei Du-Qu; Zhang So
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.
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…
[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
[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
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...
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...
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…
Final report on the application of chaos theory to an alumina sensor for aluminum reduction cells
Energy Technology Data Exchange (ETDEWEB)
Williford, R.E.; Windisch, C.F. Jr.
1992-03-01
Four chaos-related digital signal analysis (DSA) methods were applied to the analysis of voltage and current signals collected from aluminum electrolysis cells. Two separate data bases were analyzed: bench-scale laboratory experiments and a pilot-scale test. The objective was to assess the feasibility of using these types of data and analysis methods as the basis for a non-intrusive sensor to measure the alumina content in the electrolysis bath. This was the first time chaos theory approaches have been employed to analyze aluminum electrolysis cells.
Making sense of social media communications with chaos theory
DEFF Research Database (Denmark)
Gyimóthy, Szilvia; Larson, Mia
-organising, as the pattern of behaviour in the system evolves or emerges from the local interaction and adjustments between the agents. Instead of channelled flow of information, the nodes of this network transmit information in all directions simultaneously. Our goal is model the patterns of sense......: Routledge. Russell, R. & Faulkner, B. (2004). Entrepreneurship, Chaos and the Tourism Area Lifecycle. Annals of Tourism Research, 31(3), 556-579. Stacey, R.D. (2003). Strategic Management and Organisational Dynamics: The Challenge of Complexity. Harlow: FT/Prentice Hall. Wheatley, M.J. (1993). Leadership...
Text Steganography using LSB insertion method along with Chaos Theory
S., Bhavana
2012-01-01
The art of information hiding has been around nearly as long as the need for covert communication. Steganography, the concealing of information, arose early on as an extremely useful method for covert information transmission. Steganography is the art of hiding secret message within a larger image or message such that the hidden message or an image is undetectable; this is in contrast to cryptography, where the existence of the message itself is not disguised, but the content is obscure. The goal of a steganographic method is to minimize the visually apparent and statistical differences between the cover data and a steganogram while maximizing the size of the payload. Current digital image steganography presents the challenge of hiding message in a digital image in a way that is robust to image manipulation and attack. This paper explains about how a secret message can be hidden into an image using least significant bit insertion method along with chaos.
Application of periodic orbit theory in chaos-based security analysis
Institute of Scientific and Technical Information of China (English)
Long Min; Qiu Shui-Sheng
2007-01-01
Chaos-based encryption schemes have been studied extensively, while the security analysis methods for them are still problems to be resolved. Based on the periodic orbit theory, this paper proposes a novel security analysis method. The periodic orbits theory indicates that the fundamental frequency of the spiraling orbits is the natural frequency of associated linearized system, which is decided by the parameters of the chaotic system. Thus, it is possible to recover the plaintext of secure communication systems based on chaotic shift keying by getting the average time on the spiraling orbits. Analysis and simulation results show that the security analysis method can break chaos shift keying secure communication systems, which use the parameters as keys.
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 ...
Complexity Theory of Beam Halo-Chaos and Its Control Methods With Prospective Applications
Institute of Scientific and Technical Information of China (English)
2002-01-01
This article offers an overview and comprehensive survey of the complexity theory of beamhalo-chaos and its control methods with prospective applications. In recent years, there has been growinginterest in proton beams of high power linear accelerator due to its attractive features in possiblebreakthrough applications, such as production of nuclear materials (e.g., tritium, transforming 232Th to233U), transmutation of radioactive wastes, productions of radioactive isotopes for medical use, heavy ion
Directory of Open Access Journals (Sweden)
Sepideh Mirzaee
2014-10-01
Full Text Available Given that Emergentism is convincingly a novel challenge in the field of applied linguistics and is hotly under debate nowadays, its proponents especially Nick Ellis and his colleagues advocate it as a main alternative to the assumptions of Universal Grammar (UG proposed by Noam Chomsky. As its main tenet, a plethora of contemporary emergentist research contend that language acquisition can be abridged to the use of simple learning strategies to pull out statistical regularities present in regular linguistic input which is exactly harmonious with what chaos, complexity scholars believe in considering the features of chaotic complex systems. In fact, emergentist scholars believe that knowledge of language is shaped in response to opportunities to interpret and/or form utterances in the course of communication. Therefore, Emergentism is an obvious challenge to UG as it disputes some of its major assumptions. In compliance with Emergentism and chaos complexity theory, the present paper tries to illustrate the implausibility of Chomskian account of language acquisition in terms of UG. What’s more, the present paper sheds light on those aspects of language in which the Chomskian nativist paradigm fails to account including the explanatory adequacy of those cases and the reasons why both Emergentism and Chaos complexity theory are in dominant positions.
A new electricity price forecasting method based on chaos theory and data mining
International Nuclear Information System (INIS)
This paper presented a novel short-term electricity price forecasting method based on chaos theory and data mining techniques. Data pre-processing was used to characterize electricity price time sequences. A Haar wavelet was used to compress data. The effect of price nails on forecasting electricity prices was reduced using the method. The wavelet reconstruction was used to determine a threshold for each data layer's coefficient. A middle filtering method was used to compress prices located in singular sections. The largest Lyapunov exponent was larger than zero in the small data sets, which verified that electricity prices were still considered to have chaotic behaviour characteristics. Results of the study indicated that a chaos time series can be used to forecast short-term electricity prices. A case study of the California electricity market demonstrated that the forecasting method provided accurate forecasts. 9 refs., 1 tab., 8 figs.
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
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. PMID:10840901
International Nuclear Information System (INIS)
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.
The reasons for the application of chaos theory to the analysis of catastrophes.
Valery, Kudin
2014-05-01
The study of catastrophes is necessary for understanding the nature of the interaction between the individual and the universal in the process of the development of complex systems. Chaos theory, allowing describing adaptation and bifurcation mechanisms for the development of systems, defines the catastrophes as a transition of the system into a different state (change of structure). The previous state of the system is destroyed because of fluctuations, which do not play a role in the development of the system until it reaches the instability region that is inherent to any system. The catastrophe is considered in this theory as a stage in the evolution of the system, and thus emphasizes the importance of catastrophes for the development of any system. We rarely manage events comprehensively, as events are always subject to changes like gas molecules changing the trajectory of motion each moment under the influence of countless blows. The concept of catastrophes is much broader and is generally applicable to any final result of collision of opposing aspirations. Philosophical definition of catastrophes comes down to the destruction of the unity, accompanied by violent collision between different parts, the growing disruption, failure to prevent crossing the dangerous threshold... As a final vertex of action, disaster is not, however, directly its end: the action may continue after the catastrophe, but in the direction that is determined by the character of opposing aspirations. Major catastrophes, which have already destroyed and continue to ravage the world today, come from a superficial use of the laws of the development of complex systems and, in particular, of individual techniques of the chaos theory.
Waelbroeck, H
1999-01-01
We propose a theory of deterministic chaos for discrete systems, based on their representations in symbolic history spaces Ømega. These are spaces of semi-infinite sequences, as the one-sided shift spaces, but endowed with a more general topology which we call a semicausal topology. We show that define metrical properties, including the correlation dimension of the attractor. Examples are considered: Asymmetric neural networks and random cellular automata are not chaotic. A neural network model with memory, on the other hand, does appear to be an example of discrete chaos.
Energy Technology Data Exchange (ETDEWEB)
Williford, R.E.; Windisch, C.F. Jr.
1992-03-01
Four chaos-related digital signal analysis (DSA) methods were applied to the analysis of voltage and current signals collected from aluminum electrolysis cells. Two separate data bases were analyzed: bench-scale laboratory experiments and a pilot-scale test. The objective was to assess the feasibility of using these types of data and analysis methods as the basis for a non-intrusive sensor to measure the alumina content in the electrolysis bath. This was the first time chaos theory approaches have been employed to analyze aluminum electrolysis cells.
Prediction of regional seasonal fluctuations in precipitation based on chaos theory
LuValle, M
2013-01-01
In the past decade, the combined effect of flood and drought resulted in the loss of thousands of lives and billions of dollars. Multi season ahead prediction of regional precipitation extremes could significantly reduce losses. However, the evolution of climate is highly sensitive to initial conditions, or chaotic, so practical long term prediction of precipitation in time is impossible. Adding to the difficulty, the climate system is non-stationary; with the energy available to move water and air as tracked by global average surface temperature (GAST) increasing over the last several decades2. Neither purely empirical autoregression, nor global circulation models (GCM) are sufficiently accurate. Here I use statistical methods motivated by chaos theory to predict seasonal fluctuations in regional and local precipitation with high correlation. The change in GAST is accommodated using special runs of a global circulation model to build an initial set of predictive models, while ground data is used to train, co...
Application of Chaos Theory in the Prediction of Motorised Traffic Flows on Urban Networks
Directory of Open Access Journals (Sweden)
Aderemi Adewumi
2016-01-01
Full Text Available In recent times, urban road networks are faced with severe congestion problems as a result of the accelerating demand for mobility. One of the ways to mitigate the congestion problems on urban traffic road network is by predicting the traffic flow pattern. Accurate prediction of the dynamics of a highly complex system such as traffic flow requires a robust methodology. An approach for predicting Motorised Traffic Flow on Urban Road Networks based on Chaos Theory is presented in this paper. Nonlinear time series modeling techniques were used for the analysis of the traffic flow prediction with emphasis on the technique of computation of the Largest Lyapunov Exponent to aid in the prediction of traffic flow. The study concludes that algorithms based on the computation of the Lyapunov time seem promising as regards facilitating the control of congestion because of the technique’s effectiveness in predicting the dynamics of complex systems especially traffic flow.
A unified theory of chaos linking nonlinear dynamics and statistical physics
Poon, Chi-Sang; Wu, Guo-Qiang
2010-01-01
A fundamental issue in nonlinear dynamics and statistical physics is how to distinguish chaotic from stochastic fluctuations in short experimental recordings. This dilemma underlies many complex systems models from stochastic gene expression or stock exchange to quantum chaos. Traditionally, deterministic chaos is characterized by "sensitive dependence on initial conditions" as indicated by a positive Lyapunov exponent. However, ambiguity arises when applying this criterion to real-world data that are corrupted by measurement noise or perturbed nonautonomously by exogenous deterministic or stochastic inputs. Here, we show that a positive Lyapunov exponent is surprisingly neither necessary nor sufficient proof of deterministic chaos, and that a nonlinear dynamical system under deterministic or stochastic forcing may exhibit multiple forms of nonautonomous chaos assessable by a noise titration assay. These findings lay the foundation for reliable analysis of low-dimensional chaos for complex systems modeling an...
Peccati, Giovanni
2011-01-01
The concept of Wiener chaos generalizes to an infinite-dimensional setting the properties of orthogonal polynomials associated with probability distributions on the real line. It plays a crucial role in modern probability theory, with applications ranging from Malliavin calculus to stochastic differential equations and from probabilistic approximations to mathematical finance. This book is concerned with combinatorial structures arising from the study of chaotic random variables related to infinitely divisible random measures. The combinatorial structures involved are those of partitions of fi
Dynamics of hourly sea level at Hillarys Boat Harbour, Western Australia: a chaos theory perspective
Khatibi, Rahman; Ghorbani, Mohammad Ali; Aalami, Mohammad Taghi; Kocak, Kasim; Makarynskyy, Oleg; Makarynska, Dina; Aalinezhad, Mahdi
2011-11-01
Water level forecasting using recorded time series can provide a local modelling capability to facilitate local proactive management practices. To this end, hourly sea water level time series are investigated. The records collected at the Hillarys Boat Harbour, Western Australia, are investigated over the period of 2000 and 2002. Two modelling techniques are employed: low-dimensional dynamic model, known as the deterministic chaos theory, and genetic programming, GP. The phase space, which describes the evolution of the behaviour of a nonlinear system in time, was reconstructed using the delay-embedding theorem suggested by Takens. The presence of chaotic signals in the data was identified by the phase space reconstruction and correlation dimension methods, and also the predictability into the future was calculated by the largest Lyapunov exponent to be 437 h or 18 days into the future. The intercomparison of results of the local prediction and GP models shows that for this site-specific dataset, the local prediction model has a slight edge over GP. However, rather than recommending one technique over another, the paper promotes a pluralistic modelling culture, whereby different techniques should be tested to gain a specific insight from each of the models. This would enable a consensus to be drawn from a set of results rather than ignoring the individual insights provided by each model.
Understanding Chaos via Nuclei
Cejnar, Pavel; Stránský, Pavel
2014-01-01
We use two models of nuclear collective dynamics - the geometric collective model and the interacting boson model - to illustrate principles of classical and quantum chaos. We propose these models as a suitable testing ground for further elaborations of the general theory of chaos in both classical and quantum domains.
Casati, Giulio; Chirikov, Boris
2006-11-01
in two-electron atoms R. Blümel and W. P. Reinhardt; Part III. Semiclassical Approximations: 20. Semiclassical theory of spectral rigidity M. V. Berry; 21. Semiclassical structure of trace formulas R. G. Littlejohn; 22. h-Expansion for quantum trace formulas P. Gaspard; 23. Pinball scattering B. Eckhardt, G. Russberg, P. Cvitanovic, P. E. Rosenqvist and P. Scherer; 24. Logarithm breaking time in quantum chaos G. P. Berman and G. M. Zaslavsky; 25. Semiclassical propagation: how long can it last? M. A. Sepulveda, S. Tomsovic and E. J. Heller; 26. The quantized Baker's transformation N. L. Balazs and A. Voros; 27. Classical structures in the quantized baker transformation M. Saraceno; 28. Quantum nodal points as fingerprints of classical chaos P. Leboeuf and A. Voros; 29. Chaology of action billiards A. M. Ozorio de Almeida and M. A. M. de Aguiar; Part IV. Level Statistics and Random Matrix Theory: 30. Characterization of chaotic quantum spectra and universality of level fluctuation laws O. Bohigas, M. J. Giannono, and C. Schmit; 31. Quantum chaos, localization and band random matrices F. M. Izrailev; 32. Structural invariance in channel space: a step toward understanding chaotic scattering in quantum mechanics T. H. Seligman; 33. Spectral properties of a Fermi accelerating disk R. Badrinarayanan and J. J. José; 34. Spectral properties of systems with dynamical localization T. Dittrich and U. Smilansky; 35. Unbound quantum diffusion and fractal spectra T. Geisel, R. Ketzmerick and G. Petschel; 36. Microwave studies in irregularly shaped billiards H.-J. Stöckmann, J. Stein and M. Kollman; Index.
Improved PSO algorithm based on chaos theory and its application to design flood hydrograph
Institute of Scientific and Technical Information of China (English)
Si-fang DONG; Zeng-chuan DONG; Jun-jian MA; Kang-ning CHEN
2010-01-01
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.
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.
Directory of Open Access Journals (Sweden)
Matthew O’Lemmon
2013-01-01
Full Text Available The 2004 Indian Ocean Tsunami was epic in scale and scope and will go down as one of the largest natural disasters in human history. This paper presents an analysis of media coverage of the disaster and surveys of 206 local and international tourists in Khao Lak, Thailand, through the framework of chaos theory. Specifically, this paper examines the role of expert analysis as a periodic attractor during and after the tsunami. It will demonstrate how expert analysis brought disparate images and eyewitness testimony into greater focus, creating order in an otherwise chaotic environment.
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
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.
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.
International Nuclear Information System (INIS)
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
混沌理论在滚动轴承故障诊断中的应用%Application of Chaos Theory in Fault Diagnosis of Rolling Bearings
Institute of Scientific and Technical Information of China (English)
吴参; 李兴林; 孙守迁; 张燕辽; 张仰平
2013-01-01
混沌系统对初始条件和参数极度敏感,这一特点可以用于检测早期检测噪声背景下的滚动轴承故障信号.从几个方面综述了混沌理论在轴承故障诊断中的应用现状,即滚动轴承故障诊断技术的分类与特点,混沌理论在滚动轴承故障诊断中的应用基础,混沌振子系统在轴承故障诊断中的应用,混沌动力学分析在滚动轴承故障诊断中的应用.并通过分析总结,预测了混沌理论在轴承故障诊断中的下一步研究方向.%The chaos system is extremely sensitive to initial conditions and parameter. This feature is able to be used for testing rolling bearing fault signal under early detection noise background. The application status of chaos theory in fault diagnosis for rolling bearings is summarized from several aspects, namely classification and characteristics of fault diagnosis technology for rolling bearings, application basis of chaos theory in fault diagnosis for rolling bearings, application of chaotic oscillator system in fault diagnosis for rolling bearings, application of chaotic dynamics analysis in fault diagnosis for rolling bearings. Through the analysis, the next research direction of chaos theory in fault diagnosis for rolling bearings is forecasted.
Image hash algorithm based on chaos theory%一种基于混沌的图像hash算法
Institute of Scientific and Technical Information of China (English)
肖潇; 胡春强; 邓绍江
2011-01-01
To meet the needs of the Image Authentication, proposed image hash algorithm based on chaos theory. To begin with ,encrypted the original image by Logistic map. After that, difference matrix was modulated and quantified, and then obtained the fixed length of hash sequence. It discussed that the image scaling and JPEG compression were influence on the robustness of the hash sequence. It pointed that robust of the proposed scheme against the above attacks when the threshold t is 0.1. The experimental results indicate that the algorithm has the robust to against the above attacks, then the method is an effective for studying image authentication.%为了实现图像认证,提出了基于混沌理论的图像hash算法.首先将原始图像经过置乱得到加密图像,然后对差值矩阵进行调制、量化,得到固定长度的图像hash序列.算法讨论了图像的缩放和JPEG压缩对图像hash序列的影响,当阈值为0.1时,对上述的攻击方法进行了实验,结果表明,图像对这两种攻击具有一定的鲁棒性.
A STRING ENCRYPTION ALGORITHM BASED ON CHAOS THEORY%一种基于混沌理论的字符串加密算法
Institute of Scientific and Technical Information of China (English)
陈绍钧
2011-01-01
提出一种基于混沌理论的字符串加密算法.通过应用混沌理论的"随机过程"产生随机密钥和随机干扰字符串,使用密钥对明文字符串进行异或(XOR)加密,再将运算后的密文同密钥、干扰字符串按照一定规则组合构成完整的混沌密文.该算法具有运算量小、灵活性强、加密强度高的特点.%The paper presents a string encryption algorithm based on chaos theory. By applying chaos theory' s “random process”, the random key and random interference string are generated. The encryption key encodes plaintext strings with XOR operation; then composes the computed encryption text with the encryption key and interference string together according to designated rules to build a complete chaos encryption text. The algorithm bears such features as fewer calculations, greater flexibilities and stronger encryption.
Recent Developments on Chaos in Mechanical Systems
Mohammad Sajid
2013-01-01
Recent advancements in complexity of mechanical systems have led to the application of chaos theory. In this paper, some recent developments on chaos in mechanical systems are explored. The aim is to bring together researchers from various interests of mechanical systems, exposing them to chaos theory. This exposure gives researchers from the discipline of mechanical systems to find opportunity of cross disciplinary research, which may ultimately lead to novel solutions and understanding of m...
Periodic-orbit theory of universal level correlations in quantum chaos
Energy Technology Data Exchange (ETDEWEB)
Mueller, Sebastian [Department of Mathematics, University of Bristol, Bristol BS8 1TW (United Kingdom); Heusler, Stefan [Institut fuer Didaktik der Physik, Universitaet Muenster, Wilhelm-Klemm Str. 10, 48149 Muenster (Germany); Altland, Alexander [Institut fuer Theoretische Physik, Universitaet zu Koeln, Zuelpicher Str. 77, 50937 Koeln (Germany); Braun, Petr; Haake, Fritz [Fachbereich Physik, Universitaet Duisburg-Essen, 47048 Duisburg (Germany)], E-mail: Petr.Braun@uni-due.de
2009-10-15
Using Gutzwiller's semiclassical periodic-orbit theory, we demonstrate universal behavior of the two-point correlator of the density of levels for quantum systems whose classical limit is fully chaotic. We go beyond previous work in establishing the full correlator such that its Fourier transform, the spectral form factor, is determined for all times, below and above the Heisenberg time. We cover dynamics with and without time-reversal invariance (from the orthogonal and unitary symmetry classes). A key step in our reasoning is to sum the periodic-orbit expansion in terms of a matrix integral, like the one known from the sigma model of random matrix theory.
Organizational Change at the Edge of Chaos: A Complexity Theory Perspective of Autopoietic Systems
Susini, Domenico, III.
2010-01-01
This qualitative phenomenological study includes explorations of organizational change phenomena from the vantage point of complexity theory as experienced through the lived experiences of eight senior level managers and executives based in Northern N.J. who have experienced crisis situations in their organizations. Concepts from the natural…
Chaos a very short introduction
Smith, Leonard
2007-01-01
Chaos: A Very Short Introduction shows that we all have an intuitive understanding of chaotic systems. It uses accessible maths and physics (replacing complex equations with simple examples like pendulums, railway lines, and tossing coins) to explain the theory, and points to numerous examples in philosophy and literature (Edgar Allen Poe, Chang-Tzu, and Arthur Conan Doyle) that illuminate the problems. The beauty of fractal patterns and their relation to chaos, as well as the history of chaos, and its uses in the real world and implications for the philosophy of science are all discussed in this Very Short Introduction.
Bays, Harold
2005-05-01
Excessive fat (adiposity) and dysfunctional fat (adiposopathy) constitute the most common worldwide epidemics of our time -- and perhaps of all time. Ongoing efforts to explain how the micro (adipocyte) and macro (body organ) biologic systems interact through function and dysfunction in promoting Type 2 diabetes mellitus, hypertension and dyslipidemia are not unlike the mechanistic and philosophical thinking processes involved in reconciling the micro (quantum physics) and macro (general relativity) theories in physics. Currently, the term metabolic syndrome refers to a constellation of consequences often associated with excess body fat and is an attempt to unify the associations known to exist between the four fundamental metabolic diseases of obesity, hyperglycemia (including Type 2 diabetes mellitus), hypertension and dyslipidemia. However, the association of adiposity with these metabolic disorders is not absolute and the metabolic syndrome does not describe underlying causality, nor does the metabolic syndrome necessarily reflect any reasonably related pathophysiologic process. Just as with quantum physics, general relativity and the four fundamental forces of the universe, the lack of an adequate unifying theory of micro causality and macro consequence is unsatisfying, and in medicine, impairs the development of agents that may globally improve both obesity and obesity-related metabolic disease. Emerging scientific and clinical evidence strongly supports the novel concept that it is not adiposity alone, but rather it is adiposopathy that is the underlying cause of most cases of Type 2 diabetes mellitus, hypertension and dyslipidemia. Adiposopathy is a plausible Theory of Everything for mankind's greatest metabolic epidemics.
International Nuclear Information System (INIS)
In this paper, controlling chaos when chaotic ferroresonant oscillations occur in a voltage transformer with nonlinear core loss model is performed. The effect of a parallel metal oxide surge arrester on the ferroresonance oscillations of voltage transformers is studied. The metal oxide arrester (MOA) is found to be effective in reducing ferroresonance chaotic oscillations. Also the multiple scales method is used to analyze the chaotic behavior and different types of fixed points in ferroresonance of voltage transformers considering core loss. This phenomenon has nonlinear chaotic dynamics and includes sub-harmonic, quasi-periodic, and also chaotic oscillations. In this paper, the chaotic behavior and various ferroresonant oscillation modes of the voltage transformer is studied. This phenomenon consists of different types of bifurcations such as period doubling bifurcation (PDB), saddle node bifurcation (SNB), Hopf bifurcation (HB), and chaos. The dynamic analysis of ferroresonant circuit is based on bifurcation theory. The bifurcation and phase plane diagrams are illustrated using a continuous method and linear and nonlinear models of core loss. To analyze ferroresonance phenomenon, the Lyapunov exponents are calculated via the multiple scales method to obtain Feigenbaum numbers. The bifurcation diagrams illustrate the variation of the control parameter. Therefore, the chaos is created and increased in the system. (interdisciplinary physics and related areas of science and technology)
Banerjee, S; Grebogi, C; Banerjee, Soumitro; Yorke, James A.; Grebogi, Celso
1998-01-01
It has been proposed to make practical use of chaos in communication, in enhancing mixing in chemical processes and in spreading the spectrum of switch-mode power suppies to avoid electromagnetic interference. It is however known that for most smooth chaotic systems, there is a dense set of periodic windows for any range of parameter values. Therefore in practical systems working in chaotic mode, slight inadvertent fluctuation of a parameter may take the system out of chaos. We say a chaotic attractor is robust if, for its parameter values there exists a neighborhood in the parameter space with no periodic attractor and the chaotic attractor is unique in that neighborhood. In this paper we show that robust chaos can occur in piecewise smooth systems and obtain the conditions of its occurrence. We illustrate this phenomenon with a practical example from electrical engineering.
Malkov, M A
1996-01-01
The asymptotic travelling wave solution of the KdV-Burgers equation driven by the long scale periodic driver is constructed. The solution represents a shock-train in which the quasi-periodic sequence of dispersive shocks or soliton chains is interspersed by smoothly varying regions. It is shown that the periodic solution which has the spatial driver period undergoes period doublings as the governing parameter changes. Two types of chaotic behavior are considered. The first type is a weak chaos, where only a small chaotic deviation from the periodic solution occurs. The second type corresponds to the developed chaos where the solution ``ignores'' the driver period and represents a random sequence of uncorrelated shocks. In the case of weak chaos the shock coordinate being repeatedly mapped over the driver period moves on a chaotic attractor, while in the case of developed chaos it moves on a repellor. Both solutions depend on a parameter indicating the reference shock position in the shock-train. The structure...
Institute of Scientific and Technical Information of China (English)
Li Dingqi; Cheng Yuanping; Wang Lei; Wang Haifeng; Wang Liang; Zhou Hongxing
2011-01-01
Based on the evolution of geological dynamics and spatial chaos theory,we proposed the advanced prediction an advanced prediction method of a gas desorption index of drill cuttings to predict coal and gas outbursts.We investigated and verified the prediction method by a spatial series data of a gas desorption index of drill cuttings obtained from the 113112 coal roadway at the Shitai Mine.Our experimental results show that the spatial distribution of the gas desorption index of drill cuttings has some chaotic characteristics,which implies that the risk of coal and gas outbursts can be predicted by spatial chaos theory.We also found that a proper amount of sample data needs to be chosen in order to ensure the accuracy and practical maneuverability of prediction.The relative prediction error is small when the prediction pace is chosen carefully.In our experiments,it turned out that the optimum number of sample points is 80 and the optimum prediction pace 30.The corresponding advanced prediction pace basically meets the requirements of engineering applications.
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.
Chaos and fractals. Applications to nuclear engineering
International Nuclear Information System (INIS)
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)
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.
Loree, Tim; Stupka, Ed
An overview is provided of the relevant concepts from Total Quality Management (TQM), fuzzy logic, and the chaos theory of education in an effort to support the case for student success courses. First, the paper discusses student success courses, which emphasize helping students develop the skills needed to identify, create, and pursue an…
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...
The chaos theory and the quality assurance; La teoria del caos y la gestion de la calidad
Energy Technology Data Exchange (ETDEWEB)
Aguilar, Omar [Centro de Informacion de la Energia (CIEN), La Habana (Cuba); Domech More, Jesus [Centro de Tecnologia Nuclear (CTN), La Habana (Cuba)
1999-11-01
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) 6 refs., 1 fig., 1 tab.; e-mail: omar at cien.energia.inf.cu; ctn at ctnet.centis.edu.cu
Chaos Behaviour of Molecular Orbit
Institute of Scientific and Technical Information of China (English)
LIU Shu-Tang; SUN Fu-Yan; SHEN Shu-Lan
2007-01-01
Based on H(u)ckel's molecular orbit theory,the chaos and;bifurcation behaviour of a molecular orbit modelled by a nonlinear dynamic system is studied.The relationship between molecular orbit and its energy level in the nonlinear dynamic system is obtained.
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...
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...
Physics and applications of laser diode chaos
Sciamanna, M.; Shore, K. A.
2015-03-01
This Review Article provides an overview of chaos in laser diodes by surveying experimental achievements in the area and explaining the theory behind the phenomenon. The fundamental physics underpinning laser diode chaos and also the opportunities for harnessing it for potential applications are discussed. The availability and ease of operation of laser diodes, in a wide range of configurations, make them a convenient testbed for exploring basic aspects of nonlinear and chaotic dynamics. It also makes them attractive for practical tasks, such as chaos-based secure communications and random number generation. Avenues for future research and development of chaotic laser diodes are also identified.
Chaos dynamic characteristics during mine fires
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
Mine fires break out and continue in confmed scopes, studying mine fire dynamics characteristics is very usefulto prevent and control fire. The judgement index of fire chaos characteristics was introduced, chaos analysis of mine Fireprocess was described, and the reconstruction of phase space was also presented. An example of mine fire was calculated.The computations show that it is feasible to analyze mine fire dynamic characteristics with chaos theory, and indicate thatfire preoeas is a catastrophe, that is to say, the fire system changes from one state to another during mine fire
Physics and Applications of Laser Diode Chaos
Sciamanna, Marc
2015-01-01
An overview of chaos in laser diodes is provided which surveys experimental achievements in the area and explains the theory behind the phenomenon. The fundamental physics underpinning this behaviour and also the opportunities for harnessing laser diode chaos for potential applications are discussed. The availability and ease of operation of laser diodes, in a wide range of configurations, make them a convenient test-bed for exploring basic aspects of nonlinear and chaotic dynamics. It also makes them attractive for practical tasks, such as chaos-based secure communications and random number generation. Avenues for future research and development of chaotic laser diodes are also identified.
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 some degree…
Decoherence, determinism and chaos
International Nuclear Information System (INIS)
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
Chaos in the library environment
Κατσιρίκου, Ανθή
2001-01-01
Describes the impact of chaos theory in social systems and the phenomena that result from it, drawing attention to related phenomena in the state of the library today. Then considers the factors that lead library systems to exhibit chaotic behaviour. These factors are the plethora of technological tools and the variety of software and interfaces, the dependence of resource providers and the increasing supply and diversity of information resources. The changes dictated by these factors influen...
Mitchener, W Garrett; Nowak, Martin A
2004-04-01
Human language is a complex communication system with unlimited expressibility. Children spontaneously develop a native language by exposure to linguistic data from their speech community. Over historical time, languages change dramatically and unpredictably by accumulation of small changes and by interaction with other languages. We have previously developed a mathematical model for the acquisition and evolution of language in heterogeneous populations of speakers. This model is based on game dynamical equations with learning. Here, we show that simple examples of such equations can display complex limit cycles and chaos. Hence, language dynamical equations mimic complicated and unpredictable changes of languages over time. In terms of evolutionary game theory, we note that imperfect learning can induce chaotic switching among strict Nash equilibria.
The bifurcation threshold value of the chaos detection system for a weak signal
Institute of Scientific and Technical Information of China (English)
李月; 杨宝俊; 杜立志; 袁野
2003-01-01
Recently, it has become an important problem to confirm the bifurcation threshold value of a chaos detectionsystem for a weak signal in the fields of chaos detection. It is directly related to whether the results of chaos detectionare correct or not. In this paper, the discrimination system for the dynamic behaviour of a chaos detection system fora weak signal is established by using the theory of linear differential equation with periodic coefficients and computingthe Lyapunov exponents of the chaos detection system; and then, the movement state of the chaos detection system isdefined. The simulation experiments show that this method can exactly confirm the bifurcation threshold value of thechaos detection system.
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...
Toward a definition of chaos for general relativity
Witt, Donald; Schleich, Kristin
1996-01-01
General relativity exhibits a unique feature not represented in standard examples of chaotic systems; it is a spacetime diffeomorphism invariant theory. Thus many characterizations of chaos do not work. It is therefore necessary to develop a definition of chaos suitable for application to general relativity. This presentation will present results towards this goal.
Master Teachers: Making a Difference on the Edge of Chaos
Chapin, Dexter
2008-01-01
The No Child Left Behind legislation, by legitimizing a stark, one-size-fits-all, industrial model of education, has denied the inherent complexity and richness of what teachers do. Discussing teaching in terms of Chaos Theory, Chapin explains that while excellent teaching may occur at the edge of chaos, it is not chaotic. There are patterns…
Hamiltonian chaos and fractional dynamics
Zaslavsky, George M
2008-01-01
The dynamics of realistic Hamiltonian systems has unusual microscopic features that are direct consequences of its fractional space-time structure and its phase space topology. The book deals with the fractality of the chaotic dynamics and kinetics, and also includes material on non-ergodic and non-well-mixing Hamiltonian dynamics. The book does not follow the traditional scheme of most of today's literature on chaos. The intention of the author has been to put together some of the most complex and yet open problems on the general theory of chaotic systems. The importance of the discussed issues and an understanding of their origin should inspire students and researchers to touch upon some of the deepest aspects of nonlinear dynamics. The book considers the basic principles of the Hamiltonian theory of chaos and some applications including for example, the cooling of particles and signals, control and erasing of chaos, polynomial complexity, Maxwell's Demon, and others. It presents a new and realistic image ...
Quantum Chaos and Statistical Mechanics
Srednicki, Mark
1994-01-01
We briefly review the well known connection between classical chaos and classical statistical mechanics, and the recently discovered connection between quantum chaos and quantum statistical mechanics.
混沌理论对城市规划的启示%Enlightenment Of Chaos Theory On Urban Planning
Institute of Scientific and Technical Information of China (English)
徐岩; 宋伟轩
2012-01-01
自20世纪60年代混沌理论问世以来,该理论被迅速应用到包括自然科学与社会科学在内的众多学科领域.城市是一个典型的混沌系统,混沌理论所揭示出的非确定性与不可预测性、有序与无序等属性,为城市规划开辟了新的思维路径,并为城市规划方法论的创新提供了有益的启迪.城市规划师与决策者应深谙城市这一混沌系统的本质,认真积累与总结城市规划实践经验,顺应城市发展规律进行转型期城市规划决策,逐渐掌握城市秩序的真谛,以科学规划降低中国城市转型的社会空间成本.%Since the birth of Chaos Theory in 1960s, it has been applied in multiple disciplines of natural and social science. City is a typical chaotic system. Uncertainty, unpredictability, dialectic relation between order and disorder gives new thought to urban planning. Urban planners and decision makers shall understand the essence of a city's chaotic system, generalize urban planning practice, follow city development rules, grasp urban order, and lower urban transition expense.
Selvam, A. M.
2005-01-01
Non-local connections, i. e. long-range space-time correlations intrinsic to the observed subatomic dynamics of quantum systems is also exhibited by macro-scale dynamical systems as selfsimilar fractal space-time fluctuations and is identified as self-organized criticality. The author has developed a general systems theory for the observed self-organized criticality applicable to dynamical systems of all space-time scales based on the concept that spatial integration of enclosed small-scale f...
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.
CHAOS-BASED FEEDFORWARD OUTPUT FUNCTIONS FOR COMBINING KEYSTREAM GENERATORS
Institute of Scientific and Technical Information of China (English)
Sang Tao; Wang Ruli; Yan Yixun
2001-01-01
The chaos-based feedforward output functions for combining keystream generators are proposed according to chaotic dynamic theory. The generated binary signals are independently and identically distributed, and have predictable periods. All experiments correspond to the theoretical prediction very well.
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...
Contributions of plasma physics to chaos and nonlinear dynamics
Escande, Dominique
2016-01-01
This topical review focusses on the contributions of plasma physics to chaos and nonlinear dynamics bringing new methods which are or can be used in other scientific domains. It starts with the development of the theory of Hamiltonian chaos, and then deals with order or quasi order, for instance adiabatic and soliton theories. It ends with a shorter account of dissipative and high dimensional Hamiltonian dynamics, and of quantum chaos. Most of these contributions are a spin-off of the research on thermonuclear fusion by magnetic confinement, which started in the fifties. Their presentation is both exhaustive and compact. [15 April 2016
Contributions of plasma physics to chaos and nonlinear dynamics
Escande, D. F.
2016-11-01
This topical review focusses on the contributions of plasma physics to chaos and nonlinear dynamics bringing new methods which are or can be used in other scientific domains. It starts with the development of the theory of Hamiltonian chaos, and then deals with order or quasi order, for instance adiabatic and soliton theories. It ends with a shorter account of dissipative and high dimensional Hamiltonian dynamics, and of quantum chaos. Most of these contributions are a spin-off of the research on thermonuclear fusion by magnetic confinement, which started in the fifties. Their presentation is both exhaustive and compact. [15 April 2016
Quantum Chaos in Physical Systems from Super Conductors to Quarks
Bittner, E; Pullirsch, R; Bittner, Elmar; Markum, Harald; Pullirsch, Rainer
2001-01-01
This article is the written version of a talk delivered at the Bexbach Colloquium of Science 2000 and starts with an introduction into quantum chaos and its relationship to classical chaos. The Bohigas-Giannoni-Schmit conjecture is formulated and evaluated within random-matrix theory. Several examples of physical systems exhibiting quantum chaos ranging from nuclear to solid state physics are presented. The presentation concludes with recent research work on quantum chromodynamics and the quark-gluon plasma. In the case of a chemical potential the eigenvalue spectrum becomes complex and one has to deal with non-Hermitian random-matrix theory.
Many-body chaos at weak coupling
Stanford, Douglas
2016-10-01
The strength of chaos in large N quantum systems can be quantified using λ L , the rate of growth of certain out-of-time-order four point functions. We calculate λ L to leading order in a weakly coupled matrix Φ4 theory by numerically diagonalizing a ladder kernel. The computation reduces to an essentially classical problem.
Maldacena, Juan; Stanford, Douglas
2015-01-01
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 $\\lambda_L \\le 2 \\pi k_B T/\\hbar$. We give a precise mathematical argument, based on plausible physical assumptions, establishing this conjecture.
Energy Technology Data Exchange (ETDEWEB)
Bunimovich, Leonid A., E-mail: bunimovh@math.gatech.edu [ABC Program, Georgia Institute of Technology, Atlanta, Georgia 30332 (United States); School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332 (United States); Vela-Arevalo, Luz V., E-mail: luzvela@math.gatech.edu [School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332 (United States)
2015-09-15
A 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.
Atoms in static fields Chaos or Diffraction?
Dando, P A
1998-01-01
A brief review of the manifestations of classical chaos observed in atomic systems is presented. Particular attention is paid to the analysis of atomic spectra by periodic orbit-type theories. For diamagnetic non-hydrogenic Rydberg atoms, the dynamical explanation for observed spectral features has been disputed. By building on our previous work on the photoabsorption spectrum, we show how, by the addition of diffractive terms, the spectral fluctuations in the energy level spectrum of general Rydberg atoms can be obtained with remarkable precision from the Gutzwiller trace formula. This provides further evidence that non-hydrogenic systems are most naturally described in terms of diffraction rather than classical chaos.
Quantum chaos on a critical Fermi surface
Patel, Aavishkar A
2016-01-01
We compute parameters characterizing many-body quantum chaos for a critical Fermi surface without quasiparticle excitations. We examine a theory of $N$ species of fermions at non-zero density coupled to a $U(1)$ gauge field in two spatial dimensions, and determine the Lyapunov rate and the butterfly velocity in an extended RPA approximation. The thermal diffusivity is found to be universally related to these chaos parameters, i.e. the relationship is independent of $N$, the gauge coupling constant, the Fermi velocity, the Fermi surface curvature, and high energy details.
Institute of Scientific and Technical Information of China (English)
陶亮; 张运楚; 同玉洁
2015-01-01
After a single chaotic algorithm encryption, the image also left the outline of the original image, but there is a problem of insufficient strength of the encryption. This paper presents the algorithm of combining two-dimensional Arnold matrix transformation and Chaos Theory for the encryption of X-ray image, uses the features of Arnold disturbing the image position, combines with the theory of chaos encryption to effectively solve the problem of insufficient strength of the single chaotic image encryption algorithm, and finally shows the effectiveness of the algorithm through experiment. Experimental results show that the encryption of this algorithm is very safe.%图像经单一的混沌算法加密后，还留有原图像轮廓，存在加密强度不足的问题。文章提出应用二维Arnold矩阵变换和混沌理论混合加密X射线图像的算法，利用Arnold扰乱图像位置的特点，结合混沌加密理论，有效地解决了单一混沌加密算法对图像加密强度不够的问题。最后，通过实验验证了该算法的有效性。实验结果表明，该算法的加密安全性很高。
基于混沌理论下高校网络舆情引导机制研究%Guide Mechanism of University Network of Public Opinion Based on Chaos Theory
Institute of Scientific and Technical Information of China (English)
郭佳慧; 孙海英
2012-01-01
Through the analysis of public opinion,the network of public opinion and the basic concepts of chaos theory,and make chaos theory as the theoretical basis of University Network of public opinion to guide mechanism,and analysis the Practical reasons for the chaotic characteristics of the university network of public opinion and college students network public opinion,to establish coordination,communication,network management to ensure the public opinion,public opinion information collection and feedback,public opinion crisis emergency warning and handling college students network public opinion to guide the study of the mechanism.%通过对舆情、网络舆情及混沌理论的基本概念的剖析,并把混沌理论作为高校网络舆情引导机制研究的理论依据,对高校网络舆情的混沌特征及高校学生网络舆情形成的现实原因进行分析,对建立协调、交流、发布和通报、信息汇集和反馈、网络舆情管理保障、舆情危机预警和处理等高校学生网络舆情引导机制的研究。
Avoiding Quantum Chaos in Quantum Computation
Berman, G P; Izrailev, F M; Tsifrinovich, V I
2001-01-01
We study a one-dimensional chain of nuclear $1/2-$spins in an external time-dependent magnetic field. This model is considered as a possible candidate for experimental realization of quantum computation. According to the general theory of interacting particles, one of the most dangerous effects is quantum chaos which can destroy the stability of quantum operations. According to the standard viewpoint, the threshold for the onset of quantum chaos due to an interaction between spins (qubits) strongly decreases with an increase of the number of qubits. Contrary to this opinion, we show that the presence of a magnetic field gradient helps to avoid quantum chaos which turns out to disappear with an increase of the number of qubits. We give analytical estimates which explain this effect, together with numerical data supporting
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.
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.
Exploiting chaos for applications
International Nuclear Information System (INIS)
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
Hosur, Pavan; Qi, Xiao-Liang; Roberts, Daniel; Yoshida, Beni(Institute for Quantum Information & Matter and Walter Burke Institute for Theoretical Physics, California Institute of Technology, 1200 E. California Blvd., Pasadena, CA, 91125, U.S.A.)
2016-01-01
We study chaos and scrambling in unitary channels by considering their entanglement properties as states. Using out-of-time-order correlation functions to diagnose chaos, we characterize the ability of a channel to process quantum information. We show that the generic decay of such correlators implies that any input subsystem must have near vanishing mutual information with almost all partitions of the output. Additionally, we propose the negativity of the tripartite information of the channe...
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.
The bifurcation threshold value of the chaos detection system for a weak signal
Institute of Scientific and Technical Information of China (English)
李月; 杨宝俊; 杜立志; 袁野
2003-01-01
Recently, it has become an important problem to confirm the bifurcation threshold value of a chaos detection system for a weak signal in the fields of chaos detection. It is directly related to whether the results of chaos detection are correct or not. In this paper, the discrimination system for the dynamic behaviour of a chaos detection system for a weak signal is established by using the theory of linear differential equation with periodic coefficients and computing the Lyapunov exponents of the chaos detection system; and then, the movement state of the chaos detection system is defined. The simulation experiments show that this method can exactly confirm the bifurcation threshold value of the chaos detection system.
Fractal Patterns and Chaos Games
Devaney, Robert L.
2004-01-01
Teachers incorporate the chaos game and the concept of a fractal into various areas of the algebra and geometry curriculum. The chaos game approach to fractals provides teachers with an opportunity to help students comprehend the geometry of affine transformations.
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.
Chaos-assisted, broadband trapping of light in optical resonators
Liu, C; Molinari, D; Khan, Y; Ooi, B S; Krauss, T F; Fratalocchi, A
2012-01-01
Chaos is a phenomenon that occurs in many aspects of contemporary science. In classical dynamics, chaos is defined as a hypersensitivity to initial conditions. The presence of chaos is often unwanted, as it introduces unpredictability, which makes it difficult to predict or explain experimental results. Conversely, we demonstrate here how chaos can be used to enhance the ability of an optical resonator to store energy. We combine analytic theory with ab-initio simulations and experiments in photonic crystal resonators to show that a chaotic resonator can store six times more energy than its classical counterpart of the same volume. We explain the observed increase with the equipartition of energy among all degrees of freedom of the chaotic resonator, i.e. the cavity modes, which is evident from the convergence of their lifetime towards a single value. A compelling illustration of the theory is provided by demonstrating enhanced absorption in deformed polystyrene microspheres.
Study on chaos in short circuit gas metal arc welding process
Institute of Scientific and Technical Information of China (English)
Lü Xiaoqing; Cao Biao; Zeng Min; Wang Zhenmin; Huang Shisheng
2007-01-01
Based on the chaos theory, an idea is put forward to analyze the short circuit Gas Metal Arc Welding (GMAW-S) process. The theory of phase space reconstruction and related algorithms such as mutual information and so on, are applied to analyze the chaos of the GMAW-S process. The largest Lyapunov exponents of some current time series are calculated, and the results indicate that chaos exists in the GMAW-S process. The research of the chaos in the GMAW-S process can be help to get new knowledge of the process.
Quantum Graphs: Applications to Quantum Chaos and Universal Spectral Statistics
Gnutzmann, Sven; Smilansky, Uzy
2006-01-01
During the last years quantum graphs have become a paradigm of quantum chaos with applications from spectral statistics to chaotic scattering and wave function statistics. In the first part of this review we give a detailed introduction to the spectral theory of quantum graphs and discuss exact trace formulae for the spectrum and the quantum-to-classical correspondence. The second part of this review is devoted to the spectral statistics of quantum graphs as an application to quantum chaos. E...
Chaos and Nonlinear Dynamics in a Quantum Artificial Economy
Gonçalves, Carlos Pedro
2012-01-01
Chaos and nonlinear economic dynamics are addressed for a quantum coupled map lattice model of an artificial economy, with quantized supply and demand equilibrium conditions. The measure theoretic properties and the patterns that emerge in both the economic business volume dynamics' diagrams as well as in the quantum mean field averages are addressed and conclusions are drawn in regards to the application of quantum chaos theory to address signatures of chaotic dynamics in relevant discrete economic state variables.
Competitive coexistence in stoichiometric chaos
Deng, Bo; Loladze, Irakli
2007-09-01
Classical predator-prey models, such as Lotka-Volterra, track the abundance of prey, but ignore its quality. Yet, in the past decade, some new and occasionally counterintuitive effects of prey quality on food web dynamics emerged from both experiments and mathematical modeling. The underpinning of this work is the theory of ecological stoichiometry that is centered on the fact that each organism is a mixture of multiple chemical elements such as carbon (C), nitrogen (N), and phosphorus (P). The ratios of these elements can vary within and among species, providing simple ways to represent prey quality as its C:N or C:P ratios. When these ratios modeled to vary, as they frequently do in nature, seemingly paradoxical results can arise such as the extinction of a predator that has an abundant and accessible prey. Here, for the first time, we show analytically that the reduction in prey quality can give rise to chaotic oscillations. In particular, when competing predators differ in their sensitivity to prey quality then all species can coexist via chaotic fluctuations. The chaos generating mechanism is based on the existence of a junction-fold point on the nullcline surfaces of the species. Conditions on parameters are found for such a point, and the singular perturbation method and the kneading sequence analysis are used to demonstrate the existence of a period-doubling cascade to chaos as a result of the point.
Dissipative structures and chaos
Mori, Hazime
1998-01-01
This monograph consists of two parts and gives an approach to the physics of open nonequilibrium systems. Part I derives the phenomena of dissipative structures on the basis of reduced evolution equations and includes Bénard convection and Belousov-Zhabotinskii chemical reactions. Part II discusses the physics and structures of chaos. While presenting a construction of the statistical physics of chaos, the authors unify the geometrical and statistical descriptions of dynamical systems. The shape of chaotic attractors is characterized, as are the mixing and diffusion of chaotic orbits and the fluctuation of energy dissipation exhibited by chaotic systems.
Deterministic chaos an introduction
Schuster, Heinz Georg
2005-01-01
A new edition of this well-established monograph, this volume provides a comprehensive overview over the still fascinating field of chaos research. The authors include recent developments such as systems with restricted degrees of freedom but put also a strong emphasis on the mathematical foundations. Partly illustrated in color, this fourth edition features new sections from applied nonlinear science, like control of chaos, synchronisation of nonlinear systems, and turbulence, as well as recent theoretical concepts like strange nonchaotic attractors, on-off intermittency and spatio-temporal chaotic motion
Directory of Open Access Journals (Sweden)
B. Buti
1999-01-01
Full Text Available A nonlinear wave, in general, is equivalent to a nonlinear dynamical system, which exhibits the phenomena of chaos. By means of techniques of nonlinear dynamical systems, we have investigated the conditions under which nonlinear Alfvén waves and lower-hybrid waves can become chaotic. The role of heavy ions, in controlling the chaos in magnetoplasmas, is examined. Chaotic routes to Alfvénic turbulence, with k-1 spectra, are observed in case of externally driven nonlinear Alfvén waves. Anomalous heating and particle acceleration resulting from chaotic fields, generated by lower-hybrid waves, are briefly outlined.
Akhmet, Marat; Fen, Mehmet Onur
2012-01-01
Morphogenesis, as it is understood in a wide sense by Ren\\'e Thom, is considered for various types of chaos. That is, those, obtained by period-doubling cascade, Devaney's and Li-Yorke chaos. Moreover, in discussion form we consider inheritance of intermittency, the double-scroll Chua's attractor and quasiperiodical motions as a possible skeleton of a chaotic attractor. To make our introduction of the paper more clear, we have to say that one may consider other various accompanying concepts o...
Dynamic system uncertainty propagation using polynomial chaos
Institute of Scientific and Technical Information of China (English)
Xiong Fenfen; Chen Shishi; Xiong Ying
2014-01-01
The classic polynomial chaos method (PCM), characterized as an intrusive methodology, has been applied to uncertainty propagation (UP) in many dynamic systems. However, the intrusive polynomial chaos method (IPCM) requires tedious modification of the governing equations, which might introduce errors and can be impractical. Alternative to IPCM, the non-intrusive polynomial chaos method (NIPCM) that avoids such modifications has been developed. In spite of the frequent application to dynamic problems, almost all the existing works about NIPCM for dynamic UP fail to elaborate the implementation process in a straightforward way, which is important to readers who are unfamiliar with the mathematics of the polynomial chaos theory. Meanwhile, very few works have compared NIPCM to IPCM in terms of their merits and applicability. Therefore, the mathematic procedure of dynamic UP via both methods considering parametric and initial condition uncertainties are comparatively discussed and studied in the present paper. Comparison of accuracy and efficiency in statistic moment estimation is made by applying the two methods to several dynamic UP problems. The relative merits of both approaches are discussed and summarized. The detailed description and insights gained with the two methods through this work are expected to be helpful to engineering designers in solving dynamic UP problems.
R. Kříž
2011-01-01
This paper presents an analysis of GDP and finds chaos in GDP. I tried to find a nonlinear lower-dimensional discrete dynamic macroeconomic model that would characterize GDP. This model is represented by a set of differential equations. I have used the Mathematica and MS Excel programs for the analysis.
Directory of Open Access Journals (Sweden)
Kratochvíl C.
2007-10-01
Full Text Available The purpose of this article is to provide an elementary introduction to the subject of chaos in the electromechanical drive systems. In this article, we explore chaotic solutions of maps and continuous time systems. These solutions are also bounded like equilibrium, periodic and quasiperiodic solutions.
Inverse anticipating chaos synchronization.
Shahverdiev, E M; Sivaprakasam, S; Shore, K A
2002-07-01
We derive conditions for achieving inverse anticipating synchronization where a driven time-delay chaotic system synchronizes to the inverse future state of the driver. The significance of inverse anticipating chaos in delineating synchronization regimes in time-delay systems is elucidated. The concept is extended to cascaded time-delay systems.
DEFF Research Database (Denmark)
Lykke, Marianne; Lund, Haakon; Skov, Mette
2016-01-01
CHAOS (Cultural Heritage Archive Open System) provides streaming access to more than 500.000 broad-casts by the Danish Broadcast Corporation from 1931 and onwards. The archive is part of the LARM project with the purpose of enabling researchers to search, annotate, and interact with recordings. T...
Frozen spatial chaos induced by boundaries
Eguiluz, V M; Piro, O; Balle, S; Eguiluz, Victor M.; Hernandez-Garcia, Emilio; Piro, Oreste; Balle, Salvador
1999-01-01
We show that rather simple but non-trivial boundary conditions could induce the appearance of spatial chaos (that is stationary, stable, but spatially disordered configurations) in extended dynamical systems with very simple dynamics. We exemplify the phenomenon with a nonlinear reaction-diffusion equation in a two-dimensional undulated domain. Concepts from the theory of dynamical systems, and a transverse-single-mode approximation are used to describe the spatially chaotic structures.
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.
Extension of spatiotemporal chaos in glow discharge-semiconductor systems
Energy Technology Data Exchange (ETDEWEB)
Akhmet, Marat, E-mail: marat@metu.edu.tr; Fen, Mehmet Onur [Department of Mathematics, Middle East Technical University, 06800 Ankara (Turkey); Rafatov, Ismail [Department of Physics, Middle East Technical University, 06800 Ankara (Turkey)
2014-12-15
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).].
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
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.
Institute of Scientific and Technical Information of China (English)
孙景文; 常鲜戎
2014-01-01
针对现有混沌理论中嵌入维数和延迟时间的选取难以达到最优，局域预测时邻近预测点的选取不够准确，提出了改进的混沌理论：采用改进的C-C法找到嵌入维数和延迟时间；邻近预测点的选取根据参考相点的演化趋势进行判断。针对最小二乘支持向量回归机LSSVR参数难以确定，提出ACPSO-LSSVR：自适应混沌粒子群ACPSO一方面能根据群体早熟收敛程度和个体自适应值来调整惯性权重，另一方面能根据混沌变量的随机性和遍历性进行粒子的初始化，加快优化过程，防止局部极小。采用ACP-SO来优化LSSVR的待选参数，提高负荷预测的精度。实例分析验证了该方法的可行性和实用性。%In view of the existing chaos theory, the selection of the embedding dimension and delay time is difficult to determine, the choose of adjacent estimate point is not accurate enough. So an improved chaos theory is presen-ted. On one hand, embedding dimension and delay time are determined via the improved C-C theory, the accu-rate embedding dimension is determined according to the forecasting result. On the other hand, the adjacent esti-mate points are determined according to the evolution trend of reference points. In view of the parameters of LSSVR is difficult to determine, ACPSO-LSSVR is presented. ACPSO can adjust inertia weight according to the premature convergence degree and the individual fitness. The initialization of the particles is made according to the random-ness and ergodicity of chaotic variables. The parameters of LSSVR are optimized according to ACPSO, so the pre-cision of load forecasting is improved. The example analysis proves the feasibility and practicability of the method.
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…
Finite-Time Chaos Suppression of Permanent Magnet Synchronous Motor Systems
Directory of Open Access Journals (Sweden)
Yi-You Hou
2014-04-01
Full Text Available This paper considers the problem of the chaos suppression for the Permanent Magnet Synchronous Motor (PMSM system via the finite-time control. Based on Lyapunov stability theory and the finite-time controller are developed such that the chaos behaviors of PMSM system can be suppressed. The effectiveness and accuracy of the proposed methods are shown in numerical simulations.
Matsushita, Raul; Gleria, Iram; Figueiredo, Annibal; Da Silva, Sergio
2007-05-01
The yuan-dollar returns prior to the 2005 revaluation show a Sierpinski triangle in an iterated function system clumpiness test. Yet the fractal vanishes after the revaluation. The Sierpinski commonly emerges in the chaos game, where randomness coexists with deterministic rules (M.F. Barnsley, Fractals Everywhere, Academic Press, San Diego, 1988; H.O. Peitgen, H. Jurgens, D. Saupe, Chaos and Fractals: New Frontiers of Science, Springer, New York, 1992). Here, it is explained by the yuan's pegs to the US dollar, which made more than half of the data points close to zero. Extra data from the Brazilian and Argentine experiences do confirm that the fractal emerges whenever exchange rate pegs are kept for too long.
Chaos detection and predictability
Gottwald, Georg; Laskar, Jacques
2016-01-01
Distinguishing chaoticity from regularity in deterministic dynamical systems and specifying the subspace of the phase space in which instabilities are expected to occur is of utmost importance in as disparate areas as astronomy, particle physics and climate dynamics. To address these issues there exists a plethora of methods for chaos detection and predictability. The most commonly employed technique for investigating chaotic dynamics, i.e. the computation of Lyapunov exponents, however, may suffer a number of problems and drawbacks, for example when applied to noisy experimental data. In the last two decades, several novel methods have been developed for the fast and reliable determination of the regular or chaotic nature of orbits, aimed at overcoming the shortcomings of more traditional techniques. This set of lecture notes and tutorial reviews serves as an introduction to and overview of modern chaos detection and predictability techniques for graduate students and non-specialists. The book cover...
Marklof, J
2005-01-01
The central objective in the study of quantum chaos is to characterize universal properties of quantum systems that reflect the regular or chaotic features of the underlying classical dynamics. Most developments of the past 25 years have been influenced by the pioneering models on statistical properties of eigenstates (Berry 1977) and energy levels (Berry and Tabor 1977; Bohigas, Giannoni and Schmit 1984). Arithmetic quantum chaos (AQC) refers to the investigation of quantum system with additional arithmetic structures that allow a significantly more extensive analysis than is generally possible. On the other hand, the special number-theoretic features also render these systems non-generic, and thus some of the expected universal phenomena fail to emerge. Important examples of such systems include the modular surface and linear automorphisms of tori (`cat maps') which will be described below.
Hosur, Pavan; Roberts, Daniel A; Yoshida, Beni
2015-01-01
We study chaos and scrambling in unitary channels by considering their entanglement properties as states. Using out-of-time-order correlation functions to diagnose chaos, we characterize the ability of a channel to process quantum information. We show that the generic decay of such correlators implies that any input subsystem must have near vanishing mutual information with almost all partitions of the output. Additionally, we propose the negativity of the tripartite information of the channel as a general diagnostic of scrambling. This measures the delocalization of information and is closely related to the decay of out-of-time-order correlators. We back up our results with numerics in two non-integrable models and analytic results in a perfect tensor network model of chaotic time evolution. These results show that the butterfly effect in quantum systems implies the information-theoretic definition of scrambling.
Martingales, Nonlinearity, and Chaos
Barnett, William A.; Apostolos Serletis
1998-01-01
In this article we provide a review of the literature with respect to the efficient markets hypothesis and chaos. In doing so, we contrast the martingale behavior of asset prices to nonlinear chaotic dynamics, discuss some recent techniques used in distinguishing between probabilistic and deterministic behavior in asset prices, and report some evidence. Moreover, we look at the controversies that have arisen about the available tests and results, and raise the issue of whether dynamical syste...
Quantum chaos in QCD and hadrons
Markum, H; Pullirsch, R; Sengl, B; Wagenbrunn, R F; Markum, Harald; Plessas, Willibald; Pullirsch, Rainer; Sengl, Bianka; Wagenbrunn, Robert F.
2005-01-01
This article is the written version of a talk delivered at the Workshop on Nonlinear Dynamics and Fundamental Interactions in Tashkent and starts with an introduction into quantum chaos and its relationship to classical chaos. The Bohigas-Giannoni-Schmit conjecture is formulated and evaluated within random-matrix theory. In accordance to the title, the presentation is twofold and begins with research results on quantum chromodynamics and the quark-gluon plasma. We conclude with recent research work on the spectroscopy of baryons. Within the framework of a relativistic constituent quark model we investigate the excitation spectra of the nucleon and the delta with regard to a possible chaotic behavior for the cases when a hyperfine interaction of either Goldstone-boson-exchange or one-gluon-exchange type is added to the confinement interaction. Agreement with predictions from the experimental hadron spectrum is established.
Enlightening complexity: making energy with chaos
Molinari, D
2011-01-01
We study the energy harvesting of photons undergoing chaotic dynamics with different complexity degrees. Our theory employs a multiscale analysis, which combines Hamiltonian billiards, time-dependent coupled mode theory and ab-initio simulations. In analogy to classical thermodynamics, where the presence of microscopic chaos leads to a single direction for time and entropy, an increased complexity in the motion of photons yields to a monotonic accumulation of energy, which dramatically grows thanks to a constructive mechanism of energy buildup. This result could lead to the realization of novel complexity-driven, energy harvesting architectures.
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
Institute of Scientific and Technical Information of China (English)
方锦清; 罗晓曙; 陈关荣; 翁甲强
2001-01-01
Beam halo-chaos is essentially a complex spatiotemporal chaotic motion in a periodic-focusing channel of a highpower linear proton accelerator. The controllability condition for beam halo-chaos is analysed qualitatively. A special nonlinear control method, i.e. the wavelet-based function feedback, is proposed for controlling beam halochaos. Particle-in-cell simulations are used to explore the nature of halo-chaos formation, which has shown that the beam hMo-chaos is suppressed effectively after using nonlinear control for the proton beam with an initial full Gaussian distribution. The halo intensity factor Hav is reduced from 14%o to zero, and the other statistical physical quantities of beam halo-chaos are more than doubly reduced. The potential applications of such nonlinear control in experiments are briefly pointed out.
Bifurcations and Chaos in Duffing Equation
Institute of Scientific and Technical Information of China (English)
2007-01-01
The Duffing equation with even-odd asymmetrical nonlinear-restoring force and one external forcing is investigated. The conditions of existence of primary resonance, second-order, third-order subharmonics, m-order subharmonics and chaos are given by using the second-averaging method, the Melnikov method and bifurcation theory. Numerical simulations including bifurcation diagram, bifurcation surfaces and phase portraits show the consistence with the theoretical analysis. The numerical results also exhibit new dynamical behaviors including onset of chaos, chaos suddenly disappearing to periodic orbit, cascades of inverse period-doubling bifurcations, period-doubling bifurcation, symmetry period-doubling bifurcations of period-3 orbit, symmetry-breaking of periodic orbits, interleaving occurrence of chaotic behaviors and period-one orbit, a great abundance of periodic windows in transient chaotic regions with interior crises and boundary crisis and varied chaotic attractors. Our results show that many dynamical behaviors are strictly departure from the behaviors of the Duffing equation with odd-nonlinear restoring force.
Dembiński, S. T.; Makowski, A. J.; Pepłowski, P.
1993-02-01
We report for the first time quantum calculations for the so-called bouncer model, the classical analog of which is well known to manifest a chaotic behavior. Three versions of our model are fully tractable quantum mechanically and are potentially a rich source of data for establishing properties of a quantum system of which the classical mechanics can be chaotic. Among the results presented here, consequences of the varying bandwidth of infinite-dimensional transition matrices on the use of the correspondence between classical chaos and non-Poissonian quasienergy statistics are discussed.
Chaos Control in Synchronous Reluctance Motors Using the LaSalle Theory%基于拉萨尔不变集定理控制同步磁阻电动机的混沌振荡
Institute of Scientific and Technical Information of China (English)
李健昌; 韦笃取; 张波
2013-01-01
A new strategy for chaos control was investigated using the LaSalle's invariant theory. This strategy was free of the effect of uncertain equilibria in the synchronous reluctance motor. The accuracy and validity of the proposed control method were approved by the results of simulation analysis. The strategy can automatically find the balance point of the system and work when the motor balance point is unknown, so the principle is simple, direct and favorable to practical application. The study results are helpful for maintaining the secure operation of synchronous reluctance motor.%首先基于拉萨尔(LaSalle)不变集定理提出一种新的控制方法,然后证明混沌同步磁阻电动机(Syn-RMs)在该控制器作用下达到稳定.由于该控制方法能自动识别系统平衡点,在电机平衡点位置未知的情况下仍然有效,因此控制器设计原理简洁直接,有利于实际应用.研究结果对保证SynRMs的可靠运行具有重要意义.
Institute of Scientific and Technical Information of China (English)
刘霞
2011-01-01
Based on the inspiration given to the tourism destination crisis management by the chaos theory,this paper sums up the mechanism of tourism crisis on tourism destinations.This paper builds the tourism destination crisis management system from the aspects of tourism crisis warning and crisis response and establishes a general model of tourism destinations crisis prevention.%立足于混沌理论对旅游目的地危机管理的思想启示,总结出旅游危机对旅游目的地的影响机制。在此基础上,文章从旅游危机预警和危机应对两个层面构建旅游目的地危机管理体系,并分别阐述了两个层面构建的内容,最终建立了旅游目的地危机防范的一般模型。
The Origin of Chaos in the Outer Solar System
Murray, N; Holman, M.
1999-01-01
Classical analytic theories of the solar system indicate that it is stable, but numerical integrations suggest that it is chaotic. This disagreement is resolved by a new analytic theory. The theory shows that the chaos among the Jovian planets results from the overlap of the components of a mean motion resonance among Jupiter, Saturn, and Uranus, and provides rough estimates of the Lyapunov time (10 million years) and the dynamical lifetime of Uranus (10^{18} years). The Jovian planets must h...
Predicting Storm Surges: Chaos, Computational Intelligence, Data Assimilation, Ensembles
Siek, M.B.L.A.
2011-01-01
Accurate predictions of storm surge are of importance in many coastal areas. This book focuses on data-driven modelling using methods of nonlinear dynamics and chaos theory for predicting storm surges. A number of new enhancements are presented: phase space dimensionality reduction, incomplete time
Does the transition to chaos determine the dynamic aperture?
International Nuclear Information System (INIS)
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
Topological organization of (low-dimensional) chaos
International Nuclear Information System (INIS)
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
Time reversibility, computer simulation, and chaos
Hoover, William Graham
1999-01-01
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
Bose-Hubbard Hamiltonian: Quantum chaos approach
Kolovsky, Andrey R.
2016-03-01
We discuss applications of the theory of quantum chaos to one of the paradigm models of many-body quantum physics — the Bose-Hubbard (BH) model, which describes, in particular, interacting ultracold Bose atoms in an optical lattice. After preliminary, pure quantum analysis of the system we introduce the classical counterpart of the BH model and the governing semiclassical equations of motion. We analyze these equations for the problem of Bloch oscillations (BOs) of cold atoms where a number of experimental results are available. The paper is written for nonexperts and can be viewed as an introduction to the field.
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
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. PMID:27030426
Schmidt, Britney E.
2013-10-01
A critical question for the habitability of Europa remains: how does the ice shell work? The detection of shallow subsurface lenses below Europa’s chaos implies that the ice shell is recycled rapidly and that Europa may be currently active. While this is not the first time liquid water has been implicated for Europa, the location of these features combined with new perspective on their dynamics frames the question in a new way. Melt lenses are intriguing potential habitats. Moreover, their formation requires the existence of impurities within the upper ice shell that may be sources of energy for microorganisms. Geomorphic evidence also exists for hydraulic redistribution of fluids both vertically and horizontally through pores and fractures. This process, observed in terrestrial ice shelves, may preserve liquid water within the ice matrix over many kilometers from the source. Horizontal transport of material may produce interconnectivity between distinct regions of Europa, thus preserving habitable conditions within the ice over a longer duration. At a surface age of 40-90 Myr, with 25-50% covered by chaos terrain, Europa's resurfacing rate is very high and water likely plays a significant role. Because of the vigor of overturn implied by this new work, it is likely that surface and subsurface materials are well-mixed within the largest and deepest lenses, providing a mechanism for bringing oxidants and other surface contaminants to the deeper ice shell where it can reach the ocean by convective or compositional effects. The timescales over which large lenses refreeze are large compared to the timescales for vertical transport, while the timescales for smaller lenses are comparable to or shorter than convective timescales. Moreover, marine ice accretion at the bottom of the ice shell may be contributing to a compositional buoyancy engine that would change the makeup of the ice shell. From this point of view, we evaluate the habitability of Europa’s ice and
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...
Directory of Open Access Journals (Sweden)
Akio Matsumoto
1997-01-01
Full Text Available This study augments the traditional linear cobweb model with lower and upper bounds for variations of output. Its purpose is to detect the relationship between the output constraints and the dynamics of the modified model. Due to the upper and lower bounds, a transitional function takes on a tilted z-profile having three piecewise segments with two turning points. It prevents the price (or quantity dynamics from explosive oscillations. This study demonstrates, by presenting numerical examples, that the modified cobweb model can generate various dynamics ranging from stable periodic cycles to ergodic chaos if a product of the marginal propensity to consume and the marginal product is greater than unity.
Ercsey-Ravasz, Maria
2012-01-01
The mathematical structure of the widely popular Sudoku puzzles is akin to typical hard constraint satisfaction problems that lie at the heart of many applications, including protein folding and the general problem of finding the ground state of a glassy spin system. Via an exact mapping of Sudoku into a deterministic, continuous-time dynamical system, here we show that the difficulty of Sudoku translates into transient chaotic behavior exhibited by the dynamical system. In particular, we show that the escape rate $\\kappa$, an invariant characteristic of transient chaos, provides a single scalar measure of the puzzle's hardness, which correlates well with human difficulty level ratings. Accordingly, $\\eta = -\\log_{10}{\\kappa}$ can be used to define a "Richter"-type scale for puzzle hardness, with easy puzzles falling in the range $0 3$. To our best knowledge, there are no known puzzles with $\\eta > 4$.
DEFF Research Database (Denmark)
Lindberg, Erik
1996-01-01
Can we believe in the results of our circuit simulators ? Is it possible to distinguish between results due to numerical chaos and resultsdue to the eventual chaotic nature of our modelsof physical systems ?. Three experiments with SPICE are presented: (1) A "stable" active RCcircuit with poles...... in the right half plane. (2) "Chaotic" steady state behaviour of a non-chaotic dc power supply. (3) Analysis of a Colpitts oscillator with chaotic behaviour. In order to obtain reliable results from the SPICE simulators the users of these programs need insight not only in the use of the programs but also...... in the models of the circuits to be analyzed. If trimmed properly SPICE normally gives the correct result....
Wernecke, Hendrik; Gros, Claudius
2016-01-01
For a chaotic system pairs of initially close-by trajectories become eventually fully uncorrelated on the attracting set. This process of decorrelation is split into an initial decrease characterized by the maximal Lyapunov exponent and a subsequent diffusive process on the chaotic attractor causing the final loss of predictability. The time scales of both processes can be either of the same or of very different orders of magnitude. In the latter case the two trajectories linger within a finite but small distance (with respect to the overall size of the attractor) for exceedingly long times and therefore remain partially predictable. We introduce a 0-1 indicator for chaos capable of describing this scenario, arguing, in addition, that the chaotic closed braids found close to a period-doubling transition are generically partially predictable.
Quantum Instantons and Quantum Chaos
Jirari, H.; Kröger, H.; Luo, X. Q.; Moriarty, K. J. M.; Rubin, S. G.
1999-01-01
Based on a closed form expression for the path integral of quantum transition amplitudes, we suggest rigorous definitions of both, quantum instantons and quantum chaos. As an example we compute the quantum instanton of the double well potential.
Chaos and complexity by design
Roberts, Daniel A
2016-01-01
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 $k$th 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 and Quantum Computers
Shepelyansky, D L
2001-01-01
The standard generic quantum computer model is studied analytically and numerically and the border for emergence of quantum chaos, induced by imperfections and residual inter-qubit couplings, is determined. This phenomenon appears in an isolated quantum computer without any external decoherence. The onset of quantum chaos leads to quantum computer hardware melting, strong quantum entropy growth and destruction of computer operability. The time scales for development of quantum chaos and ergodicity are determined. In spite the fact that this phenomenon is rather dangerous for quantum computing it is shown that the quantum chaos border for inter-qubit coupling is exponentially larger than the energy level spacing between quantum computer eigenstates and drops only linearly with the number of qubits n. As a result the ideal multi-qubit structure of the computer remains rather robust against imperfections. This opens a broad parameter region for a possible realization of quantum computer. The obtained results are...
Ledenyov, Dimitri O.; Ledenyov, Viktor O.
2013-01-01
The investment economy is a main characteristic of prosperous society. The investment portfolio management is a main financial problem, which has to be solved by the investment, commercial and central banks with the application of modern portfolio theory in the investment economy. We use the learning analytics together with the integrative creative imperative intelligent conceptual co-lateral adaptive thinking with the purpose to advance our scientific knowledge on the diversified investment ...
Adaptive Image Encryption Algorithm Based on Chaos Theory and Hash Function%基于混沌理论和Hash函数的自适应图像加密算法
Institute of Scientific and Technical Information of China (English)
赵希奇; 柏逢明; 吕贵花
2014-01-01
In this paper, a image encryption algorithm based on chaos theory and Hash functions are proposed for achive the digital image encryption. The scrambling transformation pixel matrix of image is got from extraction chaotic signal and Hash function by using the algorithm,then the adaptive diffusion for image gray scale is carried out by using piecewise Logistic mapping. This algorithm has large key space;the statistical attack capability is strong and effective against entropy attack;secret key sensitivity is strong,good performance;the corresponding security level can be met.%为了实现对数字图像的加密，提出了一种基于混沌理论和Hash函数的自适应图像加密算法。该算法用抽取的Lorenz混沌信号及Hash函数得到像素置乱矩阵，并对图像的像素进行置乱，利用分段Logistic映射对图像灰度进行自适应扩散。理论分析和仿真实验结果表明，该算法具有密钥空间大、抗统计攻击能力强、有效抵抗熵攻击、秘钥敏感性强等良好的性能，能够达到相应的安全水平。
Lecture notes on Gaussian multiplicative chaos and Liouville Quantum Gravity
Rhodes, Rémi; Vargas, Vincent
2016-01-01
The purpose of these notes, based on a course given by the second author at Les Houches summer school, is to explain the probabilistic construction of Polyakov's Liouville quantum gravity using the theory of Gaussian multiplicative chaos. In particular, these notes contain a detailed description of the so-called Liouville measures of the theory and their conjectured relation to the scaling limit of large planar maps properly embedded in the sphere. These notes are rather short and require no ...
Chaos, brain and divided consciousness.
Bob, Petr
2007-01-01
with schizophrenia and depression. Increased level of psychopathological symptoms indicates close relationship to the right-left EDA asymmetry and asymmetry of information entropy calculated by non-linear recurrence quantification analysis of EDA records. Because epileptiform activity has specific chaotic behaviour and calculated information entropy from EDA records reflects the complexity of the deterministic structure in the system there is a relevant assumption that unilaterally increased complexity may produce interhemispheric disbalance and increased chaoticity which hypothetically may serve as a dynamic source of epileptiform discharges related to trauma induced kindling mechanism. Specific form of chaotic inner organization which cannot be explained only as a consequence of external causality support also psychophysiological data that lead to the so-called self-organizing theory of dreaming by Kahn and Hobson. This study suggests that self-organizing theory of dreaming is particularly important with respect to problem of memory formation and processing during dissociative states characteristic for dreams. Recent data and also findings of this study support the research utility of chaos theory in psychology and neuroscience, and also its conceptual view of dynamic ordering factors and self-organization underlying psychological processes and brain physiology. PMID:17867519
Institute of Scientific and Technical Information of China (English)
柴国君; 李文豪; 魏晶国
2012-01-01
In Economics research,human is the starting point and result of social economic activities.Therefore,＂the human nature hypothesis＂ has become the core basis of economic theory.According to the different perspectives,this paper induces and collates ＂the human nature hypothesis＂ from the perspectives of atomic theory and chaos theory.From the perspective of atomic theory,Smith＇s ＂economic man＂ is the core.It also combines the supplement of later new classical economics,modifies and absorbs Simon＇s＂ limited rational human view＂ and modifies the supplement of Economics to ＂economic man＂.In the perspective of chaos theory,it analyzes and elaborates from two main lines of ＂social man＂ and ＂system man＂.At last,this paper splits the hypothesis of these two branches,puts forward the hypothesis of ＂cyber economic man＂.%经济学是以社会经济活动中的人作为研究的出发点和归宿的,因此对人的基本假设成了经济学理论最核心的基础。按照对于人的假定的视角不同,本文从原子论和混沌论两个视角分别对人的假定理论进行归纳和整理,在原子论视角中以斯密的＂经济人＂为核心,结合后来新古典经济学家的补充和修正还吸收了西蒙的有限理性人观点及行为经济学对＂经济人＂的修订;在混沌论视角中以社会人和制度人两条主线进行分析阐述。最后折中了两大分支的假定,提出了＂网络经济人＂假定。
Chaos: A Very Short Introduction
International Nuclear Information System (INIS)
This book is a new volume of a series designed to introduce the curious reader to anything from ancient Egypt and Indian philosophy to conceptual art and cosmology. Very handy in pocket size, Chaos promises an introduction to fundamental concepts of nonlinear science by using mathematics that is 'no more complicated than X=2. Anyone who ever tried to give a popular science account of research knows that this is a more challenging task than writing an ordinary research article. Lenny Smith brilliantly succeeds to explain in words, in pictures and by using intuitive models the essence of mathematical dynamical systems theory and time series analysis as it applies to the modern world. In a more technical part he introduces the basic terms of nonlinear theory by means of simple mappings. He masterly embeds this analysis into the social, historical and cultural context by using numerous examples, from poems and paintings over chess and rabbits to Olbers' paradox, card games and 'phynance'. Fundamental problems of the modelling of nonlinear systems like the weather, sun spots or golf balls falling through an array of nails are discussed from the point of view of mathematics, physics and statistics by touching upon philosophical issues. At variance with Laplace's demon, Smith's 21st century demon makes 'real world' observations only with limited precision. This poses a severe problem to predictions derived from complex chaotic models, where small variations of initial conditions typically yield totally different outcomes. As Smith argues, this difficulty has direct implications on decision-making in everyday modern life. However, it also asks for an inherently probabilistic theory, which somewhat reminds us of what we are used to in the microworld. There is little to criticise in this nice little book except that some figures are of poor quality thus not really reflecting the beauty of fractals and other wonderful objects in this field. I feel that occasionally the book
Chaos: A Very Short Introduction
Energy Technology Data Exchange (ETDEWEB)
Klages, R [School of Mathematical Sciences, Mile End Road, London, E1 4NS (United Kingdom)
2007-07-20
This book is a new volume of a series designed to introduce the curious reader to anything from ancient Egypt and Indian philosophy to conceptual art and cosmology. Very handy in pocket size, Chaos promises an introduction to fundamental concepts of nonlinear science by using mathematics that is 'no more complicated than X=2. Anyone who ever tried to give a popular science account of research knows that this is a more challenging task than writing an ordinary research article. Lenny Smith brilliantly succeeds to explain in words, in pictures and by using intuitive models the essence of mathematical dynamical systems theory and time series analysis as it applies to the modern world. In a more technical part he introduces the basic terms of nonlinear theory by means of simple mappings. He masterly embeds this analysis into the social, historical and cultural context by using numerous examples, from poems and paintings over chess and rabbits to Olbers' paradox, card games and 'phynance'. Fundamental problems of the modelling of nonlinear systems like the weather, sun spots or golf balls falling through an array of nails are discussed from the point of view of mathematics, physics and statistics by touching upon philosophical issues. At variance with Laplace's demon, Smith's 21st century demon makes 'real world' observations only with limited precision. This poses a severe problem to predictions derived from complex chaotic models, where small variations of initial conditions typically yield totally different outcomes. As Smith argues, this difficulty has direct implications on decision-making in everyday modern life. However, it also asks for an inherently probabilistic theory, which somewhat reminds us of what we are used to in the microworld. There is little to criticise in this nice little book except that some figures are of poor quality thus not really reflecting the beauty of fractals and other wonderful objects in this
Controlling chaos using Takagi-Sugeno fuzzy model and adaptive adjustment
Institute of Scientific and Technical Information of China (English)
Zheng Yong-Ai
2006-01-01
In this paper, an approach to the control of continuous-time chaotic systems is proposed using the Takagi-Sugeno (TS) fuzzy model and adaptive adjustment. Sufficient conditions are derived to guarantee chaos control from Lyapunov stability theory. The proposed approach offers a systematic design procedure for stabilizing a large class of chaotic systems in the literature about chaos research. The simulation results on R(o)ssler's system verify the effectiveness of the proposed methods.
Turiaci, Gustavo
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.
Quantum chaos in multiwell potentials
International Nuclear Information System (INIS)
Till the present time signatures of quantum chaos were studied mostly for the billiard-type systems, for dumped one-dimensional systems or for two-dimensional systems with potential energy surface of simple geometry. Almost nothing is known about the quantum chaos for generic Hamiltonian systems, including multiwell potentials, though those are the models describing the dynamics of transition between different states, for example, nuclear isomeric transitions and decay of superdeformed states of nuclei. An important feature of classical dynamics in generic multiwell potentials is the so-called mixed state, namely: regular and chaotic regimes coexist at the same energy, being localized in different local minima of the potential. The aim of our work is to show that studies of quantum chaos in the mixed state are promising and in many cases optimal. (author)
Transition to Chaos in Random Neuronal Networks
Kadmon, Jonathan; Sompolinsky, Haim
2015-10-01
Firing patterns in the central nervous system often exhibit strong temporal irregularity and considerable heterogeneity in time-averaged response properties. Previous studies suggested that these properties are the outcome of the intrinsic chaotic dynamics of the neural circuits. Indeed, simplified rate-based neuronal networks with synaptic connections drawn from Gaussian distribution and sigmoidal nonlinearity are known to exhibit chaotic dynamics when the synaptic gain (i.e., connection variance) is sufficiently large. In the limit of an infinitely large network, there is a sharp transition from a fixed point to chaos, as the synaptic gain reaches a critical value. Near the onset, chaotic fluctuations are slow, analogous to the ubiquitous, slow irregular fluctuations observed in the firing rates of many cortical circuits. However, the existence of a transition from a fixed point to chaos in neuronal circuit models with more realistic architectures and firing dynamics has not been established. In this work, we investigate rate-based dynamics of neuronal circuits composed of several subpopulations with randomly diluted connections. Nonzero connections are either positive for excitatory neurons or negative for inhibitory ones, while single neuron output is strictly positive with output rates rising as a power law above threshold, in line with known constraints in many biological systems. Using dynamic mean field theory, we find the phase diagram depicting the regimes of stable fixed-point, unstable-dynamic, and chaotic-rate fluctuations. We focus on the latter and characterize the properties of systems near this transition. We show that dilute excitatory-inhibitory architectures exhibit the same onset to chaos as the single population with Gaussian connectivity. In these architectures, the large mean excitatory and inhibitory inputs dynamically balance each other, amplifying the effect of the residual fluctuations. Importantly, the existence of a transition to chaos
The dream's navel between chaos and thought.
Scalzone, F; Zontini, G
2001-04-01
The authors begin by drawing attention to the problem of the transition from the biological to the psychic, noting that Freud himself, with his background in the neurosciences, grappled with it throughout his career. Certain recent paradigms more commonly applied to the natural sciences, such as in particular chaos and complexity theory, can in their view prove fruitful in psychoanalysis too, and it is shown how these notions are inherent in some of Freud's conceptions. The unconscious is stated to operate like a neural network, performing the kind of parallel processing used in the computing of highly complex situations, whereas the conscious mind is sequential. Dreams, in the authors' opinion, are organisers of the mind, imparting order to the turbulence of the underlying wishes and unconscious fantasies and structuring them through the dream work. Through dreams, the structured linearity of conscious thought can emerge out of the non-linear chaos of the drives. The dream's navel can be seen as the chaotic link, or interface, between the unconscious wish, which constitutes an attractor, and the conscious thought. The attractor may be visualised as having an hourglass or clepsydra shape, the narrow section being the dream's navel, and, being the same at any scale of observation, has the property of fractality. PMID:11341062
Chaos: A historical perspective
Lighthill, James
In this introductory lecture I'd like to offer a broad historical perspective regarding the relatively recent general recognition: (a) that mechanical systems satisfying Newton's laws may be subject to the essentially unpredictable type of behavior which the word CHAOS describes—in other words, the recognition (b) that quantum effects are not required; (c) so that, notwithstanding Heisenberg, uncertainty is there on the basis of the good old classical mechanics based on Newton's Laws. But first of all I'll remind you that there are two kinds of laws in science, which we may exemplify by Kepler's Laws and Newton's Laws. Kepler in 1609 completed some very detailed observations of the motions of Mars; together with a full geometrical description of them, in the Copernican sun-centered flame of reference, as motions in a constant orbit in the shape of an ellipse with the Sun as focus. A decade later Kepler had published the Epitome Astronomiae Copernicanae (a rather more substantial work than the Dialogo which later got Galileo into some difficulties), and had there described in detail his most famous discovery: Kepler's three empirical laws concerning planetary orbits. These laws, of the elliptical shapes of orbits, of the radius covering equal areas in equal times, and of the proportionality of the square of the orbital period to the cube of the major axis, were shown from the observations to be closely satisfied by the Earth and by the five then known planets; and furthermore, by the four satellites of Jupiter which Galileo had recently discovered.
Slight fault diagnosis for rolling bearing based on chaos and fractal theory%基于混沌分形理论的滚动轴承微小故障诊断
Institute of Scientific and Technical Information of China (English)
张忠云; 吴建德; 马军; 王晓东
2016-01-01
为提取轴承微小故障的故障特征，提出一种基于混沌分形理论的滚动轴承故障诊断方法。通过计算滚动轴承振动信号的最大 Lyapunov 指数，进行轴承运动的混沌识别；然后，对具有混沌特性的振动信号，计算关联维数和盒维数作为故障诊断的状态特征量。当关联维数不能明显区别轴承故障时，利用关联维数与盒维数相结合的方法判别故障；最后，选取滚动轴承滚动体、内圈、外圈存在微小故障和较明显故障以及正常状态7种工况的振动信号进行实验。研究结果表明：该方法能准确提取故障特征并完成滚动轴承的微小故障诊断。该方法为滚动轴承故障诊断提供了新的有效途径。%In order to extract the fault features of bearing slight fault, a new fault diagnosis method for rolling bearing based on chaos and fractal theory was put forward. Firstly, the largest lyapunov exponent of rolling bearing vibration signal was calculated to identify whether the bearing running gets in chaotic or not. Then, the correlation dimension and box dimension of the chaotic signal were calculated as the state character for fault diagnosis. When the correlation dimension can’t obviously separate bearing faults, the box dimension is used to combine with it for fault diagnosis. Finally, the inner ring, outer ring and rolling element signal of bearing in slight fault, serious fault and the normal state signal in total 7 kinds of conditions were selected to do the experiments. The experimental results show that the method can accurately extract fault feature and complete slight fault diagnosis of rolling bearing. The proposed method provides a new effective approach to the fault diagnosis of rolling bearing.
Institute of Scientific and Technical Information of China (English)
曲富丽
2015-01-01
The consumer price index has chaotic changes rules,the traditional models are difficult to accurately mining the change tendency,in order to obtain more ideal prediction results of consumer price index,a consumer price index prediction model by using chaos theory and improved neural network is put forward in this paper.Firstly,the phase space reconstruction is used to find the changes rules of consumer price index data,and then neural network is used to establish the prediction model of consumer price index which particle swarm optimization algorithm is used to select parameters of neural network,lastly,some consumer price index data are used to tested the performance.The experimental results show that,the proposed model can accurately reflect the changes of consumer price index,and the prediction results are conducive to macroeconomic analysis and decision making.%提出一种混沌理论和改进神经网络相融合的居民消费价格指数预测模型(Chaotic-NN)。首先对居民消费价格指数历史样本进行相空间重构,从中发现居民消费价格指数的变化信息,然后采用神经网络建立居民消费价格指数预测模型,并采用粒子群算法优化神经网络参数,最后利用多个居民消费价格指数预测实例对其性能进行验证性测试。结果表明,Chaotic-NN 可以全面描述居民消费价格指数变化的非线性和混沌性,拟合度和预测精度都比较高,真实地反映了居民消费价格指数的变化规律。
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.
Role of nonlinear dynamics and chaos in applied sciences
International Nuclear Information System (INIS)
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)
Deterministic polarization chaos from a laser diode
Virte, Martin; Thienpont, Hugo; Sciamanna, Marc
2014-01-01
Fifty years after the invention of the laser diode and fourty years after the report of the butterfly effect - i.e. the unpredictability of deterministic chaos, it is said that a laser diode behaves like a damped nonlinear oscillator. Hence no chaos can be generated unless with additional forcing or parameter modulation. Here we report the first counter-example of a free-running laser diode generating chaos. The underlying physics is a nonlinear coupling between two elliptically polarized modes in a vertical-cavity surface-emitting laser. We identify chaos in experimental time-series and show theoretically the bifurcations leading to single- and double-scroll attractors with characteristics similar to Lorenz chaos. The reported polarization chaos resembles at first sight a noise-driven mode hopping but shows opposite statistical properties. Our findings open up new research areas that combine the high speed performances of microcavity lasers with controllable and integrated sources of optical chaos.
Distributed chaos in turbulent wakes
Bershadskii, A
2016-01-01
Soft and hard spontaneous breaking of space translational symmetry (homogeneity) have been studied in turbulent wakes by means of distributed chaos. In the case of the soft translational symmetry breaking the vorticity correlation integral $\\int_{V} \\langle {\\boldsymbol \\omega} ({\\bf x},t) \\cdot {\\boldsymbol \\omega} ({\\bf x} + {\\bf r},t) \\rangle_{V} d{\\bf r}$ dominates the distributed chaos and the chaotic spectra $\\exp-(k/k_{\\beta})^{\\beta }$ have $\\beta =1/2$. In the case of the hard translational symmetry breaking, control on the distributed chaos is switched from one type of fundamental symmetry to another (in this case to Lagrangian relabeling symmetry). Due to the Noether's theorem the relabeling symmetry results in the inviscid helicity conservation and helicity correlation integral $I=\\int \\langle h({\\bf x},t)~h({\\bf x}+{\\bf r}, t)\\rangle d{\\bf r}$ (Levich-Tsinober invariant) dominates the distributed chaos with $\\beta =1/3$. Good agreement with the experimatal data has been established for turbulent ...
MHD turbulence and distributed chaos
Bershadskii, A
2016-01-01
It is shown, using results of recent direct numerical simulations, that spectral properties of distributed chaos in MHD turbulence with zero mean magnetic field are similar to those of hydrodynamic turbulence. An exception is MHD spontaneous breaking of space translational symmetry, when the stretched exponential spectrum $\\exp(-k/k_{\\beta})^{\\beta}$ has $\\beta=4/7$.
Synchronization of chaos in non-identical parametrically excited systems
Energy Technology Data Exchange (ETDEWEB)
Idowu, B.A. [Department of Physics, Lagos State University, Ojo (Nigeria)], E-mail: babaidowu@yahoo.com; Vincent, U.E. [Department of Physics, Olabisi Onabanjo University, P.M.B 2002, Ago-Iwoye (Nigeria)], E-mail: ue_vincent@yahoo.com; Njah, A.N. [Department of Physics, University of Agriculture, Abeokuta (Nigeria)
2009-03-15
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.
Quantum chaos, thermalization and dissipation in nuclear systems
Indian Academy of Sciences (India)
Sudhir R Jain
2001-08-01
Nuclei have complex energy-level sequence with statistical properties in agreement with canonical random matrix theory. This agreement appears when the one-particle one-hole states are mixed completely with two-particle two-hole states. In the transition, there is a new universality which we present here, bringing about a relation between dynamics and statistics. We summarize also the role of chaos in thermalization and dissipation in isolated systems like nuclei. The methods used to bring forth this understanding emerge from random matrix theory, semiclassical physics, and the theory of dynamical systems.
Chaos, Dirac observables and constraint quantization
Dittrich, Bianca; Koslowski, Tim A; Nelson, Mike I
2015-01-01
There is good evidence that full general relativity is non-integrable or even chaotic. We point out the severe repercussions: differentiable Dirac observables and a reduced phase space do not exist in non-integrable constrained systems and are thus unlikely to occur in a generic general relativistic context. Instead, gauge invariant quantities generally become discontinuous, thus not admitting Poisson-algebraic structures and posing serious challenges to a quantization. Non-integrability also renders the paradigm of relational dynamics cumbersome, thereby straining common interpretations of the dynamics. We illustrate these conceptual and technical challenges with simple toy models. In particular, we exhibit reparametrization invariant models which fail to be integrable and, as a consequence, can either not be quantized with standard methods or lead to sick quantum theories without a semiclassical limit. These troubles are qualitatively distinct from semiclassical subtleties in unconstrained quantum chaos and...
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.
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...
Metallogenic Districts of Yangtze Cratonic Rim at the Edge of Chaos
Institute of Scientific and Technical Information of China (English)
无
1999-01-01
Combining the science of complexity with ore geology, the author puts forward a new theory of metallogenesis: "complexity and self-organized criticality of metallogenic dynamic systems", and three fundamental theories are raised for it. The ore genesis and regularity of ore formation of four metallogenic districts around the Yangtze craton in China are studied with this theory. It is found that"metallogenic districts of Yangtze cratonic rim are all at the edge of chaos". This proposition is expounded by four determinative criteria of the edge of chaos for metallogenic districts of Yangtze cratonic rim.
AUTO-EXTRACTING TECHNIQUE OF DYNAMIC CHAOS FEATURES FOR NONLINEAR TIME SERIES
Institute of Scientific and Technical Information of China (English)
CHEN Guo
2006-01-01
The main purpose of nonlinear time series analysis is based on the rebuilding theory of phase space, and to study how to transform the response signal to rebuilt phase space in order to extract dynamic feature information, and to provide effective approach for nonlinear signal analysis and fault diagnosis of nonlinear dynamic system. Now, it has already formed an important offset of nonlinear science. But, traditional method cannot extract chaos features automatically, and it needs man's participation in the whole process. A new method is put forward, which can implement auto-extracting of chaos features for nonlinear time series. Firstly, to confirm time delay τ by autocorrelation method; Secondly, to compute embedded dimension m and correlation dimension D;Thirdly, to compute the maximum Lyapunov index λmax; Finally, to calculate the chaos degree Dch of features extracting has important meaning to fault diagnosis of nonlinear system based on nonlinear chaos features. Examples show validity of the proposed method.
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.
Controlling neuronal noise using chaos control
Christini, D J; Christini, David J; Collins, James J
1995-01-01
Chaos control techniques have been applied to a wide variety of experimental systems, including magneto-elastic ribbons, lasers, chemical reactions, arrhythmic cardiac tissue, and spontaneously bursting neuronal networks. An underlying assumption in all of these studies is that the system being controlled is chaotic. However, the identification of chaos in experimental systems, particularly physiological systems, is a difficult and often misleading task. Here we demonstrate that the chaos criteria used in a recent study can falsely classify a noise-driven, non-chaotic neuronal model as being chaotic. We apply chaos control, periodic pacing, and anticontrol to the non-chaotic model and obtain results which are similar to those reported for apparently chaotic, {\\em in vitro} neuronal networks. We also obtain similar results when we apply chaos control to a simple stochastic system. These novel findings challenge the claim that the aforementioned neuronal networks were chaotic and suggest that chaos control tech...
Fitzpatrick, A Liam
2016-01-01
We use results on Virasoro conformal blocks to study chaotic dynamics in CFT$_2$ at large central charge c. The Lyapunov exponent $\\lambda_L$, which is a diagnostic for the early onset of chaos, receives $1/c$ corrections that may be interpreted as $\\lambda_L = \\frac{2 \\pi}{\\beta} \\left( 1 + \\frac{12}{c} \\right)$. However, out of time order correlators receive other equally important $1/c$ suppressed contributions that do not have such a simple interpretation. We revisit the proof of a bound on $\\lambda_L$ that emerges at large $c$, focusing on CFT$_2$ and explaining why our results do not conflict with the analysis leading to the bound. We also comment on relationships between chaos, scattering, causality, and bulk locality.
Spatiotemporal chaos from bursting dynamics
Energy Technology Data Exchange (ETDEWEB)
Berenstein, Igal; De Decker, Yannick [Nonlinear Physical Chemistry Unit and Interdisciplinary Center for Nonlinear Phenomena and Complex Systems (CENOLI), Faculté des Sciences, Université libre de Bruxelles (ULB), Campus Plaine, C.P. 231, B-1050 Brussels (Belgium)
2015-08-14
In this paper, we study the emergence of spatiotemporal chaos from mixed-mode oscillations, by using an extended Oregonator model. We show that bursting dynamics consisting of fast/slow mixed mode oscillations along a single attractor can lead to spatiotemporal chaotic dynamics, although the spatially homogeneous solution is itself non-chaotic. This behavior is observed far from the Hopf bifurcation and takes the form of a spatiotemporal intermittency where the system locally alternates between the fast and the slow phases of the mixed mode oscillations. We expect this form of spatiotemporal chaos to be generic for models in which one or several slow variables are coupled to activator-inhibitor type of oscillators.
Urban chaos and replacement dynamics in nature and society
Chen, Yanguang
2014-11-01
Replacements resulting from competition are ubiquitous phenomena in both nature and society. The evolution of a self-organized system is always a physical process substituting one type of components for another type of components. A logistic model of replacement dynamics has been proposed in terms of technical innovation and urbanization, but it fails to arouse widespread attention in the academia. This paper is devoted to laying the foundations of general replacement principle by using analogy and induction. The empirical base of this study is urban replacement, including urbanization and urban growth. The sigmoid functions can be employed to model various processes of replacement. Many mathematical methods such as allometric scaling and head/tail breaks can be applied to analyzing the processes and patterns of replacement. Among varied sigmoid functions, the logistic function is the basic and the simplest model of replacement dynamics. A new finding is that replacement can be associated with chaos in a nonlinear system, e.g., urban chaos is just a part of replacement dynamics. The aim of developing replacement theory is at understanding complex interaction and conversion. This theory provides a new way of looking at urbanization, technological innovation and diffusion, Volterra-Lotka’s predator-prey interaction, man-land relation, and dynastic changes resulting from peasant uprising, and all that. Especially, the periodic oscillations and chaos of replacement dynamics can be used to explain and predict the catastrophic occurrences in the physical and human systems.
Chaos and multiple photon absorption
International Nuclear Information System (INIS)
An anharmonic vibrational mode of a molecule, driven by an intense infrared laser and coupled to a quasi-continuum of background modes, is found to undergo chaotic oscillations. This chaos leads to predominantly fluence-dependent rather than intensity-dependent multiple-photon absorption, as is found experimentally. The loss of coherence is associated with the decay of temporal correlation of background-mode oscillations
Random Behaviour in Quantum Chaos
Garbaczewski, P
2001-01-01
We demonstrate that a family of radial Ornstein-Uhlenbeck stochastic processes displays an ergodic behaviour appropriate for known quantum chaos universality classes of nearest neighbour spacing distributions. A common feature of those parametric processes is an asymptotic balance between the radial (Bessel-type) repulsion and the harmonic attraction, as manifested in the general form of forward drifts $b(x) = {{N-1}\\over {2x}} - x$, ($N = 2,3,5$ correspond respectively to the familiar GOE, GUE and GSE cases).
Analysis of FBC deterministic chaos
Energy Technology Data Exchange (ETDEWEB)
Daw, C.S.
1996-06-01
It has recently been discovered that the performance of a number of fossil energy conversion devices such as fluidized beds, pulsed combustors, steady combustors, and internal combustion engines are affected by deterministic chaos. It is now recognized that understanding and controlling the chaotic elements of these devices can lead to significantly improved energy efficiency and reduced emissions. Application of these techniques to key fossil energy processes are expected to provide important competitive advantages for U.S. industry.
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
Master stability analysis in transient spatiotemporal chaos.
Wackerbauer, Renate
2007-11-01
The asymptotic stability of spatiotemporal chaos is difficult to determine, since transient spatiotemporal chaos may be extremely long lived. A master stability analysis reveals that the asymptotic state of transient spatiotemporal chaos in the Gray-Scott system and in the Bär-Eiswirth system is characterized by negative transverse Lyapunov exponents on the attractor of the invariant synchronization manifold. The average lifetime of transient spatiotemporal chaos depends on the number of transverse directions that are unstable along a typical excitation cycle. PMID:18233739
Chaos synchronization between two different 4D hyperchaotic Chen systems
Institute of Scientific and Technical Information of China (English)
Liu Yang-Zheng; Jiang Chang-Sheng; Lin Chang-Sheng; Jiang Yao-Mei
2007-01-01
This paper presents chaos synchronization between two different four-dimensional (4D) hyperchaotic Chen systems by nonlinear feedback control laws.A modified 4D hyperchaotic Chen system is obtained by changing the nonlinear function of the 4D hyperchaotic Chen system,furthermore,an electronic circuit to realize two different 4D hyperchaotic Chen systems is designed.With nonlinear feedback control method,chaos synchronization between two different 4D hyperchaotic Chen systems is achieved.Based on the stability theory,the functions of the nonlinear feedback control for synchronization of two different 4D hyperchaotic Chen systems is derived,the range of feedback gains is determined.Numerical simulations are shown to verify the theoretical results.
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.
Quantum biology on the edge of quantum chaos.
Directory of Open Access Journals (Sweden)
Gabor Vattay
Full Text Available We give a new explanation for why some biological systems can stay quantum coherent for a long time at room temperature, one of the fundamental puzzles of quantum biology. We show that systems with the right level of complexity between chaos and regularity can increase their coherence time by orders of magnitude. Systems near Critical Quantum Chaos or Metal-Insulator Transition (MIT can have long coherence times and coherent transport at the same time. The new theory tested in a realistic light harvesting system model can reproduce the scaling of critical fluctuations reported in recent experiments. Scaling of return probability in the FMO light harvesting complex shows the signs of universal return probability decay observed at critical MIT. The results may open up new possibilities to design low loss energy and information transport systems in this Poised Realm hovering reversibly between quantum coherence and classicality.
Kasimov, Aslan R.
2013-03-08
We propose the following model equation, ut+1/2(u2−uus)x=f(x,us) that predicts chaotic shock waves, similar to those in detonations in chemically reacting mixtures. The equation is given on the half line, x<0, and the shock is located at x=0 for any t≥0. Here, us(t) is the shock state and the source term f is taken to mimic the chemical energy release in detonations. This equation retains the essential physics needed to reproduce many properties of detonations in gaseous reactive mixtures: 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 thanks to an interplay between the nonlinearity of the inviscid Burgers equation and a novel forcing term that is nonlocal in nature and has deep physical roots in reactive Euler equations.
Transient chaos - a resolution of breakdown of quantum-classical correspondence in optomechanics
Wang, Guanglei; Lai, Ying-Cheng; Grebogi, Celso
2016-10-01
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.
Quantum chaos inside space-temporal Sinai billiards
Addazi, Andrea
2016-01-01
We discuss general aspects of non-relativistic quantum chaos theory of scattering of a quantum particle on a system of a large number of naked singularities. We define such a system space-temporal Sinai billiard We dis- cuss the problem in semiclassical approach. We show that in semiclassical regime the formation of trapped periodic semiclassical orbits inside the sys- tem is unavoidable. This leads to general expression of survival probabilities and scattering time delays, expanded to the chaotic Pollicott-Ruelle reso- nances. Finally, we comment on possible generalizations of these aspects to relativistic quantum field theory.
Stochastic Chaos with Its Control and Synchronization
Institute of Scientific and Technical Information of China (English)
Zhang Ying; Xu Wei; Zhang Tianshu; Yang Xiaoli; Wu Cunli; Fang Tong
2008-01-01
The discovery of chaos in the sixties of last century was a breakthrough in concept,revealing the truth that some disorder behavior, called chaos, could happen even in a deterministic nonlinear system under barely deterministic disturbance. After a series of serious studies, people begin to acknowledge that chaos is a specific type of steady state motion other than the conventional periodic and quasi-periodic ones, featuring a sensitive dependence on initial conditions, resulting from the intrinsic randomness of a nonlinear system itself. In fact, chaos is a collective phenomenon consisting of massive individual chaotic responses, corresponding to different initial conditions in phase space. Any two adjacent individual chaotic responses repel each other, thus causing not only the sensitive dependence on initial conditions but also the existence of at least one positive top Lyapunov exponent (TLE) for chaos. Meanwhile, all the sample responses share one common invariant set on the Poincaré map, called chaotic attractor,which every sample response visits from time to time ergodically. So far, the existence of at least one positive TLE is a commonly acknowledged remarkable feature of chaos. We know that there are various forms of uncertainties in the real world. In theoretical studies, people often use stochastic models to describe these uncertainties, such as random variables or random processes.Systems with random variables as their parameters or with random processes as their excitations are often called stochastic systems. No doubt, chaotic phenomena also exist in stochastic systems, which we call stochastic chaos to distinguish it from deterministic chaos in the deterministic system. Stochastic chaos reflects not only the intrinsic randomness of the nonlinear system but also the external random effects of the random parameter or the random excitation.Hence, stochastic chaos is also a collective massive phenomenon, corresponding not only to different initial
Weak chaos in the asymmetric heavy top
Barrientos, M; Ranada, A F
1995-01-01
We consider the dynamics of the slightly asymmetric heavy top, a non-integrable system obtained from the Lagrange top by breaking the symmetry of its inertia tensor. It shows signs of weak chaos, which we study numerically. We argue that it is a good example for introducing students to non-integrability and chaos. (author)
Chaos desynchronization in strongly coupled systems
Energy Technology Data Exchange (ETDEWEB)
Wu Ye [Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071 (China); Graduate School of the Chinese Academy of Sciences, Beijing 100049 (China); School of Science, Beijing University of Posts and Telecommunications, Beijing 100876 (China); Liu Weiqing [Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071 (China); Graduate School of the Chinese Academy of Sciences, Beijing 100049 (China); School of Science, Beijing University of Posts and Telecommunications, Beijing 100876 (China); School of Science, Jiangxi University of Science and Technology, Ganzhou 341000 (China); Xiao, Jinghua [School of Science, Beijing University of Posts and Telecommunications, Beijing 100876 (China); Zhan Meng [Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071 (China)], E-mail: zhanmeng@wipm.ac.cn
2007-10-01
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.
Radio lighting based on dynamic chaos generators
Dmitriev, Alexander; Gerasimov, Mark; Itskov, Vadim
2016-01-01
A problem of lighting objects and surfaces with artificial sources of noncoherent microwave radiation with the aim to observe them using radiometric equipment is considered. Transmitters based on dynamic chaos generators are used as sources of noncoherent wideband microwave radiation. An experimental sample of such a device, i.e., a radio lighting lamp based on a chaos microgenerator and its performance are presented.
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 deter...
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 a...
Kinematic dynamo, supersymmetry breaking, and chaos
Ovchinnikov, Igor V.; Enßlin, Torsten A.
2016-04-01
The kinematic dynamo (KD) describes the growth of magnetic fields generated by the flow of a conducting medium in the limit of vanishing backaction of the fields onto the flow. The KD is therefore an important model system for understanding astrophysical magnetism. Here, the mathematical correspondence between the KD and a specific stochastic differential equation (SDE) viewed from the perspective of the supersymmetric theory of stochastics (STS) is discussed. The STS is a novel, approximation-free framework to investigate SDEs. The correspondence reported here permits insights from the STS to be applied to the theory of KD and vice versa. It was previously known that the fast KD in the idealistic limit of no magnetic diffusion requires chaotic flows. The KD-STS correspondence shows that this is also true for the diffusive KD. From the STS perspective, the KD possesses a topological supersymmetry, and the dynamo effect can be viewed as its spontaneous breakdown. This supersymmetry breaking can be regarded as the stochastic generalization of the concept of dynamical chaos. As this supersymmetry breaking happens in both the diffusive and the nondiffusive cases, the necessity of the underlying SDE being chaotic is given in either case. The observed exponentially growing and oscillating KD modes prove physically that dynamical spectra of the STS evolution operator that break the topological supersymmetry exist with both real and complex ground state eigenvalues. Finally, we comment on the nonexistence of dynamos for scalar quantities.
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...... attractors. We also study the subcritical frequency-splitting bifurcation at the onset of desynchronization and demonstrate that the transition to phase chaos takes place via a torus destruction process....
Nature of the narrow optical band in H*-aggregates: Dozy-chaos-exciton coupling
Egorov, Vladimir V.
2014-07-01
Dozy chaos emerges as a combined effect of the collective chaotic motion of electrons and nuclei, and their chaotic electromagnetic interactions in the transient state of molecules experiencing quantum transitions. Following earlier discussions of the well-known Brönsted relations for proton-transfer reactions; the temperature-dependent electron transfer in Langmuir-Blodgett films; the shape of the optical bands of polymethine dye monomers, their dimers, and J-aggregates, this paper reports one more application of the dozy-chaos theory of molecular quantum transitions. The qualitative and quantitative explanations for shape of a narrow and blue-shifted optical absorption band in H*-aggregates is given on the basis of the dozy-chaos theory by taking into account the dozy-chaos-exciton coupling effect. It is emphasized that in the H*-aggregate chromophore (dimer of cyclic bis-thiacarbocyanines) there is a competition between two Frenkel exciton transitions through the chaotic reorganization motion of nuclear environment. As a result, the highly organized quantum transition to the upper exciton state becomes an exciton-induced source of dozy chaos for the low organized transition to the lower exciton state. This manifests itself in appearing the narrow peak and broad wing in the optical spectrum pattern of H*-aggregates. A similar enhancement in the H*-effect caused by the strengthening of the exciton coupling in H*-dimers, which could be achieved by synthesizing tertiary and quarternary thiacarbocyanine monomers, is predicted.
On the Mechanisms Behind Chaos
DEFF Research Database (Denmark)
Lindberg, Erik
2006-01-01
Chaotic systems are observed everywhere. Electronic circuit analogues based on the differential equations of the models for the chaotic systems are often used to study the nature of chaotic systems. This tutorial is an attempt to classify electronic chaotic oscillators according to the mechanism...... 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...
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.
Geology and Origin of Europa's Mitten Feature (Murias Chaos)
Figueredo, P. H.; Chuang, F. C.; Rathbun, J.; Kirk, R. L.; Greeley, R.
2002-01-01
The "Mitten" (provisionally named Murias Chaos by the International Astronomical Union) is a region of elevated chaos-like terrain in the leading hemisphere of Europa. Its origin had been explained under the currently debated theories of melting through a thin lithosphere or convection within a thick one. Galileo observations reveal several characteristics that suggest that the Mitten is distinct from typical chaos terrain and point to a different formational process. Photoclinometric elevation estimates suggest that the Mitten is slightly elevated with respect to the surrounding terrain; geologic relations indicate that it must have raised significantly from the plains in its past, resembling disrupted domes on Europa's trailing hemisphere. Moreover, the Mitten material appears to have extruded onto the plains and flowed for tens of kilometers. The area subsequently subsided as a result of isostatic adjustment, viscous relaxation, and/or plains loading. Using plate flexure models, we estimated the elastic lithosphere in the area to be several kilometers thick. We propose that the Mitten originated by the ascent and extrusion of a large thermal diapir. Thermal-mechanical modeling shows that a Mitten-sized plume would remain sufficiently warm and buoyant to pierce through the crust and flow unconfined on the surface. Such a diapir probably had an initial radius between 5 and 8 km and an initial depth of 20-40 km, consistent with a thick-lithosphere model. In this scenario the Mitten appears to represent the surface expression of the rare ascent of a large diapir, in contrast to lenticulae and chaos terrain, which may form by isolated and clustered small diapirs, respectively.
Chaos suppression through asymmetric coupling
Bragard, J.; Vidal, G.; Mancini, H.; Mendoza, C.; Boccaletti, S.
2007-12-01
We study pairs of identical coupled chaotic oscillators. In particular, we have used Roessler (in the funnel and no funnel regimes), Lorenz, and four-dimensional chaotic Lotka-Volterra models. In all four of these cases, a pair of identical oscillators is asymmetrically coupled. The main result of the numerical simulations is that in all cases, specific values of coupling strength and asymmetry exist that render the two oscillators periodic and synchronized. The values of the coupling strength for which this phenomenon occurs is well below the previously known value for complete synchronization. We have found that this behavior exists for all the chaotic oscillators that we have used in the analysis. We postulate that this behavior is presumably generic to all chaotic oscillators. In order to complete the study, we have tested the robustness of this phenomenon of chaos suppression versus the addition of some Gaussian noise. We found that chaos suppression is robust for the addition of finite noise level. Finally, we propose some extension to this research.
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
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
Distributed chaos and helicity in turbulence
Bershadskii, A
2016-01-01
The distributed chaos driven by Levich-Tsinober (helicity) integral: $I=\\int \\langle h({\\bf x},t)~h({\\bf x}+{\\bf r}, t)\\rangle d{\\bf r}$ has been studied. It is shown that the helical distributed chaos can be considered as basis for complex turbulent flows with interplay between large-scale coherent structures and small-scale turbulence, such as Cuette-Taylor flow, wake behind cylinder and turbulent flow in the Large Plasma Device (LAPD) with inserted limiters. In the last case appearance of the helical distributed chaos, caused by the limiters, results in improvement of radial particle confinement.
Chaos Transfer in Fluidized Beds Accompanied with Biomass Pyrolysis
Institute of Scientific and Technical Information of China (English)
唐松涛; 李定凯; 吕子安; 沈幼庭
2003-01-01
Experiments of biomass pyrolysis were carried out in a fiuidized bed, and dynamic signals of pressure and temperature were recorded. Correlation dimension was employed to characterize the chaotic behavior of pressure and temperature signals. Both pressure and temperature signals exhibit chaotic behavior, and the chaotic behavior of temperature signals is always weaker than that of pressure signals. Chaos transfer theory was advanced to explain the above phenomena. The discussion on the algorithm of the correlation dimension shows that the distance definition based on rhombic neighborhood is a better choice than the traditional one based on spherical neighborhood. The former provides a satisfactory result in a much shorter time.
Prediction of quantum many-body chaos in protactinium atom
Viatkina, A V; Flambaum, V V
2016-01-01
Energy level spectrum of protactinium atom (Pa, Z=91) is simulated with a CI calculation. Levels belonging to the separate manifolds of a given total angular momentum and parity $J^\\pi$ exhibit distinct properties of many-body quantum chaos. Moreover, an extremely strong enhancement of small perturbations takes place. As an example, effective three-electron interaction is investigated and found to play a significant role in the system. Chaotic properties of the eigenstates allow one to develop a statistical theory and predict probabilities of different processes in chaotic systems.
Detection of phase randomly distributed weak transient signal using chaos
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
In practical communication and radar system s, the phase of the received signal is random, the arrival time is unknown, the lasting time is limited and the SNR is often very low. In order to realize the detection of the signal, the method of using a group of nonlinear differential equations is presented. The theory of this chaos-based detection is analyzed. Computer simulation indicates that the shortest lasting time of the transient signal that can be detected out is 12 periods, the detection error of arrival time is less than 7/8 signal's period, the detection characteristics are got using Monte-Carlo simulation.
Institute of Scientific and Technical Information of China (English)
Zhang Qing-Ling; Lu Ling; Zhang Yi
2011-01-01
A method to eliminate spiral waves and spatiotemporal chaos by using the synchronization transmission technology of network signals is proposed in this paper. The character of the spiral waves and the spatiotemporal chaos in the Fitzhugh-Nagumo model is presented. The network error evolution equation with spatiotemporal variables and the corresponding eigenvalue equation are determined based on the stability theory,and the global synchronization condition is obtained. Simulations are made in a complex network with Fitzhugh-Nagumo models as the nodes to verify the effectiveness of the synchronization transmission principle of the network signal.
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
Muthuswamy, Bharathwaj
2015-01-01
The purpose of this introductory book is to couple the teaching of chaotic circuit and systems theory with the use of field programmable gate arrays (FPGAs). As such, it differs from other texts on chaos: first, it puts emphasis on combining theoretical methods, simulation tools and physical realization to help the reader gain an intuitive understanding of the properties of chaotic systems. Second, the "medium" used for physical realization is the FPGA. These devices are massively parallel architectures that can be configured to realize a variety of logic functions. Hence, FPGAs can be configured to emulate systems of differential equations. Nevertheless maximizing the capabilities of an FPGA requires the user to understand the underlying hardware and also FPGA design software. This is achieved by the third distinctive feature of this book: a lab component in each chapter. Here, readers are asked to experiment with computer simulations and FPGA designs, to further their understanding of con...
Nonadiabatic quantum chaos in atom optics
Prants, S V
2012-01-01
Coherent dynamics of atomic matter waves in a standing-wave laser field is studied. In the dressed-state picture, wave packets of ballistic two-level atoms propagate simultaneously in two optical potentials. The probability to make a transition from one potential to another one is maximal when centroids of wave packets cross the field nodes and is given by a simple formula with the single exponent, the Landau--Zener parameter $\\kappa$. If $\\kappa \\gg 1$, the motion is essentially adiabatic. If $\\kappa \\ll 1$, it is (almost) resonant and periodic. If $\\kappa \\simeq 1$, atom makes nonadiabatic transitions with a splitting of its wave packet at each node and strong complexification of the wave function as compared to the two other cases. This effect is referred as nonadiabatic quantum chaos. Proliferation of wave packets at $\\kappa \\simeq 1$ is shown to be connected closely with chaotic center-of-mass motion in the semiclassical theory of point-like atoms with positive values of the maximal Lyapunov exponent. Th...
ICT Capstone projects: The edge of chaos
Directory of Open Access Journals (Sweden)
Sue Chard
Full Text Available Capstone project processes and assessment methodologies continue to be problematic. Experience has led us to review our assessment rubrics and methods with every iteration in an attempt to refine and improve the practice and outcomes. This review has surveyed a broad range of capstone projects describing approaches to practice, assessment and sizing. In their widest sense capstone projects are described as being ambiguous and complex, tantamount, as the title of this paper implies, to artfully practising as if one is \\'on the edge of chaos.\\' There have been promising taxonomies mooted or developed to give insight into evidence of the skills, practice, knowledge and understanding associated with capstone projects. There appears to be, however, a dilemma in terms of creating a succinct vision that might inform the sizing and assessment of projects and enable us to capture its ephemeral nature. Complexity theory appears to go some way towards unpacking relevant factors which could inform the development of tools for assessment and sizing of projects. There are professional heuristics employed in the sizing of projects and standards for the assessment of capstone projects. From this review it can be seen that a fluid but accurate methodology should be developed which addresses the dilemma in such a way as to provide robust conceptual, pedagogical and sociological sizing and assessment practices.
Implementation of LT codes based on chaos
Institute of Scientific and Technical Information of China (English)
Zhou Qian; Li Liang; Chen Zeng-Qiang; Zhao Jia-Xiang
2008-01-01
Fountain codes provide an efficient way to transfer information over erasure channels like the Internet.LT codes are the first codes fully realizing the digital fountain concept.They are asymptotically optimal rateless erasure codes with highly efficient encoding and decoding algorithms.In theory,for each encoding symbol of LT codes,its degree is randomly chosen according to a predetermined degree distribution,and its neighbours used to generate that encoding symbol are chosen uniformly at random.Practical implementation of LT codes usually realizes the randomness through pseudo-randomness number generator like linear congruential method.This paper applies the pseudo-randomness of chaotic sequence in the implementation of LT codes.Two Kent chaotic maps are used to determine the degree and neighbour(s)of each encoding symbol.It is shown that the implemented LT codes based on chaos perform better than the LT codes implemented by the traditional pseudo-randomness number generator.
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.
Controlling DC-DC converters by chaos-based pulse width modulation to reduce EMI
Energy Technology Data Exchange (ETDEWEB)
Li Hong [Department of Mathematics and Computer Science, FernUniversitaet in Hagen, 58084 Hagen (Germany)], E-mail: hong.li@FernUni-Hagen.de; Zhang Bo [School of Electric Power, South China University of Technology, Guangzhou (China); Li Zhong; Halang, Wolfgang A. [Department of Mathematics and Computer Science, FernUniversitaet in Hagen, 58084 Hagen (Germany); Chen Guanrong [Department of Electronic Engineering, City University of Hong Kong, Hong Kong (China)
2009-11-15
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.
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...
No evidence of chaos but some evidence of dependence in the US stock market
International Nuclear Information System (INIS)
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
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.
Chaos-induced transparency in an ultrahigh-Q optical microcavity
Xiao, Yun-Feng; Yang, Qi-Fan; Wang, Li; Shi, Kebin; Li, Yan; Gong, Qihuang
2012-01-01
We demonstrate experimentally a new form of induced transparency, i.e., chaos-induced transparency, in a slightly deformed microcavity which support both continuous chaotic modes and discrete regular modes with Q factors exceeding 3X?10^7. When excited by a focused laser beam, the induced transparency in the transmission spectrum originates from the destructive interference of two parallel optical pathways: (i) directly refractive excitation of the chaotic modes, and (ii) excitation of the ultra-high-Q regular mode via chaos-assisted dynamical tunneling mechanism coupling back to the chaotic modes. By controlling the focal position of the laser beam, the induced transparency experiences a highly tunable Fano-like asymmetric lineshape. The experimental results are modeled by a quantum scattering theory and show excellent agreement. This chaos-induced transparency is accompanied by extremely steep normal dispersion, and may open up new possibilities a dramatic slow light behavior and a significant enhancement o...
P. Tallapragada; Ross, Shane. D.; Schmale, D. G., III
2011-01-01
Many microorganisms are advected in the lower atmosphere from one habitat to another with scales of motion being hundreds to thousands of kilometers. The concentration of these microbes in the lower atmosphere at a single geographic location can show rapid temporal changes. We used autonomous unmanned aerial vehicles equipped with microbe-sampling devices to collect fungi in the genus Fusarium 100 m above ground level at a single sampling location in Blacksburg, Virginia, USA. Some Fusarium s...
Sándor, Bulcsú; Tél, Tamás; Néda, Zoltán
2013-01-01
The dynamics of a spring-block train placed on a moving conveyor belt is investigated both by simple experiments and computer simulations. The first block is connected by spring to an external static point, and due to the dragging effect of the belt the blocks undergo complex stick-slip dynamics. A qualitative agreement with the experimental results can only be achieved by taking into account the spatial inhomogeneity of the friction force on the belt's surface, modeled as noise. As a function of the velocity of the conveyor belt and the noise strength, the system exhibits complex, self-organized critical, sometimes chaotic dynamics and phase transition-like behavior. Noise induced chaos and intermittency is also observed. Simulations suggest that the maximum complexity of the dynamical states is achieved for a relatively small number of blocks, around five.
Ordered and Disordered Defect Chaos
Granzow, G D; Granzow, Glen D.; Riecke, Hermann
1997-01-01
Defect-chaos is studied numerically in coupled Ginzburg-Landau equations for parametrically driven waves. The motion of the defects is traced in detail yielding their life-times, annihilation partners, and distances traveled. In a regime in which in the one-dimensional case the chaotic dynamics is due to double phase slips, the two-dimensional system exhibits a strongly ordered stripe pattern. When the parity-breaking instability to traveling waves is approached this order vanishes and the correlation function decays rapidly. In the ordered regime the defects have a typical life-time, whereas in the disordered regime the life-time distribution is exponential. The probability of large defect loops is substantially larger in the disordered regime.
Superfluid (quantum) turbulence and distributed chaos
Bershadskii, A
2016-01-01
Properties of distributed chaos in superfluid (quantum) turbulence have been studied using the data of recent direct numerical simulations (HVBK two-fluid model for He II, and a moving grid in the frames of Gross-Pitaevskii model of the Bose-Einstein condensates at low temperatures). It is found that for the viscous (normal) component of the velocity field in He II the viscosity dominates the distributed chaos with the stretched exponential spectrum $\\exp(-k/k_{\\beta})^{\\beta}$ and $\\beta = 2/3$. For the superfluid component the distributed chaos is dominated by the vorticity correlation integral with $\\beta =1/2$ (the soft spontaneous breaking of the space translational symmetry - homogeneity). For very low temperature the distributed chaos is tuned to the large-scale coherent motions: the viscous (normal) component is tuned to the fundamental mode, whereas the superfluid component is subharmonically tuned. For the Gross-Pitaevskii superfluid turbulence incompressible part of the energy spectrum (containing ...
Symmetry vs. Chaos in collective dynamics
International Nuclear Information System (INIS)
Models of nuclear collective dynamics are used to study the interplay of order (approximate dynamical symmetry) and chaos in general physical systems. We report on some recent results obtained within the interacting boson model and the geometric model. (author)
Detecting nonlinearity and chaos in epidemic data
Energy Technology Data Exchange (ETDEWEB)
Ellner, S.; Gallant, A.R. [North Carolina State Univ., Raleigh, NC (United States). Dept. of Statistics; Theiler, J. [Santa Fe Inst., NM (United States)]|[Los Alamos National Lab., NM (United States)
1993-08-01
Historical data on recurrent epidemics have been central to the debate about the prevalence of chaos in biological population dynamics. Schaffer and Kot who first recognized that the abundance and accuracy of disease incidence data opened the door to applying a range of methods for detecting chaos that had been devised in the early 1980`s. Using attractor reconstruction, estimates of dynamical invariants, and comparisons between data and simulation of SEIR models, the ``case for chaos in childhood epidemics`` was made through a series of influential papers beginning in the mid 1980`s. The proposition that the precise timing and magnitude of epidemic outbreaks are deterministic but chaotic is appealing, since it raises the hope of finding determinism and simplicity beneath the apparently stochastic and complicated surface of the data. The initial enthusiasm for methods of detecting chaos in data has been followed by critical re-evaluations of their limitations. Early hopes of a ``one size fits all`` algorithm to diagnose chaos vs. noise in any data set have given way to a recognition that a variety of methods must be used, and interpretation of results must take into account the limitations of each method and the imperfections of the data. Our goals here are to outline some newer methods for detecting nonlinearity and chaos that have a solid statistical basis and are suited to epidemic data, and to begin a re-evaluation of the claims for nonlinear dynamics and chaos in epidemics using these newer methods. We also identify features of epidemic data that create problems for the older, better known methods of detecting chaos. When we ask ``are epidemics nonlinear?``, we are not questioning the existence of global nonlinearities in epidemic dynamics, such as nonlinear transmission rates. Our question is whether the data`s deviations from an annual cyclic trend (which would reflect global nonlinearities) are described by a linear, noise-driven stochastic process.
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.
From Order to Chaos in Earth Satellite Orbits
Gkolias, Ioannis; Daquin, Jérôme; Gachet, Fabien; Rosengren, Aaron J.
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.
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. PMID:26639923
Variations on chaos in physics: from unpredictability to universal laws
Mouchet, Amaury
2016-01-01
The tremendous popular success of Chaos Theory shares some common points with the not less fortunate Relativity: they both rely on a misunderstanding. Indeed, ironically , the scientific meaning of these terms for mathematicians and physicists is quite opposite to the one most people have in mind and are attracted by. One may suspect that part of the psychological roots of this seductive appeal relies in the fact that with these ambiguous names, together with some superficial clich{\\'e}s or slogans immediately related to them ("the butterfly effect" or "everything is relative"), some have the more or less secret hope to find matter that would undermine two pillars of science, namely its ability to predict and to bring out a universal objectivity. Here I propose to focus on Chaos Theory and illustrate on several examples how, very much like Relativity, it strengthens the position it seems to contend with at first sight: the failure of predictability can be overcome and leads to precise, stable and even more un...
Urban chaos and replacement dynamics in nature and society
Chen, Yanguang
2011-01-01
Many growing phenomena in both nature and society can be predicted with sigmoid function. The growth curve of the level of urbanization is a typical S-shaped one, and can be described by using logistic function. The logistic model implies a replacement process, and the logistic substitution suggests non-linear dynamical behaviors such as bifurcation and chaos. Using mathematical transform and numerical computation, we can demonstrate that the 1-dimensional map comes from a 2-dimensional two-group interaction map. By analogy with urbanization, a general theory of replacement dynamics is presented in this paper, and the replacement process can be simulated with the 2-dimansional map. If the rate of replacement is too high, periodic oscillations and chaos will arise, and the system maybe breaks down. The replacement theory can be used to interpret various complex interaction and conversion in physical and human systems. The replacement dynamics provides a new way of looking at Volterra-Lotka's predator-prey inte...
Contrasting chaos with noise via local versus global information quantifiers
Energy Technology Data Exchange (ETDEWEB)
Olivares, Felipe, E-mail: folivares@fisica.unlp.edu.ar [Departamento de Física, Facultad de Ciencias Exactas, Universidad Nacional de La Plata (UNLP), C.C. 67, 1900 La Plata (Argentina); Plastino, Angelo, E-mail: plastino@fisica.unlp.edu.ar [Instituto de Física, IFLP-CCT, Universidad Nacional de La Plata (UNLP), C.C. 727, 1900 La Plata (Argentina); Fellow of CONICET (Argentina); Rosso, Osvaldo A., E-mail: oarosso@fibertel.com.ar [LaCCAN/CPMAT – Instituto de Computação, Universidade Federal de Alagoas, BR 104 Norte km 97, 57072-970 Maceió, Alagoas (Brazil); Laboratorio de Sistemas Complejos, Facultad de Ingeniería, Universidad de Buenos Aires, 1063 Av. Paseo Colón 840, Ciudad Autónoma de Buenos Aires (Argentina); Fellow of CONICET (Argentina)
2012-04-09
At issue here is the distinction between noise and chaos. They are different phenomena but sometimes produce results that resemble each other. From a numerical viewpoint, in particular, subtle differences that exist between them are often difficult to discern. We present here a conceptual scheme, based on Information Theory, that successfully distinguishes between these two regimes. The idea is to look for the location of the pertinent signal on a special plane, called the information-one, whose axes are entropic-like measures. Using these quantifiers (one local, the other global), the contrast between the two dynamical regimes becomes apparent. -- Highlights: ► Distinctions between noise and chaos represented by time series are studied. ► A scheme, based on Information Theory tools is presented. ► The Bandt–Pompe approach for associating PDF's to time-series is used. ► The causality Shannon–Fisher information plane is introduces. ► Using this plane, the two dynamical regimes become apparent.
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.
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.
Many-body quantum chaos: Recent developments and applications to nuclei
Energy Technology Data Exchange (ETDEWEB)
Gomez, J.M.G. [Grupo de Fisica Nuclear, Departamento de Fisica Atomica, Molecular y Nuclear, Universidad Complutense de Madrid, E-28040 Madrid (Spain); Kar, K. [Theory Division, Saha Institute of Nuclear Physics, Calcutta 700 064 (India); Kota, V.K.B. [Physical Research Laboratory, Ahmedabad 380 009 (India); Molina, R.A. [Instituto de Estructura de la Materia, CSIC, Serrano 123, E-28006 Madrid (Spain); Relano, A. [Grupo de Fisica Nuclear, Departamento de Fisica Atomica, Molecular y Nuclear, Universidad Complutense de Madrid, E-28040 Madrid (Spain); Instituto de Estructura de la Materia, CSIC, Serrano 123, E-28006 Madrid (Spain); Retamosa, J., E-mail: iokin@nuc3.fis.ucm.e [Grupo de Fisica Nuclear, Departamento de Fisica Atomica, Molecular y Nuclear, Universidad Complutense de Madrid, E-28040 Madrid (Spain)
2011-03-15
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.
Synchronization Control of Macroeconomics Chaos Systems%宏观经济混沌系统同步控制研究
Institute of Scientific and Technical Information of China (English)
李华
2014-01-01
将宏观经济建模为向量自回归模型（Vector Autoregressive Modle），并研究了其同步控制问题及滑模变结构同步控制问题，根据Lyapunov稳定性理论给出了系统混沌同步的充分性条件。%This paper gives the chaos modle based on vector autoregressive modle and studies the problem of chaos synchronization control and sliding mode variable structure chaos synchronization control. The sufficient conditions for achieving the synchronization of two systems are derived based on Lyapunov stability theory.
Quantum chaos in nanoelectromechanical systems
Gusso, André; da Luz, M. G. E.; Rego, Luis G. C.
2006-01-01
We present a theoretical study of the electron-phonon coupling in suspended nanoelectromechanical systems and investigate the resulting quantum chaotic behavior. The phonons are associated with the vibrational modes of a suspended rectangular dielectric plate, with free or clamped boundary conditions, whereas the electrons are confined to a large quantum dot (QD) on the plate’s surface. The deformation potential and piezoelectric interactions are considered. By performing standard energy-level statistics we demonstrate that the spectral fluctuations exhibit the same distributions as those of the Gaussian orthogonal ensemble or the Gaussian unitary ensemble (GUE), therefore evidencing the emergence of quantum chaos. That is verified for a large range of material and geometry parameters. In particular, the GUE statistics occurs only in the case of a circular QD. It represents an anomalous phenomenon, previously reported for just a small number of systems, since the problem is time-reversal invariant. The obtained results are explained through a detailed analysis of the Hamiltonian matrix structure.
Regularly timed events amid chaos
Blakely, Jonathan N.; Cooper, Roy M.; Corron, Ned J.
2015-11-01
We show rigorously that the solutions of a class of chaotic oscillators are characterized by regularly timed events in which the derivative of the solution is instantaneously zero. The perfect regularity of these events is in stark contrast with the well-known unpredictability of chaos. We explore some consequences of these regularly timed events through experiments using chaotic electronic circuits. First, we show that a feedback loop can be implemented to phase lock the regularly timed events to a periodic external signal. In this arrangement the external signal regulates the timing of the chaotic signal but does not strictly lock its phase. That is, phase slips of the chaotic oscillation persist without disturbing timing of the regular events. Second, we couple the regularly timed events of one chaotic oscillator to those of another. A state of synchronization is observed where the oscillators exhibit synchronized regular events while their chaotic amplitudes and phases evolve independently. Finally, we add additional coupling to synchronize the amplitudes, as well, however in the opposite direction illustrating the independence of the amplitudes from the regularly timed events.
Review: Characterizing and quantifying quantum chaos with quantum tomography
Madhok, Vaibhav; Riofrío, Carlos A.; Deutsch, Ivan H.
2016-11-01
We explore quantum signatures of classical chaos by studying the rate of information gain in quantum tomography. The tomographic record consists of a time series of expectation values of a Hermitian operator evolving under application of the Floquet operator of a quantum map that possesses (or lacks) time reversal symmetry. We find that the rate of information gain, and hence the fidelity of quantum state reconstruction, depends on the symmetry class of the quantum map involved. Moreover, we find an increase in information gain and hence higher reconstruction fidelities when the Floquet maps employed increase in chaoticity. We make predictions for the information gain and show that these results are well described by random matrix theory in the fully chaotic regime. We derive analytical expressions for bounds on information gain using random matrix theory for different class of maps and show that these bounds are realized by fully chaotic quantum systems.
Controlling chaos based on an adaptive nonlinear compensator mechanism
Institute of Scientific and Technical Information of China (English)
Tian Ling-Ling; Li Dong-Hai; Sun Xian-Fang
2008-01-01
The control problems of chaotic systems are investigated in the presence of parametric uncertainty and persistent external disturbances based on nonlinear control theory.By using a designed nonlinear compensator mechanism,the system deterministic nonlinearity,parametric uncertainty and disturbance effect can be compensated effectively.The renowned chaotic Lorenz system subjected to parametric variations and external disturbances is studied as an illustrative example.From the Lyapunov stability theory,sufficient conditions for choosing control parameters to guarantee chaos control are derived.Several experiments are carried out,including parameter change experiments,set-point change experiments and disturbance experiments.Simulation results indicate that the chaotic motion can be regulated not only to steady states but also to any desired periodic orbits with great immunity to parametric variations and external disturbances.
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?
BOOK REVIEW: Chaos: A Very Short Introduction
Klages, R.
2007-07-01
This book is a new volume of a series designed to introduce the curious reader to anything from ancient Egypt and Indian philosophy to conceptual art and cosmology. Very handy in pocket size, Chaos promises an introduction to fundamental concepts of nonlinear science by using mathematics that is `no more complicated than X=2. Anyone who ever tried to give a popular science account of research knows that this is a more challenging task than writing an ordinary research article. Lenny Smith brilliantly succeeds to explain in words, in pictures and by using intuitive models the essence of mathematical dynamical systems theory and time series analysis as it applies to the modern world. In a more technical part he introduces the basic terms of nonlinear theory by means of simple mappings. He masterly embeds this analysis into the social, historical and cultural context by using numerous examples, from poems and paintings over chess and rabbits to Olbers' paradox, card games and `phynance'. Fundamental problems of the modelling of nonlinear systems like the weather, sun spots or golf balls falling through an array of nails are discussed from the point of view of mathematics, physics and statistics by touching upon philosophical issues. At variance with Laplace's demon, Smith's 21st century demon makes `real world' observations only with limited precision. This poses a severe problem to predictions derived from complex chaotic models, where small variations of initial conditions typically yield totally different outcomes. As Smith argues, this difficulty has direct implications on decision-making in everyday modern life. However, it also asks for an inherently probabilistic theory, which somewhat reminds us of what we are used to in the microworld. There is little to criticise in this nice little book except that some figures are of poor quality thus not really reflecting the beauty of fractals and other wonderful objects in this field. I feel that occasionally the book
Reliable Computational Predictions by Modeling Uncertainties Using Arbitrary Polynomial Chaos
Witteveen, J.A.S.; Bijl, H
2006-01-01
Inherent physical uncertainties can have a significant influence on computational predictions. It is therefore important to take physical uncertainties into account to obtain more reliable computational predictions. The Galerkin polynomial chaos method is a commonly applied uncertainty quantification method. However, the polynomial chaos expansion has some limitations. Firstly, the polynomial chaos expansion based on classical polynomials can achieve exponential convergence for a limited set ...
God's Stuff: The Constructive Powers of Chaos for Teaching Religion
Willhauck, Susan
2010-01-01
Order and organization are valued in the classroom, and there is a prevailing understanding that chaos should be avoided. Yet chaos can also be potent space or a source from which new things spring forth. This article investigates biblical, scientific, and cultural understandings of chaos to discover how these contribute to a revelatory metaphor…
FRUSTRATION EFFECT ON SYNCHRONIZATION AND CHAOS IN COUPLED OSCILLATORS
Institute of Scientific and Technical Information of China (English)
ZHENG ZHI-GANG
2001-01-01
Synchronization dynamics in an array of coupled periodic oscillators with quenched natural frequencies are discussed in the presence of homogeneous phase shifts (frustrations). Frustration-induced desynchronization and chaos are found. The torus-doubling route to chaos, toroidal chaos and torus crisis are investigated.
Bogdanov, A. V.; Gevorkyan, A. S.; Grigoryan, A. G.; S.A. Matveev
1998-01-01
A new formulation of the theory of quantum mechanical multichannel scattering for three-body collinear systems is proposed. It is shown, that in this simple case the principle of quantum determinism in the general case breaks down and we have a micro-irreversible quantum mechanics. The first principle calculations of the quantum chaos (wave chaos) were pursued on the example of an elementary chemical reaction Li+(FH)->(LiFH)*->(LiF)+H.
Bogdanov, A V
1998-01-01
A new formulation of the theory of quantum mechanical multichannel scattering for three-body collinear systems is proposed. It is shown, that in this simple case the principle of quantum determinism in the general case breaks down and we have a micro-irreversible quantum mechanics. The first principle calculations of the quantum chaos (wave chaos) were pursued on the example of an elementary chemical reaction Li+t(FH)->(LiFH)*->(LiF)+H.
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...
Associative memory with spatiotemporal chaos control
Kushibe, Masanori; Liu, Yun; Ohtsubo, Junji
1996-05-01
Control of spatiotemporal chaos in a neural network with discrete time and continuous state variables is investigated. The chaos control is performed with the knowledge of only a part of the target information in the memory patterns. The success rate for the pattern associations and the dependence of the search time on the sampling number in the proposed chaos neural network are studied. By the introduction of the reinforcement factor in the learning process, the recognition rate of the network can be much enhanced. Random and regular samplings of the pattern for the control are tested and the successful results of the associations are demonstrated. The chaotic behavior and recalling ability of the system are evaluated based on the analysis of the Lyapunov spectrum of the network.
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...... include a 1 minute time resolution for the RC index and anisotropic weighting of vector field data depending on quasi-dipole latitude. We shall also report on the perspective given by the initial Swarm data on rapid field changes currently taking place in the Atlantic sector....
Ventilatory chaos is impaired in carotid atherosclerosis.
Directory of Open Access Journals (Sweden)
Laurence Mangin
Full Text Available Ventilatory chaos is strongly linked to the activity of central pattern generators, alone or influenced by respiratory or cardiovascular afferents. We hypothesized that carotid atherosclerosis should alter ventilatory chaos through baroreflex and autonomic nervous system dysfunctions. Chaotic dynamics of inspiratory flow was prospectively evaluated in 75 subjects undergoing carotid ultrasonography: 27 with severe carotid stenosis (>70%, 23 with moderate stenosis (<70%, and 25 controls. Chaos was characterized by the noise titration method, the correlation dimension and the largest Lyapunov exponent. Baroreflex sensitivity was estimated in the frequency domain. In the control group, 92% of the time series exhibit nonlinear deterministic chaos with positive noise limit, whereas only 68% had a positive noise limit value in the stenoses groups. Ventilatory chaos was impaired in the groups with carotid stenoses, with significant parallel decrease in the noise limit value, correlation dimension and largest Lyapunov exponent, as compared to controls. In multiple regression models, the percentage of carotid stenosis was the best in predicting the correlation dimension (p<0.001, adjusted R(2: 0.35 and largest Lyapunov exponent (p<0.001, adjusted R(2: 0.6. Baroreflex sensitivity also predicted the correlation dimension values (p = 0.05, and the LLE (p = 0.08. Plaque removal after carotid surgery reversed the loss of ventilatory complexity. To conclude, ventilatory chaos is impaired in carotid atherosclerosis. These findings depend on the severity of the stenosis, its localization, plaque surface and morphology features, and is independently associated with baroreflex sensitivity reduction. These findings should help to understand the determinants of ventilatory complexity and breathing control in pathological conditions.
Nonlinear aeroelastic analysis of airfoils: bifurcation and chaos
Lee, B. H. K.; Price, S. J.; Wong, Y. S.
1999-04-01
Different types of structural and aerodynamic nonlinearities commonly encountered in aeronautical engineering are discussed. The equations of motion of a two-dimensional airfoil oscillating in pitch and plunge are derived for a structural nonlinearity using subsonic aerodynamics theory. Three classical nonlinearities, namely, cubic, freeplay and hysteresis are investigated in some detail. The governing equations are reduced to a set of ordinary differential equations suitable for numerical simulations and analytical investigation of the system stability. The onset of Hopf-bifurcation, and amplitudes and frequencies of limit cycle oscillations are investigated, with examples given for a cubic hardening spring. For various geometries of the freeplay, bifurcations and chaos are discussed via the phase plane, Poincaré maps, and Lyapunov spectrum. The route to chaos is investigated from bifurcation diagrams, and for the freeplay nonlinearity it is shown that frequency doubling is the most commonly observed route. Examples of aerodynamic nonlinearities arising from transonic flow and dynamic stall are discussed, and special attention is paid to numerical simulation results for dynamic stall using a time-synthesized method for the unsteady aerodynamics. The assumption of uniform flow is usually not met in practice since perturbations in velocities are encountered in flight. Longitudinal atmospheric turbulence is introduced to show its effect on both the flutter boundary and the onset of Hopf-bifurcation for a cubic restoring force.
Chaos in an imperfectly premixed model combustor
Energy Technology Data Exchange (ETDEWEB)
Kabiraj, Lipika, E-mail: lipika.kabiraj@tu-berlin.de; Saurabh, Aditya; Paschereit, Christian O. [Hermann Föttinger Institut, Technische Universität Berlin (Germany); Karimi, Nader [School of Engineering, University of Glasgow (United Kingdom); Sailor, Anna [University of Wisconsin-Madison, Madison 53706 (United States); Mastorakos, Epaminondas; Dowling, Ann P. [Department of Engineering, University of Cambridge (United Kingdom)
2015-02-15
This article reports nonlinear bifurcations observed in a laboratory scale, turbulent combustor operating under imperfectly premixed mode with global equivalence ratio as the control parameter. The results indicate that the dynamics of thermoacoustic instability correspond to quasi-periodic bifurcation to low-dimensional, deterministic chaos, a route that is common to a variety of dissipative nonlinear systems. The results support the recent identification of bifurcation scenarios in a laminar premixed flame combustor (Kabiraj et al., Chaos: Interdiscip. J. Nonlinear Sci. 22, 023129 (2012)) and extend the observation to a practically relevant combustor configuration.
Distributed chaos and inertial ranges in turbulence
Bershadskii, A
2016-01-01
It is shown that appearance of inertial range of scales, adjacent to distributed chaos range, results in adiabatic invariance of an energy correlation integral for isotropic homogeneous turbulence and for buoyancy driven turbulence (with stable or unstable stratification, including Rayleigh-Taylor mixing zone). Power spectrum of velocity field for distributed chaos dominated by this adiabatic invariant has a stretched exponential form $\\propto \\exp(-k/k_{\\beta})^{3/5}$. Results of recent direct numerical simulations have been used in order to support these conclusions.
Controlling chaos in an economic model
Chen, Liang; Chen, Guanrong
2007-01-01
A Cournot duopoly, with a bounded inverse demand function and different constant marginal production costs, can be modeled as a discrete-time dynamical system, which exhibits complex bifurcating and chaotic behaviors. Based on some essential features of the model, we show how bifurcation and chaos can be controlled via the delayed feedback control method. We then propose and evaluate an adaptive parameter-tuning algorithm for control. In addition, we discuss possible economic implications of the chaos control strategies described in the paper.
USING OPTIMAL FEEDBACK CONTROL FOR CHAOS TARGETING
Institute of Scientific and Technical Information of China (English)
PENG ZHAO-WANG; ZHONG TING-XIU
2000-01-01
Since the conventional open-loop optimal targeting of chaos is very sensitive to noise, a close-loop optimal targeting method is proposed to improve the targeting performance under noise. The present optimal targeting model takes into consideration both precision and speed of the targeting procedure. The parameters, rather than the output, of the targeting controller, are directly optimized to obtain optimal chaos targeting. Analysis regarding the mechanism is given from physics aspect and numerical experiment on the Hénon map is carried out to compare the targeting performance under noise between the close-loop and the open-loop methods.
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...... 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......, and demonstrate, in addition, that the transition to the phase chaos takes place through the torus destruction scenario....
Womack, Scott Ellis
1995-01-01
What can theory tell us about war and the role of planning therein? This thesis attempts to answer that question by using Carl von Clausewitz's theories on war and the mathematical theory of chaos to analyze war in general and the Vietnam War in particular. It offers a critical analysis of operational planning conducted by the United States Military Assistance Command - Vietnam (MACV) during the years of greatest involvement by American forces, 1966-1971. Viewing war through the dual lenses o...
Institute of Scientific and Technical Information of China (English)
徐国宾; 杨志达
2012-01-01
This paper expounds the basic principle and research method of the theories of minimum entropy production, dissipative structure and chaos, and introduces how to apply the theories and methods to analyze the river bed changes process. It considers that there are only two states for rivers including the near balance state and far from balance state. Rivers bed changes follow the principle of minimum entropy production or principle of the minimum rate of energy dissipation when it is near the balance state and its variation process tends to the relative balance state adapted to external conditions, and in which the entropy production or the rate of energy dissipation of water is minimum. Rivers will leave the primary relative balance state, and seek relative balance state adapted to new constraint conditions after the constraint conditions on the river change. In this adjustment process, the entropy production or the rate of energy dissipation is not drably decreased, but sometimes increased and sometimes decreased, until the new state of rela- tive balance whose entropy production or the rate of energy dissipation is the minimum adapted to the new constraint conditions. The river bed changes process can undergo mutation, causing the change of river patterns when it is far from the balance state. The change of river patterns is a mutation when it surpasses a certain critical value in the transformation process of gradual change of external conditions which is equivalent to the non-equilibrium phase transition of thermodynamics, so that it can be explained by the theories of dissipative structure and chaos.%阐述了最小熵产生、耗散结构和混沌理论的基本原理和研究方法，并介绍了如何应用这些理论和方法对河床演变过程进行分析。认为：河流只可能处于近平衡态和远离平衡态。河流处于近平衡态时，遵循最小熵产生原理或最小能耗率原理，其演变过程表现为逐渐趋向于与外界条
Quantum dynamical entropies in discrete classical chaos
Energy Technology Data Exchange (ETDEWEB)
Benatti, Fabio [Dipartimento di Fisica Teorica, Universita di Trieste, Strada Costiera 11, 34014 Trieste (Italy); Cappellini, Valerio [Dipartimento di Fisica Teorica, Universita di Trieste, Strada Costiera 11, 34014 Trieste (Italy); Zertuche, Federico [Instituto de Matematicas, UNAM, Unidad Cuernavaca, AP 273-3, Admon. 3, 62251 Cuernavaca, Morelos (Mexico)
2004-01-09
We discuss certain analogies between quantization and discretization of classical systems on manifolds. In particular, we will apply the quantum dynamical entropy of Alicki and Fannes to numerically study the footprints of chaos in discretized versions of hyperbolic maps on the torus.
Chaos in the Belousov-Zhabotinsky reaction
Field, Richard J.
The dynamics of reacting chemical systems is governed by typically polynomial differential equations that may contain nonlinear terms and/or embedded feedback loops. Thus the dynamics of such systems may exhibit features associated with nonlinear dynamical systems, including (among others): temporal oscillations, excitability, multistability, reaction-diffusion-driven formation of spatial patterns, and deterministic chaos. These behaviors are exhibited in the concentrations of intermediate chemical species. Bifurcations occur between particular dynamic behaviors as system parameters are varied. The governing differential equations of reacting chemical systems have as variables the concentrations of all chemical species involved, as well as controllable parameters, including temperature, the initial concentrations of all chemical species, and fixed reaction-rate constants. A discussion is presented of the kinetics of chemical reactions as well as some thermodynamic considerations important to the appearance of temporal oscillations and other nonlinear dynamic behaviors, e.g., deterministic chaos. The behavior, chemical details, and mechanism of the oscillatory Belousov-Zhabotinsky Reaction (BZR) are described. Furthermore, experimental and mathematical evidence is presented that the BZR does indeed exhibit deterministic chaos when run in a flow reactor. The origin of this chaos seems to be in toroidal dynamics in which flow-driven oscillations in the control species bromomalonic acid couple with the BZR limit cycle...
Chaos control applied to heart rhythm dynamics
Energy Technology Data Exchange (ETDEWEB)
Borem Ferreira, Bianca, E-mail: biaborem@gmail.com [Universidade Federal do Rio de Janeiro, COPPE, Department of Mechanical Engineering, P.O. Box 68.503, 21.941.972 Rio de Janeiro, RJ (Brazil); Souza de Paula, Aline, E-mail: alinedepaula@unb.br [Universidade de Brasi' lia, Department of Mechanical Engineering, 70.910.900 Brasilia, DF (Brazil); Amorim Savi, Marcelo, E-mail: savi@mecanica.ufrj.br [Universidade Federal do Rio de Janeiro, COPPE, Department of Mechanical Engineering, P.O. Box 68.503, 21.941.972 Rio de Janeiro, RJ (Brazil)
2011-08-15
Highlights: > A natural cardiac pacemaker is modeled by a modified Van der Pol oscillator. > Responses related to normal and chaotic, pathological functioning of the heart are investigated. > Chaos control methods are applied to avoid pathological behaviors of heart dynamics. > Different approaches are treated: stabilization of unstable periodic orbits and chaos suppression. - Abstract: The dynamics of cardiovascular rhythms have been widely studied due to the key aspects of the heart in the physiology of living beings. Cardiac rhythms can be either periodic or chaotic, being respectively related to normal and pathological physiological functioning. In this regard, chaos control methods may be useful to promote the stabilization of unstable periodic orbits using small perturbations. In this article, the extended time-delayed feedback control method is applied to a natural cardiac pacemaker described by a mathematical model. The model consists of a modified Van der Pol equation that reproduces the behavior of this pacemaker. Results show the ability of the chaos control strategy to control the system response performing either the stabilization of unstable periodic orbits or the suppression of chaotic response, avoiding behaviors associated with critical cardiac pathologies.
Chaos in a Bose-Einstein condensate
Institute of Scientific and Technical Information of China (English)
Wang Zhi-Xia; Ni Zheng-Guo; Cong Fu-Zhong; Liu Xue-Shen; Chen Lei
2010-01-01
It is demonstrated that Smale-horseshoe chaos exists in the time evolution of the one-dimensional Bose-Einstein condensate driven by time-periodic harmonic or inverted-harmonic potential.A formally exact solution of the timedependent Gross-Pitaevskii equation is constructed,which describes the matter shock waves with chaotic or periodic amplitudes and phases.
Chaos in a Bose—Einstein condensate
International Nuclear Information System (INIS)
It is demonstrated that Smale-horseshoe chaos exists in the time evolution of the one-dimensional Bose—Einstein condensate driven by time-periodic harmonic or inverted-harmonic potential. A formally exact solution of the time-dependent Gross—Pitaevskii equation is constructed, which describes the matter shock waves with chaotic or periodic amplitudes and phases
Chaos and fractals an elementary introduction
Feldman, David P
2012-01-01
For students with a background in elementary algebra, this text provides a vivid introduction to the key phenomena and ideas of chaos and fractals, including the butterfly effect, strange attractors, fractal dimensions, Julia sets and the Mandelbrot set, power laws, and cellular automata.
Spatio-temporal chaos : A solvable model
Diks, C; Takens, F; DeGoede, J
1997-01-01
A solvable coupled map lattice model exhibiting spatio-temporal chaos is studied. Exact expressions are obtained for the spectra of Lyapunov exponents as a function of the model parameters. Although the model has spatio-temporal structure, the time series measured at a single lattice site are shown
Miller, Kristen
2007-01-01
Through the use of some purposeful anachronisms, Tom Stoppard uses his 1993 play "Arcadia" to explore the effects on man's psyche of the transition from Newton's Laws to the laws of thermodynamics and from thermodynamics to chaos theory. However, remarkably similar reactions to these changes are also reflected in works from the actual time periods…
Conte, E; Federici, A; Zbilut, J P
2007-01-01
We developed a new method for analysis of fundamental brain waves as recorded by EEG. To this purpose we introduce a Fractal Variance Function that is based on the calculation of the variogram. The method is completed by using Random Matrix Theory. Some examples are given.
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
Endodontic inter-appointment flare-ups: An example of chaos?
Poorya Jalali; Gunnar Hasselgren
2015-01-01
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 ...
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 d...
Shimon L. Dolan; Garc??a, Salvador; Diegoli, Samantha; Auerbach, Alan
2000-01-01
Business organisations are excellent representations of what in physics and mathematics are designated "chaotic" systems. Because a culture of innovation will be vital for organisational survival in the 21st century, the present paper proposes that viewing organisations in terms of "complexity theory" may assist leaders in fine-tuning managerial philosophies that provide orderly management emphasizing stability within a culture of organised chaos, for it is on ...
Projective synchronization of a complex network with different fractional order chaos nodes
Institute of Scientific and Technical Information of China (English)
wang Ming-Jun; wang Xing-Yuan; Niu Yu-Jun
2011-01-01
Based on the stability theory of the linear fractional order system, projective synchronization of a complex network is studied in the paper, and the coupling functions of the connected nodes are identified. With this method, the projective synchronization of the network with different fractional order chaos nodes can be achieved, besides, the number of the system, Liu system and Coullet system are chosen as examples to show the effectiveness of the scheme.
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.
Nonlinearly-enhanced energy transport in many dimensional quantum chaos
Brambila, D. S.
2013-08-05
By employing a nonlinear quantum kicked rotor model, we investigate the transport of energy in multidimensional quantum chaos. This problem has profound implications in many fields of science ranging from Anderson localization to time reversal of classical and quantum waves. We begin our analysis with a series of parallel numerical simulations, whose results show an unexpected and anomalous behavior. We tackle the problem by a fully analytical approach characterized by Lie groups and solitons theory, demonstrating the existence of a universal, nonlinearly-enhanced diffusion of the energy in the system, which is entirely sustained by soliton waves. Numerical simulations, performed with different models, show a perfect agreement with universal predictions. A realistic experiment is discussed in two dimensional dipolar Bose-Einstein-Condensates (BEC). Besides the obvious implications at the fundamental level, our results show that solitons can form the building block for the realization of new systems for the enhanced transport of matter.
Introduction to modern dynamics chaos, networks, space and time
Nolte, David D
2015-01-01
The best parts of physics are the last topics that our students ever see. These are the exciting new frontiers of nonlinear and complex systems that are at the forefront of university research and are the basis of many high-tech businesses. Topics such as traffic on the World Wide Web, the spread of epidemics through globally-mobile populations, or the synchronization of global economies are governed by universal principles just as profound as Newton's laws. Nonetheless, the conventional university physics curriculum reserves most of these topics for advanced graduate study. Two justifications are given for this situation: first, that the mathematical tools needed to understand these topics are beyond the skill set of undergraduate students, and second, that these are speciality topics with no common theme and little overlap. Introduction to Modern Dynamics dispels these myths. The structure of this book combines the three main topics of modern dynamics - chaos theory, dynamics on complex networks, and gener...
Controlling halo-chaos via wavelet-based feedback
Directory of Open Access Journals (Sweden)
Jin-Qing Fang
2002-01-01
Full Text Available Halo-chaos in high-current accelerator has become one of the key issues because it can cause excessive radioactivity from the accelerators and significantly limits the applications of the new accelerators in industrial and other fields. Some general engineering methods for chaos control have been developed, but they generally are unsuccessful for halo-chaos suppression due to many technical constraints. In this article, controllability condition for beam halo-chaos is analyzed qualitatively. Then Particles-in-Cell (PIC simulations explore the nature of beam halo-chaos formation. A nonlinear control method and wavelet function feedback controller are proposed for controlling beam halo-chaos. After control of beam halo-chaos for initial proton beam with water bag distributions, the beam halo strength factor H is reduced to zero, and other statistical physical quantities of beam halo-chaos are doubly reduced. The results show that the developed methods in this paper are very effective for proton beam halo-chaos suppression. Potential application of the halo-chaos control method is finally pointed out.
Institute of Scientific and Technical Information of China (English)
顾岱泉; 张媛妮
2014-01-01
In the current field of career counseling ,failure in career development is not only still an issue rarely involved ,but always is set forth from single factors and is non-systematic in the researches having existed .While the Chaos Theory of Careers provides a systematic account of failure in career development :career development can be characterized as a dynamical system w hich is complex ,ever-changing and of mu-tual influence ,also it is affected by a variety of factors .People tend to inevitably face many unpredictable things despite trying our best ,and most of those are beyond the scope of ability for most people ,thus fail-ure is an unavoidable result in this case .In career counseling ,we did researches on the failure in career de-velopment based on Chaos Theory of Careers ,meanwhile could provide learning opportunities for clients , stimulating their creativity and building reasonable cognition as well .Counselors utilize this technique to assist clients to learn to accept and examine failure ,formulating strategies that clients can solve the trouble of anxiety from failure ,developing the habits of continuously monitoring and evaluating their goals ,and learning to evaluate personal risk tolerance as well as the ability to grasp the opportunities .%生涯混沌理论从系统论的角度对职业发展失败进行解释：职业发展是一个复杂、多变、相互影响的动态系统，它受到多种因素的影响，尽管人们努力去工作，但仍不可避免地会面对诸多不可预知的事情发生，而且大多超出人们能力的掌控范围，在这种情况下失败也是一种不可避免的结果。在职业咨询中根据生涯混沌理论对职业发展失败进行研究，可以为咨询者提供一次学习的机会，激发他们的创造力，建构合理认知。职业咨询师运用这一理论可以帮助咨询者学会接受和审视失败，构建缓解失败中的焦虑情绪的策略，养成不断评估和修订目
Proceedings of the 2nd Experimental Chaos Conference
Ditto, William; Pecora, Lou; Shlesinger, Michael; Spano, Mark; Vohra, Sandeep
1995-02-01
The Table of Contents for the full book PDF is as follows: * Introduction * Spatiotemporal Phenomena * Experimental Studies of Chaotic Mixing * Using Random Maps in the Analysis of Experimental Fluid Flows * Transition to Spatiotemporal Chaos in a Reaction-Diffusion System * Ion-Dynamical Chaos in Plasmas * Optics * Chaos in a Synchronously Driven Optical Resonator * Chaos, Patterns and Defects in Stimulated Scattering Phenomena * Test of the Normal Form for a Subcritical Bifurcation * Observation of Bifurcations and Chaos in a Driven Fiber Optic Coil * Applications -- Communications * Robustness and Signal Recovery in a Synchronized Chaotic System * Synchronizing Nonautonomous Chaotic Circuits * Synchronization of Pulse-Coupled Chaotic Oscillators * Ocean Transmission Effects on Chaotic Signals * Controlling Symbolic Dynamics for Communication * Applications -- Control * Analysis of Nonlinear Actuators Using Chaotic Waveforms * Controlling Chaos in a Quasiperiodic Electronic System * Control of Chaos in a CO2 Laser * General Research * Video-Based Analysis of Bifurcation Phenomena in Radio-Frequency-Excited Inert Gas Plasmas * Transition from Soliton to Chaotic Motion During the Impact of a Nonlinear Structure * Sonoluminescence in a Single Bubble: Periodic, Quasiperiodic and Chaotic Light Source * Quantum Chaos Experiments Using Microwave Cavities * Experiments on Quantum Chaos With and Without Time Reversibility * When Small Noise Imposed on Deterministic Dynamics Becomes Important * Biology * Chaos Control for Cardiac Arrhythmias * Irregularities in Spike Trains of Cat Retinal Ganglion Cells * Broad-Band Synchronization in Monkey Neocortex * Applicability of Correlation Dimension Calculations to Blood Pressure Signal in Rats * Tests for Deterministic Chaos in Noisy Time Series * The Crayfish Mechanoreceptor Cell: A Biological Example of Stochastic Resonance * Chemistry * Chaos During Heterogeneous Chemical Reactions * Stabilizing and Tracking Unstable Periodic
Quantum Trilogy: Discrete Toda, Y-System and Chaos
Yamazaki, Masahito
2016-01-01
We discuss a discretization of the quantum Toda field theory associated with a semisimple finite-dimensional Lie algebra or a tamely-laced infinite-dimensional Kac-Moody algebra $G$, generalizing the previous construction of discrete quantum Liouville theory for the case $G=A_1$. The model is defined on a discrete two-dimensional lattice, whose spatial direction is of length $L$. In addition we also find a "discretized extra dimension" whose width is given by the rank $r$ of $G$, which decompactifies in the large $r$ limit. For the case of $G=A_N$ or $A_{N-1}^{(1)}$, we find a symmetry exchanging $L$ and $N$ under appropriate spatial boundary conditions. The dynamical time evolution rule of the model is a quantizations of the so-called Y-system, and the theory can be well-described by the quantum cluster algebra. We discuss possible implications for recent discussions of quantum chaos, and comment on the relation with the quantum higher Teichmuller theory of type $A_N$.
Chaos and complexity in astrophysics
Regev, Oded
2007-01-01
Methods and techniques of the theory of nonlinear dynamical systems and patterns can be useful in astrophysical applications. Some works on the subjects of dynamical astronomy, stellar pulsation and variability, as well as spatial complexity in extended systems, in which such approaches have already been utilized, are reviewed. Prospects for future directions in applications of this kind are outlined.
Computers, pattern, chaos and beauty
Pickover, Clifford A
1980-01-01
Combining fractal theory with computer art, this book introduces a creative use of computers. It describes graphic methods for detecting patterns in complicated data and illustrates simple techniques for visualizing chaotic behavior. ""Beautiful."" - Martin Gardner, Scientific American. Over 275 illustrations, 29 in color.
Optomechanically induced stochastic resonance and chaos transfer between optical fields
Monifi, Faraz; Zhang, Jing; Özdemir, Şahin Kaya; Peng, Bo; Liu, Yu-Xi; Bo, Fang; Nori, Franco; Yang, Lan
2016-06-01
Chaotic dynamics has been reported in many physical systems and has affected almost every field of science. Chaos involves hypersensitivity to the initial conditions of a system and introduces unpredictability into its output. Thus, it is often unwanted. Interestingly, the very same features make chaos a powerful tool to suppress decoherence, achieve secure communication and replace background noise in stochastic resonance—a counterintuitive concept that a system's ability to transfer information can be coherently amplified by adding noise. Here, we report the first demonstration of chaos-induced stochastic resonance in an optomechanical system, as well as the optomechanically mediated chaos transfer between two optical fields such that they follow the same route to chaos. These results will contribute to the understanding of nonlinear phenomena and chaos in optomechanical systems, and may find applications in the chaotic transfer of information and for improving the detection of otherwise undetectable signals in optomechanical systems.
CONGENITAL HIGH AIRWAY OBSTRUCTION (CHAOS SYNDROME: A RARE CASE PRESENTATION
Directory of Open Access Journals (Sweden)
Dinakara
2014-04-01
Full Text Available Congenital high airway obstruction syndrome (CHAOS results in a predictable constellation of findings: large echogenic lungs flattened or inverted diaphragms, dilated airways distal to the obstruction, and fetal ascites and/or hydrops.1 The finding of CHAOS on prenatal ultrasound examination is diagnostic of complete or near-complete obstruction of the fetal upper airway, most likely caused by laryngeal atresia. A greater understanding of the natural history of CHAOS may permit improved prenatal and perinatal management
Comments on microcausality, chaos, and gravitational observables
Marolf, Donald
2015-12-01
Observables in gravitational systems must be non-local so as to be invariant under diffeomorphism gauge transformations. But at the classical level some such observables can nevertheless satisfy an exact form of microcausality. This property is conjectured to remain true at all orders in the semiclassical expansion, though with limitations at finite ℏ or {{\\ell }}{Planck}. We also discuss related issues concerning observables in black hole spacetimes and comment on the senses in which they do and do not experience the form of chaos identified by Shenker and Stanford. In particular, in contrast to the situation in a reflecting cavity, this chaos does not afflict observables naturally associated with Hawking radiation for evaporating black holes.
Comments on Microcausality, Chaos, and Gravitational Observables
Marolf, Donald
2015-01-01
Observables in gravitational systems must be non-local so as to be invariant under diffeomorphism gauge transformations. But at the classical level some such observables can nevertheless satisfy an exact form of microcausality. This property is conjectured to remain true at all orders in the semiclassical expansion, though with limitations at finite $\\hbar$ or $\\ell_{Planck}$. We also discuss related issues concerning observables in black hole spacetimes and comment on the senses in which they do and do not experience the form of chaos identified by Shenker and Stanford. In particular, in contrast to the situation in a reflecting cavity, this chaos does not afflict observables naturally associated with Hawking radiation for evaporating black holes.
Buoyancy driven turbulence and distributed chaos
Bershadskii, A
2016-01-01
It is shown, using results of recent direct numerical simulations, laboratory experiments and atmospheric measurements, that buoyancy driven turbulence exhibits a broad diversity of the types of distributed chaos with its stretched exponential spectrum $\\exp(-k/k_{\\beta})^{\\beta}$. The distributed chaos with $\\beta = 1/3$ (determined by the helicity correlation integral) is the most common feature of the stably stratified turbulence (due to the strong helical waves presence). These waves mostly dominate spectral properties of the vertical component of velocity field, while the horizontal component is dominated by the diffusive processes both for the weak and strong stable stratification ($\\beta =2/3$). For the last case influence of the low boundary can overcome the wave effects and result in $\\beta =1/2$ for the vertical component of the velocity field (the spontaneous breaking of the space translational symmetry - homogeneity). For the unstably stratified turbulence in the Rayleigh-Taylor mixing zone the di...
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...... resolution (allowing for investigations of sub-annual core field changes). More than 14 years of data from the satellites Ørsted (March 1999 to June 2013), CHAMP (July 2000 to September 2010) and SAC-C (2000 to 2004), augmented with ground observatory revised monthly mean values (1997 to 2013) have been used...... for this model. Maximum spherical harmonic degree of the static (crustal) field is n=100. The core field time changes are expressed by spherical harmonic expansion coefficients up to n=20, described by order 6 splines (with 6-month knot spacing) spanning the time interval 1997.0 to 2013.5. The third time...
Chaos in hydrodynamic BL Herculis models
Smolec, R
2014-01-01
We present non-linear, convective, BL Her-type hydrodynamic models that show complex variability characteristic for deterministic chaos. The bifurcation diagram reveals a rich structure, with many phenomena detected for the first time in hydrodynamic models of pulsating stars. The phenomena include not only period doubling cascades en route to chaos (detected in earlier studies) but also periodic windows within chaotic band, type-I and type-III intermittent behaviour, interior crisis bifurcation and others. Such phenomena are known in many textbook chaotic systems, from the simplest discrete logistic map, to more complex systems like Lorenz equations. We discuss the physical relevance of our models. Although except of period doubling such phenomena were not detected in any BL Her star, chaotic variability was claimed in several higher luminosity siblings of BL Her stars - RV Tau variables, and also in longer-period, luminous irregular pulsators. Our models may help to understand these poorly studied stars. Pa...
Chaos synchronization in networks of semiconductor superlattices
Li, Wen; Aviad, Yaara; Reidler, Igor; Song, Helun; Huang, Yuyang; Biermann, Klaus; Rosenbluh, Michael; Zhang, Yaohui; Grahn, Holger T.; Kanter, Ido
2015-11-01
Chaos synchronization has been demonstrated as a useful building block for various tasks in secure communications, including a source of all-electronic ultrafast physical random number generators based on room temperature spontaneous chaotic oscillations in a DC-biased weakly coupled GaAs/Al0.45Ga0.55As semiconductor superlattice (SSL). Here, we experimentally demonstrate the emergence of several types of chaos synchronization, e.g. leader-laggard, face-to-face and zero-lag synchronization in network motifs of coupled SSLs consisting of unidirectional and mutual coupling as well as self-feedback coupling. Each type of synchronization clearly reflects the symmetry of the topology of its network motif. The emergence of a chaotic SSL without external feedback and synchronization among different structured SSLs open up the possibility for advanced secure multi-user communication methods based on large networks of coupled SSLs.
Chaos in a Hydraulic Control Valve
Hayashi, S.; Hayase, T.; Kurahashi, T.
1997-08-01
In this paper we have studied the instability and chaos occurring in a pilot-type poppet valve circuit. The system consists of a poppet valve, an upstream plenum chamber, a supply pipeline and an orifice inserted between the pelnum and the pipeline. Although the poppet valve rests on the seat stably for a supply pressure lower than the cracking pressure, the circuit becomes unstable for an initial disturbance beyond a critical value and develops a self-excited vibration. In this unstable region, chaotic vibration appears at the period-doubling bifurcation. We have investigated the stability of the circuit and the chaotic phenomenon numerically, and elucidated it by power spectra, a bifurcation diagram and Lyapunov exponent calculations, showing that the phenomenon follows the Feigenbaum route to chaos.Copyright 1997 Academic Press Limited
Experimental Study of the Sampled Labyrinth Chaos
Directory of Open Access Journals (Sweden)
J. Petrzela
2011-12-01
Full Text Available In this paper, some new numerical as well as experimental results connected with the so-called labyrinth chaos are presented. This very unusual chaotic motion can be generated by mathematical model involving the scalar goniometrical functions which makes a three-dimensional autonomous dynamical system strongly nonlinear. Final circuitry implementation with analog core and digital parts can be used for modeling Brownian motion. From the viewpoint of generating chaotic motion by some electronic circuit, first step is to solve problems associated with the two-port nonlinear transfer functions synthesis. In the case of labyrinth chaos the finite dynamical range of the input variables introduced by the used active elements usually limits the performance greatly, similarly as it holds for the multi-grid spiral attractors. This paper shows an elegant way how to remove these obstacles by using uni-versal multiple-port with internal digital signal processing.
Delayed Self-Synchronization in Homoclinic Chaos
Arecchi, F. T.; Meucci, R.; E. Allaria; Di Garbo, A.; Tsimring, L. S.
2001-01-01
The chaotic spike train of a homoclinic dynamical system is self-synchronized by re-inserting a small fraction of the delayed output. Due to the sensitive nature of the homoclinic chaos to external perturbations, stabilization of very long periodic orbits is possible. On these orbits, the dynamics appears chaotic over a finite time, but then it repeats with a recurrence time that is slightly longer than the delay time. The effect, called delayed self-synchronization (DSS), displays analogies ...
Gravity Waves, Chaos, and Spinning Compact Binaries
Levin, Janna
1999-01-01
Spinning compact binaries are shown to be chaotic in the Post-Newtonian expansion of the two body system. Chaos by definition is the extreme sensitivity to initial conditions and a consequent inability to predict the outcome of the evolution. As a result, the spinning pair will have unpredictable gravitational waveforms during coalescence. This poses a challenge to future gravity wave observatories which rely on a match between the data and a theoretical template.
Classical and Quantum Chaos in Atom Optics
Saif, Farhan
2006-01-01
The interaction of an atom with an electromagnetic field is discussed in the presence of a time periodic external modulating force. It is explained that a control on atom by electromagnetic fields helps to design the quantum analog of classical optical systems. In these atom optical systems chaos may appear at the onset of external fields. The classical and quantum chaotic dynamics is discussed, in particular in an atom optics Fermi accelerator. It is found that the quantum dynamics exhibits ...
Quantum chaos in small quantum networks
Kim, I; Kim, Ilki; Mahler, Guenter
1999-01-01
We study a 2-spin quantum Turing architecture, in which discrete local rotations \\alpha_m of the Turing head spin alternate with quantum controlled NOT-operations. We show that a single chaotic parameter input \\alpha_m leads to a chaotic dynamics in the entire Hilbert space. The instability of periodic orbits on the Turing head and `chaos swapping' onto the Turing tape are demonstrated explicitly as well as exponential parameter sensitivity of the Bures metric.
Chaos in a topologically transitive system
Institute of Scientific and Technical Information of China (English)
XIONG; Jincheng
2005-01-01
The chaotic phenomena have been studied in a topologically transitive system and it has been shown that the erratic time dependence of orbits in such a topologically transitive system is more complicated than what described by the well-known technology "Li-Yorke chaos". The concept "sensitive dependency on initial conditions" has been generalized, and the chaotic phenomena has been discussed for transitive systems with the generalized sensitive dependency property.
Reducing or enhancing chaos using periodic orbits.
Bachelard, R; Chandre, C; Leoncini, X
2006-06-01
A method to reduce or enhance chaos in Hamiltonian flows with two degrees of freedom is discussed. This method is based on finding a suitable perturbation of the system such that the stability of a set of periodic orbits changes (local bifurcations). Depending on the values of the residues, reflecting their linear stability properties, a set of invariant tori is destroyed or created in the neighborhood of the chosen periodic orbits. An application on a paradigmatic system, a forced pendulum, illustrates the method.
Chaos in free electron laser oscillators
Energy Technology Data Exchange (ETDEWEB)
Bruni, C. [Univ Paris 11, LAL, UMR 8607, F-91898 Orsay, (France); Bachelard, R.; Couprie, M.E. [Synchrotron SOLEIL, F-91192 Gif Sur Yvette, (France); Garzella, D. [CEA DSM DRECAM SPAM, F-91191 Gif Sur Yvette, (France); Orlandi, G.L. [CR Frascati FIM FISACC, ENEA, I-00044 Frascati, (Italy)
2009-07-01
The chaotic nature of a storage-ring free electron laser (FEL) is investigated. The derivation of a low embedding dimension for the dynamics allows the low-dimensionality of this complex system to be observed, whereas its unpredictability is demonstrated, in some ranges of parameters, by a positive Lyapounov exponent. The route to chaos is then explored by tuning a single control parameter, and a period-doubling cascade is evidenced, as well as intermittence. (authors)
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.
Microscopic dynamics of plasmas and chaos
International Nuclear Information System (INIS)
Some of the key intellectual foundations of plasma physics are in danger of becoming a lost art. Fortunately, however, this threat recedes with the publication of this valuable book. It renders accessible those aspects of theoretical plasma physics that are best approached from the perspectives of classical mechanics, in both its early nineteenth century and late twentieth century manifestations. Half a century has elapsed since the publication of seminal papers such as those by Bohm and Pines (1951), van Kampen (1955), and Bernstein, Greene and Kruskal (1957). These papers served to address a fundamental question of physics - namely the relation between degrees of freedom that exist at the individual particle level of description, and those that exist at the collective level - in the plasma context. The authors of the present book have played a major role in the investigation of this question from an N-body standpoint, which can be divided into two linked themes. First, those topics that can be illuminated by analytical methods that lie in the tradition of classical mechanics that stretches back to Lagrange, Legendre and Hamilton. Second, those topics that benefit from the insights developed following the redevelopment of classical mechanics in relation to chaos theory in the 1980s and subsequently. The working plasma physicist who wishes to dig more deeply in this field is faced at present with a number of challenges. These may include a perception that this subfield is of limited relevance to mission-oriented questions of plasma performance; a perception of the research literature as being self-contained and inaccessible; and, linked to this, unfamiliarity with the mathematical tools. The latter problem is particularly pressing, given the limited coverage of classical mechanics in many undergraduate physics courses. The book by Elskens and Escande meets many of the challenges outlined above. The rewards begin early, by the end of the second chapter, with
Dynamics between order and chaos in conceptual models of glacial cycles
Mitsui, Takahito
2013-01-01
The dynamics of glacial cycles is studied in terms of the dynamical systems theory. We explore the dependence of the climate state on the phase of astronomical forcing by examining five conceptual models of glacial cycles proposed in the literature. The models can be expressed as quasiperiodically forced dynamical systems. It is shown that four of them exhibit a strange nonchaotic attractor (SNA), which is an intermediate regime between quasiperiodicity and chaos. Then, the dependence of the climate state on the phase of astronomical forcing is not given by smooth relations, but constitutes a geometrically strange set. Our result suggests that the dynamics of SNA is a candidate for the dynamics of glacial cycles, in addition to the well-known dynamics of quasiperiodicity and chaos.
The computational complexity of symbolic dynamics at the edge of order and chaos
Lakdawala, P
1995-01-01
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 behaviour of cellular automata, that the computational basis for modelling 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.
CHAOS IN FAMILY LAW: A MODEL FOR THE RECOGNITION OF INTIMATE RELATIONSHIPS IN SOUTH AFRICA
Directory of Open Access Journals (Sweden)
Pieter Bakker
2013-08-01
Full Text Available The chaos theory is utilised in a metaphorical manner to describe the current state of family law and more specifically law regulating intimate relationships in South Africa. A bird's eye view of the law of intimate relationships is provided to indicate that the current system of law regulating intimate relationships is in a state of chaos. Deregulation of intimate relationships and regulation by contract as well as a singular Act regulating intimate relationships are investigated as alternatives to the current system. The paper concludes that deregulation does not pose a viable alternative model to recognise intimate relationships. The ideal will be to have a singular Act regulating all intimate relationships. The conclusion and termination of these relationships should be less formal than the current system. The parties should be free to regulate the consequences of their intimate relationship by a relationship contract. Default contracts should be contained in the Act to ensure substantive equality in intimate relationships.
Dynamics and chaos control of gyrostat satellite
International Nuclear Information System (INIS)
Highlights: ► Free dual-spin gyrostat with a small rotor asymmetry is considered. ► Equations in Andoyer-Deprit canonical dimensionless variables are obtained. ► Phase space heteroclinic and homoclinic trajectories are written in closed form. ► Modified Melnikov function is used to construct the control that eliminates chaos. - Abstract: We consider the chaotic motion of the free gyrostat consisting of a platform with a triaxial inertia ellipsoid and a rotor with a small asymmetry with respect to the axis of rotation. Dimensionless equations of motion of the system with perturbations caused by small asymmetries of the rotor are written in Andoyer-Deprit variables. These perturbations lead to separatrix chaos. For gyrostats with different ratios of moments of inertia heteroclinic and homoclinic trajectories are written in closed-form. These trajectories are used for constructing modified Melnikov function, which is used for determine the control that eliminates separatrix chaos. Melnikov function and phase space trajectory are built to show the effectiveness of the control.
Emergence of integer quantum Hall effect from chaos
Tian, Chushun; Chen, Yu; Wang, Jiao
2016-02-01
We present an analytic microscopic theory showing that in a large class of spin-1/2 quasiperiodic quantum kicked rotors, a dynamical analog of the integer quantum Hall effect (IQHE) emerges from an intrinsic chaotic structure. Specifically, the inverse of the Planck's quantum (he) and the rotor's energy growth rate mimic the "filling fraction" and the "longitudinal conductivity" in conventional IQHE, respectively, and a hidden quantum number is found to mimic the "quantized Hall conductivity." We show that for an infinite discrete set of critical values of he, the long-time energy growth rate is universal and of order of unity ("metallic" phase), but otherwise vanishes ("insulating" phase). Moreover, the rotor insulating phases are topological, each of which is characterized by a hidden quantum number. This number exhibits universal behavior for small he, i.e., it jumps by unity whenever he decreases, passing through each critical value. This intriguing phenomenon is not triggered by the likes of Landau band filling, well known to be the mechanism for conventional IQHE, and far beyond the canonical Thouless-Kohmoto-Nightingale-Nijs paradigm for quantum Hall transitions. Instead, this dynamical phenomenon is of strong chaos origin; it does not occur when the dynamics is (partially) regular. More precisely, we find that a topological object, similar to the topological theta angle in quantum chromodynamics, emerges from strongly chaotic motion at microscopic scales, and its renormalization gives the hidden quantum number. Our analytic results are confirmed by numerical simulations. Our findings indicate that rich topological quantum phenomena can emerge from chaos and might point to a new direction of study in the interdisciplinary area straddling chaotic dynamics and condensed matter physics. This work is a substantial extension of a short paper published earlier by two of us [Y. Chen and C. Tian, Phys. Rev. Lett. 113, 216802 (2014), 10.1103/PhysRevLett.113.216802].
Adaptive sparse polynomial chaos expansion based on least angle regression
Blatman, Géraud; Sudret, Bruno
2011-03-01
Polynomial chaos (PC) expansions are used in stochastic finite element analysis to represent the random model response by a set of coefficients in a suitable (so-called polynomial chaos) basis. The number of terms to be computed grows dramatically with the size of the input random vector, which makes the computational cost of classical solution schemes (may it be intrusive (i.e. of Galerkin type) or non intrusive) unaffordable when the deterministic finite element model is expensive to evaluate. To address such problems, the paper describes a non intrusive method that builds a sparse PC expansion. First, an original strategy for truncating the PC expansions, based on hyperbolic index sets, is proposed. Then an adaptive algorithm based on least angle regression (LAR) is devised for automatically detecting the significant coefficients of the PC expansion. Beside the sparsity of the basis, the experimental design used at each step of the algorithm is systematically complemented in order to avoid the overfitting phenomenon. The accuracy of the PC metamodel is checked using an estimate inspired by statistical learning theory, namely the corrected leave-one-out error. As a consequence, a rather small number of PC terms are eventually retained ( sparse representation), which may be obtained at a reduced computational cost compared to the classical "full" PC approximation. The convergence of the algorithm is shown on an analytical function. Then the method is illustrated on three stochastic finite element problems. The first model features 10 input random variables, whereas the two others involve an input random field, which is discretized into 38 and 30 - 500 random variables, respectively.
The chaos and order in nuclear molecular dynamics; Chaos i porzadek w jadrowej dynamice molekularnej
Energy Technology Data Exchange (ETDEWEB)
Srokowski, T. [Institute of Nuclear Physics, Cracow (Poland)
1995-12-31
The subject of the presented report is role of chaos in scattering processes in the frame of molecular dynamics. In this model, it is assumed that scattering particles (nuclei) consist of not-interacted components as alpha particles or {sup 12}C, {sup 16}O and {sup 20}Ne clusters. The results show such effects as dynamical in stabilities and fractal structure as well as compound nuclei decay and heavy-ion fusion. The goal of the report is to make the reader more familiar with the chaos model and its application to nuclear phenomena. 157 refs, 40 figs.
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.
Wave Physics Oscillations - Solitons - Chaos
Nettel, Stephen
2009-01-01
This textbook is intended for those second year undergraduates in science and engineering who will later need an understanding of electromagnetic theory and quantum mechanics. The classical physics of oscillations and waves is developed at a more advanced level than has been customary for the second year, providing a basis for the quantum mechanics that follows. In this new edition the Green's function is explained, reinforcing the integration of quantum mechanics with classical physics. The text may also form the basis of an "introduction to theoretical physics" for physics majors. The concluding chapters give special attention to topics in current wave physics: nonlinear waves, solitons, and chaotic behavior.
Stratified Spatiotemporal Chaos in Anisotropic Reaction-Diffusion Systems
Energy Technology Data Exchange (ETDEWEB)
Baer, M.; Thiele, U. [Max-Planck-Institut fuer Physik Komplexer Systeme, Noethnitzer Strasse 38, 01187 Dresden (Germany); Hagberg, A. [Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Baer, M.; Meron, E. [The Jacob Blaustein Institute for Desert Research and the Physics Department, Ben-Gurion University, Sede Boker Campus 84990 (Israel); Thiele, U. [Instituto Pluridisciplinar, Universidad Complutense Madrid, Paseo Juan XXIII 1, E-28040 Madrid (Spain)
1999-09-01
Numerical simulations of two-dimensional pattern formation in an anisotropic bistable reaction-diffusion medium reveal a new dynamical state, stratified spatiotemporal chaos, characterized by strong correlations along one of the principal axes. Equations that describe the dependence of front motion on the angle illustrate the mechanism leading to stratified chaos. {copyright} {ital 1999} {ital The American Physical Society}
Controlling Beam Halo-Chaos via Time-Delayed Feedback
Institute of Scientific and Technical Information of China (English)
FANG Jin-Qing; WENG Jia-Qiang; ZHU Lun-Wu; LUO Xiao-Shu
2004-01-01
The study of controlling high-current proton beam halo-chaos has become a key concerned issue for many important applications. In this paper, time-delayed feedback control method is proposed for beam halo-chaos. Particle in cell simulation results show that the method is very effective and has some advantages for high-current beam experiments and engineering.
Using a quantum computer to investigate quantum chaos
Schack, Ruediger
1997-01-01
We show that the quantum baker's map, a prototypical map invented for theoretical studies of quantum chaos, has a very simple realization in terms of quantum gates. Chaos in the quantum baker's map could be investigated experimentally on a quantum computer based on only 3 qubits.
The Chaos Game on a General Iterated Function System
Barnsley, Michael
2010-01-01
The main theorem of this paper establishes conditions under which the "chaos game" algorithm almost surely yields the attractor of an iterated function system. The theorem holds in a very general setting, even for non contractive iterated function systems, and under weaker conditions on the random orbit of the chaos game than obtained previously.
Research on a family of n-scroll chaos generators
International Nuclear Information System (INIS)
This paper studies a family of n-scroll chaos generators using a modified Chua's circuit. A mathematic model of the generators is established, the relationship between equilibrium points and scrolls is also analyzed, and a general theorem for generation of n-scroll chaos attractors is given. Numerical simulation is illustrated, showing excellent agreement with our theoretical predictions
Nonlinear Resonance Leading to Beam Halo-chaos-complexity
Institute of Scientific and Technical Information of China (English)
2002-01-01
In this paper,nonlinear resonances of the particle-core taken placed in a space-charge dominatedbeam are suited. Overlapping resonance leads to chaos and halo formation. That is one of most importantphysical mechanisms. Duo to beam halo-chaos is essentially a spatiotemporal chaotic motion, Such beam
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...
Dynamical chaos in chip-scale optomechanical oscillators
Wu, Jiagui; Huang, Yongjun; Zhou, Hao; Yang, Jinghui; Liu, Jia-Ming; Yu, Mingbin; Lo, Guoqiang; Kwong, Dim-Lee; Xia, Guangqiong; Wong, Chee Wei
2016-01-01
Chaos has revolutionized the field of nonlinear science and stimulated foundational studies from neural networks, extreme event statistics, to physics of electron transport. Recent studies in cavity optomechanics provide a new platform to uncover quintessential architectures of chaos generation and the underlying physics. Here we report the first generation of dynamical chaos in silicon optomechanical oscillators, enabled by the strong and coupled nonlinearities of Drude electron-hole plasma. Deterministic chaotic oscillation is achieved, and statistical and entropic characterization quantifies the complexity of chaos. The correlation dimension D2 is determined at ~ 1.67 for the chaotic attractor, along with a maximal Lyapunov exponent rate about 2.94*the fundamental optomechanical oscillation. The corresponding nonlinear dynamical maps demonstrate the plethora of subharmonics, bifurcations, and stable regimes, along with distinct transitional routes into chaotic states. The chaos generation in our mesoscopic...
Quantitative and qualitative Kac's chaos on the Boltzmann's sphere
Carrapatoso, Kleber
2012-01-01
We investigate the construction of chaotic probability measures on the Boltzmann's sphere, which is the state space of the stochastic process of a many-particle system undergoing a dynamics preserving energy and momentum. Firstly, based on a version of the local Central Limit Theorem (or Berry-Essenn theorem), we construct a sequence of probabilities that is Kac chaotic and we prove a quantitative rate of convergence. Then, we investigate a stronger notion of chaos, namely entropic chaos introduced in \\cite{CCLLV}, and we prove, with quantitative rate, that this same sequence is also entropically chaotic. Furthermore, we investigate more general class of probability measures on the Boltzmann's sphere. Using the HWI inequality we prove that a Kac chaotic probability with bounded Fisher's information is entropically chaotic and we give a quantitative rate. We also link different notions of chaos, proving that Fisher's information chaos, introduced in \\cite{HaurayMischler}, is stronger than entropic chaos, which...
The Chaos Dynamic of Multiproduct Cournot Duopoly Game with Managerial Delegation
Directory of Open Access Journals (Sweden)
Fang Wu
2014-01-01
Full Text Available Although oligopoly theory is generally concerned with the single-product firm, what is true in the real word is that most of the firms offer multiproducts rather than single products in order to obtain cost-saving advantages, cater for the diversity of consumer tastes, and provide a barrier to entry. We develop a dynamical multiproduct Cournot duopoly model in discrete time, where each firm has an owner who delegates the output decision to a manager. The principle of decision-making is bounded rational. And each firm has a nonlinear total cost function due to the multiproduct framework. The Cournot Nash equilibrium and the local stability are investigated. The tangential bifurcation and intermittent chaos are reported by numerical simulations. The results show that high output adjustment speed can lead to output fluctuations which are characterized by phases of low volatility with small output changes and phases of high volatility with large output changes. The intermittent route to chaos of Flip bifurcation and another intermittent route of Flip bifurcation which contains Hopf bifurcation can exist in the system. The study can improve our understanding of intermittent chaos frequently observed in oligopoly economy.
ORDER IN THE CHAOS IN SPORTS ORGANIZATIONS
Directory of Open Access Journals (Sweden)
Mehran Azarian
2014-07-01
Full Text Available Purpose: Nowadays, scientists consider the world as a combination of some systems that work in a self -organizing way and the result of such a way is unpredictable and accidential states. Compulsory Natural rules are affective in such circumstances. Also it is known that systems work in a circular form in which order ends in disorder and vice versa. The idea of world as something simple has already replaced by a complicated and contradictory world. The study aim is to survey chaordic organizations characters of sport organizations. Materials and methods : For this purpose we used a standard questionnaire with appropriate reliability and validity. The statistical population of the study are whole staff of sport and youth head-quarter of west Azarbaijan province that are 89 (sample number is equal to the population's. We used Kolmogrov- Smirnov test to study data normal distribution, and in respect of normal distribution of data to test hypothesis we used sample t test and also descriptive statistical methods like mean and standard deviation, through SPSS 18. Questionnaires were filled out by whole staff of sport and youth head-quarters of west Azarbaijan province. Results: Results of this study, which have got through a single-sample t-test, show that sport organizations have six characteristics of welcoming to innovation, coherence, uncertainty, non-linearity, unpredictability, and ugly structure. It’s just the grade of the characteristic of recruiting competent staffs that is low in sport organizations; in fact they don’t enjoy it. But, within assessing the main hypothesis of the research that was around the feature of chaos-order, it was resulted that sport organizations have characteristics of a chaos-order organization and they can be considered as a chaos-order organization. Conclusions: According to the results of this study and t-table we can deduce that sport organizations are chaordic organization.
Asano, Yuhma; Kawai, Daisuke; Yoshida, Kentaroh
2015-06-01
We study classical chaotic motions in the Berenstein-Maldacena-Nastase (BMN) matrix model. For this purpose, it is convenient to focus upon a reduced system composed of two-coupled anharmonic oscillators by supposing an ansatz. We examine three ansätze: 1) two pulsating fuzzy spheres, 2) a single Coulomb-type potential, and 3) integrable fuzzy spheres. For the first two cases, we show the existence of chaos by computing Poincaré sections and a Lyapunov spectrum. The third case leads to an integrable system. As a result, the BMN matrix model is not integrable in the sense of Liouville, though there may be some integrable subsectors.
Asano, Yuhma; Yoshida, Kentaroh
2015-01-01
We study classical chaotic motions in the Berenstein-Maldacena-Nastase (BMN) matrix model. For this purpose, it is convenient to focus upon a reduced system composed of two-coupled anharmonic oscillators by supposing an ansatz. We examine three ans\\"atze: 1) two pulsating fuzzy spheres, 2) a single Coulomb-type potential, and 3) integrable fuzzy spheres. For the first two cases, we show the existence of chaos by computing Poincar\\'e sections and a Lyapunov spectrum. The third case leads to an integrable system. As a result, the BMN matrix model is not integrable in the sense of Liouville, though there may be some integrable subsectors.
Delayed self-synchronization in homoclinic chaos
Arecchi, F. T.; Meucci, R.; Allaria, E.; di Garbo, A.; Tsimring, L. S.
2002-04-01
The chaotic spike train of a homoclinic dynamical system is self-synchronized by applying a time-delayed correction proportional to the laser output intensity. Due to the sensitive nature of the homoclinic chaos to external perturbations, stabilization of very long-periodic orbits is possible. On these orbits, the dynamics appears chaotic over a finite time, but then it repeats with a recurrence time that is slightly longer than the delay time. The effect, called delayed self-synchronization, displays analogies with neurodynamic events that occur in the buildup of long-term memories.
A new optimization algorithm based on chaos
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In this article, some methods are proposed for enhancing the converging velocity of the COA (chaos optimization algorithm) based on using carrier wave two times, which can greatly increase the speed and efficiency of the first carrier wave's search for the optimal point in implementing the sophisticated searching during the second carrier wave is faster and more accurate.In addition, the concept of using the carrier wave three times is proposed and put into practice to tackle the multi-variables optimization problems, where the searching for the optimal point of the last several variables is frequently worse than the first several ones.
The CHAOS-4 Geomagnetic Field Model
Olsen, N.; Finlay, C. C.; Luhr, H.; Sabaka, T. J.; Michaelis, I.; Rauberg, J.; Tøffner-clausen, L.
2013-12-01
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 resolution (allowing for investigations of sub-annual core field changes). More than 14 years of data from the satellites Ørsted (March 1999 to June 2013), CHAMP (July 2000 to September 2010) and SAC-C (2000 to 2004), augmented with ground observatory revised monthly mean values (1997 to 2013) have been used for this model. Maximum spherical harmonic degree of the static (crustal) field is n=100. The core field time changes are expressed by spherical harmonic expansion coefficients up to n=20, described by order 6 splines (with 6-month knot spacing) spanning the time interval 1997.0 to 2013.5. The third time derivative of the squared magnetic field intensity is regularized at the core-mantle boundary. No spatial regularization is applied for the core field, but the high-degree crustal field is regularized for n>85. As part of the modeling effort we co-estimate a model of the large-scale magnetospheric field (with expansions in the GSM and SM coordinate system up to degree n = 2 and parameterization of the time dependence using the decomposition of Dst into external (Est) and induced (Ist) parts) and perform an in-flight alignment of the vector data (co-estimation of the Euler describing the rotation 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 of course including newer satellite observations), while its high-degree crustal field part is solely determined from low-altitude CHAMP satellite observations between January 2009 and
Chaos caused by fatigue crack growth
International Nuclear Information System (INIS)
The nonlinear dynamic responses including chaotic oscillations caused by a fatigue crack growth are presented. Fatigue tests have been conducted on a novel fatigue-testing rig, where the loading is generated from inertial forces. The nonlinearity is in the form of discontinuous stiffness caused by the opening and closing of a growing crack. Nonlinear dynamic tools such as Poincare maps and bifurcation diagrams are used to unveil the global dynamics of the system. The results obtained indicate that fatigue crack growth strongly influences the dynamic response of the system leading to chaos
Chaos caused by fatigue crack growth
Energy Technology Data Exchange (ETDEWEB)
Foong, C.-H.; Pavlovskaia, Ekaterina; Wiercigroch, Marian; Deans, William
2003-06-01
The nonlinear dynamic responses including chaotic oscillations caused by a fatigue crack growth are presented. Fatigue tests have been conducted on a novel fatigue-testing rig, where the loading is generated from inertial forces. The nonlinearity is in the form of discontinuous stiffness caused by the opening and closing of a growing crack. Nonlinear dynamic tools such as Poincare maps and bifurcation diagrams are used to unveil the global dynamics of the system. The results obtained indicate that fatigue crack growth strongly influences the dynamic response of the system leading to chaos.
Chaos Synchronization in Two Coupled Duffing Oscillators
Institute of Scientific and Technical Information of China (English)
方见树; 荣曼生; 方焯; 刘小娟
2001-01-01
We have obtained two general unstable periodic solutions near the homoclinic orbits of two coupled Duffing oscillators with weak periodic perturbations by using the direct perturbation technique. Theoretical analysis reveals that the stable periodic orbits are embedded in the Melnikov chaotic attractors. The corresponding numerical results show that the phase portraits in the (x, u) and (y, v) planes are identical and are synchronized when the parameters of the two coupled oscillators are identical, but they are different and asynchronized when there is any difference between these parameters. It has been shown that the system parameters play a very important role in chaos control and synchronization.
Quantum chaos and the black hole horizon
CERN. Geneva
2016-01-01
Thanks to AdS/CFT, the analogy between black holes and thermal systems has become a practical tool, shedding light on thermalization, transport, and entanglement dynamics. Continuing in this vein, recent work has shown how chaos in the boundary CFT can be analyzed in terms of high energy scattering right on the horizon of the dual black hole. The analysis revolves around certain out-of-time-order correlation functions, which are simple diagnostics of the butterfly effect. We will review this work, along with a general bound on these functions that implies black holes are the most chaotic systems in quantum mechanics. (NB Room Change to Main Auditorium)
Controlling chaos in Internet congestion control model
International Nuclear Information System (INIS)
The TCP end-to-end congestion control plus RED router queue management can be modeled as a discrete-time dynamical system, which may create complex bifurcating and chaotic behavior. Based on the basic features of the TCP-RED model, we propose a time-dependent delayed feedback control algorithm to control chaos in the system by perturbing the accessible RED parameter pmax. This method is able to stabilized a router queue occupancy at a level without knowing the exact knowledge of the network. Further, we study the situation of the presence of the UDP traffic
Importance of packing in spiral defect chaos
Indian Academy of Sciences (India)
Kapilanjan Krishna
2008-04-01
We develop two measures to characterize the geometry of patterns exhibited by the state of spiral defect chaos, a weakly turbulent regime of Rayleigh-Bénard convection. These describe the packing of contiguous stripes within the pattern by quantifying their length and nearest-neighbor distributions. The distributions evolve towards unique distribution with increasing Rayleigh number that suggests power-law scaling for the dynamics in the limit of infinite system size. The techniques are generally applicable to patterns that are reducible to a binary representation.
Congenital laryngomucocoele: a rare cause for CHAOS
M. Cunha; Janeiro, P; Fernandes, R.; Carreiro, H; Laurini, R
2009-01-01
Congenital high airway obstruction syndrome (CHAOS) is a rare but life-threatening condition that results from the obstruction of the upper airways. We describe a female newborn, from a Grávida II, Para 0, 36-year-old woman, with a routine ultrasound at 30 weeks’ gestation that showed polyhydramnios. She delivered a live-born female baby at 36 weeks without any dismorphic features but with respiratory distress. Attempts at endotracheal intubation were unsuccessful due to the presence of a ...
Experimental Chaos - Proceedings of the 3rd Conference
Harrison, Robert G.; Lu, Weiping; Ditto, William; Pecora, Lou; Spano, Mark; Vohra, Sandeep
1996-10-01
The Table of Contents for the full book PDF is as follows: * Preface * Spatiotemporal Chaos and Patterns * Scale Segregation via Formation of Domains in a Nonlinear Optical System * Laser Dynamics as Hydrodynamics * Spatiotemporal Dynamics of Human Epileptic Seizures * Experimental Transition to Chaos in a Quasi 1D Chain of Oscillators * Measuring Coupling in Spatiotemporal Dynamical Systems * Chaos in Vortex Breakdown * Dynamical Analysis * Radial Basis Function Modelling and Prediction of Time Series * Nonlinear Phenomena in Polyrhythmic Hand Movements * Using Models to Diagnose, Test and Control Chaotic Systems * New Real-Time Analysis of Time Series Data with Physical Wavelets * Control and Synchronization * Measuring and Controlling Chaotic Dynamics in a Slugging Fluidized Bed * Control of Chaos in a Laser with Feedback * Synchronization and Chaotic Diode Resonators * Control of Chaos by Continuous-time Feedback with Delay * A Framework for Communication using Chaos Sychronization * Control of Chaos in Switching Circuits * Astrophysics, Meteorology and Oceanography * Solar-Wind-Magnetospheric Dynamics via Satellite Data * Nonlinear Dynamics of the Solar Atmosphere * Fractal Dimension of Scalar and Vector Variables from Turbulence Measurements in the Atmospheric Surface Layer * Mechanics * Escape and Overturning: Subtle Transient Behavior in Nonlinear Mechanical Models * Organising Centres in the Dynamics of Parametrically Excited Double Pendulums * Intermittent Behaviour in a Heating System Driven by Phase Transitions * Hydrodynamics * Size Segregation in Couette Flow of Granular Material * Routes to Chaos in Rotational Taylor-Couette Flow * Experimental Study of the Laminar-Turbulent Transition in an Open Flow System * Chemistry * Order and Chaos in Excitable Media under External Forcing * A Chemical Wave Propagation with Accelerating Speed Accompanied by Hydrodynamic Flow * Optics * Instabilities in Semiconductor Lasers with Optical Injection * Spatio
Chaos induced by coupling between Josephson junctions
Shukrinov, Yu. M.; Azemtsa-Donfack, H.; Botha, A. E.
2015-02-01
It is found that, in a stack of intrinsic Josephson junctions in layered high temperature superconductors under external electromagnetic radiation, the chaotic features are triggered by interjunction coupling, i.e., the coupling between different junctions in the stack. While the radiation is well known to produce chaotic effects in the single junction, the effect of interjunction coupling is fundamentally different and it can lead to the onset of chaos via a different route to that of the single junction. A precise numerical study of the phase dynamics of intrinsic Josephson junctions, as described by the CCJJ+DC model, is performed. We demonstrate the charging of superconducting layers, in a bias current interval corresponding to a Shapiro step subharmonic, due to the creation of a longitudinal plasma wave along the stack of junctions. With increase in radiation amplitude chaotic behavior sets in. The chaotic features of the coupled Josephson junctions are analyzed by calculations of the Lyapunov exponents. We compare results for a stack of junctions to the case of a single junction and prove that the observed chaos is induced by the coupling between the junctions. The use of Shapiro step subharmonics may allow longitudinal plasma waves to be excited at low radiation power.
Order and chaos in soft condensed matter
Indian Academy of Sciences (India)
A K Sood; Rajesh Ganapathy
2006-07-01
Soft matter, like colloidal suspensions and surfactant gels, exhibit strong response to modest external perturbations. This paper reviews our recent experiments on the nonlinear flow behaviour of surfactant worm-like micellar gels. A rich dynamic behaviour exhibiting regular, quasi-periodic, intermittency and chaos is observed. In particular, we have shown experimentally that the route to chaos is via Type-II intermittency in shear thinning worm-like micellar solution of cetyltrimethylammonium tosylate where the strength of flow-concentration coupling is tuned by the addition of sodium chloride. A Poincaré first return map of the time series and the probability distribution of laminar length between burst events show that our data are consistent with Type-II intermittency. The existence of a `Butterfly' intensity pattern in small angle light scattering (SALS) measurements performed simultaneously with the rheological measurements confirms the coupling of flow to concentration fluctuations in the system under study. The scattered depolarised intensity in SALS, sensitive to orientational order fluctuations, shows the same time-dependence (like intermittency) as that of shear stress.
Chaos and structure of level densities
Energy Technology Data Exchange (ETDEWEB)
Moller, Peter [Los Alamos National Laboratory; Aberg, Sven [LUND SWEDEN; Uhrenholt, Henrik [LUND SWEDEN; Ickhikawa, Takatoshi [RIKEN
2008-01-01
The energy region of the first few MeV above the ground state shows interesting features of the nucleus. Beyond an ordered energy region just above the ground-state the dynamics changes, and chaotic features are observed in the neutron resonance region. The statistical properties of energies and wave-functions are common to all chaotic nuclei. However, if instead a global property, like the local level-density function is studied, strong structure effects emerge. In this contribution we discuss these two different facets of warm nuclei. In section 2 the onset of chaos with increasing excitation energy is discussed, with both experimental observations and proposed theoretical mechanisms as starting points. The structure of level densities in the same excitation energy region based on the two different starting points, is treated in section 3, where we give a short presentation of a newly developed combinatorial level-density modell. Some results from the model are presented and discussed. Two coexisting facets of warm nuclei, quantum chaos and structure of the level density, are considered. A newly developed combinatorial level-density model is presented, and the role of collective enhancements discussed. An example of extreme parity enhancement is shown.
Equilibrium behavior of coarse-grained chaos
Egolf, David A.; Ballard, Christopher C.; Esty, C. Clark
2015-03-01
A wide variety of systems exhibiting spatiotemporal chaos have been shown to be extensive, in that their fractal dimensions grow linearly with volume. Ruelle argued that this extensivity is evidence that these systems can be viewed as a gas of weakly-interacting regions. We have tested this idea by performing large-scale computational studies of spatiotemporal chaos in the 1D complex Ginzburg-Landau equation, and we have found that aspects of the coarse-grained system are well-described not only as a gas, but as an equilibrium gas -- in particular, a Tonks gas (and variants) in the grand canonical ensemble. Furthermore, for small system sizes, the average number of particles in the corresponding Tonks gas exhibits oscillatory, decaying deviations from extensivity in agreement with deviations in the fractal dimension found by Fishman and Egolf. This result not only supports Ruelle's picture but also suggests that the coarse-grained behavior of this far-from-equilibrium system might be understood using equilibrium statistical mechanics.
Decrease of cardiac chaos in congestive heart failure
Poon, Chi-Sang; Merrill, Christopher K.
1997-10-01
The electrical properties of the mammalian heart undergo many complex transitions in normal and diseased states. It has been proposed that the normal heartbeat may display complex nonlinear dynamics, including deterministic chaos,, and that such cardiac chaos may be a useful physiological marker for the diagnosis and management, of certain heart trouble. However, it is not clear whether the heartbeat series of healthy and diseased hearts are chaotic or stochastic, or whether cardiac chaos represents normal or abnormal behaviour. Here we have used a highly sensitive technique, which is robust to random noise, to detect chaos. We analysed the electrocardiograms from a group of healthy subjects and those with severe congestive heart failure (CHF), a clinical condition associated with a high risk of sudden death. The short-term variations of beat-to-beat interval exhibited strongly and consistently chaotic behaviour in all healthy subjects, but were frequently interrupted by periods of seemingly non-chaotic fluctuations in patients with CHF. Chaotic dynamics in the CHF data, even when discernible, exhibited a high degree of random variability over time, suggesting a weaker form of chaos. These findings suggest that cardiac chaos is prevalent in healthy heart, and a decrease in such chaos may be indicative of CHF.
Diffusive Lorenz dynamics： Coherent structures and spatiotemporal chaos
Institute of Scientific and Technical Information of China (English)
YuehongQIAN; HudongCHEN; Da-HsuanFENG
2000-01-01
In this paper, we are interested in collective behaviors of many interacting Lorenz strange attractors. With an intermediate diffusion coupling between the attractors,a new remarkable synchronization of well organized structures merges as a result of two competing mechanisms: temporal chaos and spatial diffusive stabilization. A window of the coupling parameter for coherent structures is found numerically. Different from all existing scenarios of routes to chaos (period doubling, intermittency and strange attractors), an algorithmetic increase of wavenumbers before an abrupt change to chaos (compared to the periodic doubling geometrical) is unexpectedly discovered. Meta-stable states are also observed in simulations.
Manifestation of resonance-related chaos in coupled Josephson junctions
Energy Technology Data Exchange (ETDEWEB)
Shukrinov, Yu.M. [BLTP, JINR, Dubna, Moscow Region, 141980 (Russian Federation); Hamdipour, M. [BLTP, JINR, Dubna, Moscow Region, 141980 (Russian Federation); Institute for Advanced Studies in Basic Sciences, P.O. Box 45195-1159, Zanjan (Iran, Islamic Republic of); Kolahchi, M.R. [Institute for Advanced Studies in Basic Sciences, P.O. Box 45195-1159, Zanjan (Iran, Islamic Republic of); Botha, A.E., E-mail: bothaae@unisa.ac.za [Department of Physics, University of South Africa, P.O. Box 392, Pretoria 0003 (South Africa); Suzuki, M. [Photonics and Electronics Science and Engineering Center and Department of Electronic Science and Engineering, Kyoto University, Kyoto 615-8510 (Japan)
2012-11-01
Manifestation of chaos in the temporal dependence of the electric charge is demonstrated through the calculation of the maximal Lyapunov exponent, phase–charge and charge–charge Lissajous diagrams and correlation functions. It is found that the number of junctions in the stack strongly influences the fine structure in the current–voltage characteristics and a strong proximity effect results from the nonperiodic boundary conditions. The observed resonance-related chaos exhibits intermittency. The criteria for a breakpoint region with no chaos are obtained. Such criteria could clarify recent experimental observations of variations in the power output from intrinsic Josephson junctions in high temperature superconductors.
Manifestation of resonance-related chaos in coupled Josephson junctions
Shukrinov, Yu. M.; Hamdipour, M.; Kolahchi, M. R.; Botha, A. E.; Suzuki, M.
2012-11-01
Manifestation of chaos in the temporal dependence of the electric charge is demonstrated through the calculation of the maximal Lyapunov exponent, phase-charge and charge-charge Lissajous diagrams and correlation functions. It is found that the number of junctions in the stack strongly influences the fine structure in the current-voltage characteristics and a strong proximity effect results from the nonperiodic boundary conditions. The observed resonance-related chaos exhibits intermittency. The criteria for a breakpoint region with no chaos are obtained. Such criteria could clarify recent experimental observations of variations in the power output from intrinsic Josephson junctions in high temperature superconductors.
Evolution to the Edge of Chaos in Imitation Game
Kaneko, K; Kaneko, Kunihiko; Suzuki, Junji
1993-01-01
Motivated by the evolution of complex bird songs, an abstract imitation game is proposed to study the increase of dynamical complexity: Artificial "birds" display a "song" time series to each other, and those that imitate the other's song better win the game. With the introduction of population dynamics according to the score of the game and the mutation of parameters for the song dynamics, the dynamics is found to evolve towards the borderline between chaos and a periodic window, after punctuated equilibria. The importance of edge of chaos with topological chaos for complexity is stressed.
New chaos-based encryption scheme for digital sequence
Institute of Scientific and Technical Information of China (English)
Zhang Zhengwei; Fan Yangyu; Zeng Li
2007-01-01
To enhance the anti-breaking performance of privacy information, this article proposes a new encryption method utilizing the leaping peculiarity of the periodic orbits of chaos systems. This method maps the secret sequence to several chaos periodic orbits, and a short sequence obtained by evolving the system parameters of the periodic orbits in another nonlinear system will be the key to reconstruct these periodic orbits. In the decryption end, the shadowing method of chaos trajectory based on the modified Newton-Raphson algorithm is adopted to restore these system parameters. Through deciding which orbit each pair coordinate falls on, the original digital sequence can be decrypted.
Chaos behavior in the discrete Fitzhugh nerve system
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The discrete Fitzhugh nerve systems obtained by the Euler method is investigated and it is proved that there exist chaotic phenomena in the sense of Marotto's definition of chaos. And numerical simulations not only show the consistence with the theoretical analysis but also exhibit the complex dynamical behaviors, including the ten-periodic orbit, a cascade of period-doubling bifurcation, quasiperiodic orbits and the chaotic orbits and intermittent chaos. The computations of Lyapunov exponents confirm the chaos behaviors. Moreover we also find a strange attractor having the self-similar orbit structure as that of Henon attractor.
From chaos to order methodologies, perspectives and applications
Chen Guan Rong
1998-01-01
Chaos control has become a fast-developing interdisciplinary research field in recent years. This book is for engineers and applied scientists who want to have a broad understanding of the emerging field of chaos control. It describes fundamental concepts, outlines representative techniques, provides case studies, and highlights recent developments, putting the reader at the forefront of current research.Important topics presented in the book include: Fundamentals of nonlinear dynamical systems, essential for understanding and developing chaos control methods.; Parametric variation and paramet
Controlling beam halo-chaos via backstepping design
Institute of Scientific and Technical Information of China (English)
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.
From chaos to disorder: Statistics of the eigenfunctions of microwave cavities
Indian Academy of Sciences (India)
Prabhakar Pradhan; S Sridhar
2002-02-01
We study the statistics of the experimental eigenfunctions of chaotic and disordered microwave billiards in terms of the moments of their spatial distributions, such as the inverse participation ratio (IPR) and density-density auto-correlation. A path from chaos to disorder is described in terms of increasing IPR. In the chaotic, ballistic limit, the data correspond well with universal results from random matrix theory. Deviations from universal distributions are observed due to disorder induced localization, and for the weakly disordered case the data are well-described by including ﬁnite conductance and mean free path contributions in the framework of nonlinear sigma models of supersymmetry.
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
A New Approach for Controlling Chaos Based on Direct Optimizing Predictive Control
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
We introduce the predictive control theory into the study of chaos control and propose a direct optimizing predictive control algorithm based on a neural network model. The proposed control system stabilizes the chaotic motion in an unknown chaotic system onto the desired target trajectory. Compared with the existing similar algorithms, the proposed control system has faster response, so it requires much shorter time for the stabilization of the chaotic systems.The proposed approach can control hyperchaos and the algorithm is simple. The convergence of the control algorithm and the stability of the control system can be guaranteed. The theoretic analysis and simulations demonstrate the effectiveness of the algorithm.
Systems Thinking Managing Chaos and Complexity A Platform for Designing Business Architecture
Gharajedaghi, Jamshid
2011-01-01
In a global market economy, a viable business cannot be locked into a single form or function anymore. Rather, success is contingent upon a self-renewing capacity to spontaneously create structures, functions, and processes responsive to a fluctuating business landscape. Now in its third edition, Systems Thinking synthesizes systems theory and interactive design, providing an operational methodology for defining problems and designing solutions in an environment increasingly characterized by chaos and complexity. The current edition has been updated to include all new chapters on self-organiz
Fluctuation of USA Gold Price - Revisited with Chaos-based Complex Network Method
Bhaduri, Susmita; Ghosh, Subhadeep
2016-01-01
We give emphasis on the use of chaos-based rigorous nonlinear technique called Visibility Graph Analysis, to study one economic time series - gold price of USA. This method can offer reliable results with fiinite data. This paper reports the result of such an analysis on the times series depicting the fluctuation of gold price of USA for the span of 25 years(1990 - 2013). This analysis reveals that a quantitative parameter from the theory can explain satisfactorily the real life nature of fluctuation of gold price of USA and hence building a strong database in terms of a quantitative parameter which can eventually be used for forecasting purpose.
Phase control of resonant systems: interference, chaos and high periodicity.
Greenman, J V; Pasour, V B
2011-06-01
Much progress has been made in understanding the effect of periodic forcing on epidemiological and ecological systems when that forcing acts on just one part of the system. Much less is known about situations in which several parts of the system are affected. In this case the interaction between the impacts of the different forcing components can lead to reinforcement of system responses or to their interference. This interference phenomenon is significant if some forcing components are anthropogenic for then management might be able to exercise sufficient control to bring about suppression of undesirable aspects of the forcing, for example resonant amplification and the problems this can cause. We set out the algebraic theory when forcing is weak and illustrate by example what can happen when forcing is strong enough to create subharmonics and chaotic states. Phase is the key control variable that can bring about interference, advantageously shift nonlinear response curves and create periodic states out of chaos. The phenomenon in which high period fluctuations appear to be generated by low period forcing is examined and different mechanisms compared in a two-strain epidemiological model. The effect of noise as a source of high period fluctuations is also considered. PMID:21397609
Learning from myocarditis: mimicry, chaos and black holes.
Rose, Noel R
2014-01-01
Autoimmune myocarditis and its sequel, dilated cardiomyopathy, are major causes of heart failure, especially in children and young adults. We have developed animal models to investigate their pathogenesis by infecting genetically susceptible mice with coxsackievirus B3 or by immunizing them with cardiac myosin or its immunodominant peptide. A number of valuable lessons have emerged from our study of this paradigm of an infection-induced autoimmune disease. We understand more clearly how natural autoimmunity, as an important component of normal physiology, must be recalibrated regularly due to changes caused by infection or other internal and external stimuli. A new normal homeostatic platform will be established based on its evolutionary fitness. A loss of homeostasis with out-of-control normal autoimmunity leads to autoimmune disease. It is signified early on by a spread of an adaptive autoimmune response to novel epitopes and neighboring antigens. The progression from infection to normal, well-balanced autoimmunity to autoimmune disease and on to irreversible damage is a complex, step-wise process. Yet, chaos theory provides hope that the pattern is potentially predictable. Infection-induced autoimmune disease represents a sequence of events heading for a train wreck at the end of the line. Our aim in autoimmune disease research must be to stop the train before this happens.
ƒ(R Gravity, Relic Coherent Gravitons and Optical Chaos
Directory of Open Access Journals (Sweden)
Lawrence B. Crowell
2014-03-01
Full Text Available We discuss the production of massive relic coherent gravitons in a particular class of ƒ(R gravity, which arises from string theory, and their possible imprint in the Cosmic Microwave Background. In fact, in the very early Universe, these relic gravitons could have acted as slow gravity waves. They may have then acted to focus the geodesics of radiation and matter. Therefore, their imprint on the later evolution of the Universe could appear as filaments and a domain wall in the Universe today. In that case, the effect on the Cosmic Microwave Background should be analogous to the effect of water waves, which, in focusing light, create optical caustics, which are commonly seen on the bottom of swimming pools. We analyze this important issue by showing how relic massive gravity waves (GWs perturb the trajectories of the Cosmic Microwave Background photons (gravitational lensing by relic GWs. The consequence of the type of physics discussed is outlined by illustrating an amplification of what might be called optical chaos.
Classical and wave chaos in asymmetric resonant cavities
Stone, A. Douglas
2000-12-01
Deformed cylindrical and spherical dielectric optical resonators are analyzed from the perspective of non-linear dynamics and quantum chaos theory. In the short-wavelength limit such resonators behave like billiard systems with non-zero escape probability due to refraction. A ray model is introduced to predict the resonance lifetimes and emission patterns from such a cavity. A universal wavelength-independent broadening is predicted and found for large deformations of the cavity, however there are significant wave-chaotic corrections as well. Highly directional emission is predicted from chaotic “whispering gallery” modes for index of refraction less than two. The detailed nature of the emission pattern can be understood from the nature of the phase space flow in the billiard, and a dramatic variation of this pattern with index of refraction is found due to an effect called “dynamical eclipsing”. Semiconductor resonators of this type also show highly directional emission and high output power but from different modes associated with periodic orbits. A semiclassical approach to these modes is briefly reviewed. These asymmetric resonant cavities (ARCs) show promise as components in future integrated optical devices.
Uncertainty Quantification for Airfoil Icing using Polynomial Chaos Expansions
DeGennaro, Anthony M; Martinelli, Luigi
2014-01-01
The formation and accretion of ice on the leading edge of a wing can be detrimental to airplane performance. Complicating this reality is the fact that even a small amount of uncertainty in the shape of the accreted ice may result in a large amount of uncertainty in aerodynamic performance metrics (e.g., stall angle of attack). The main focus of this work concerns using the techniques of Polynomial Chaos Expansions (PCE) to quantify icing uncertainty much more quickly than traditional methods (e.g., Monte Carlo). First, we present a brief survey of the literature concerning the physics of wing icing, with the intention of giving a certain amount of intuition for the physical process. Next, we give a brief overview of the background theory of PCE. Finally, we compare the results of Monte Carlo simulations to PCE-based uncertainty quantification for several different airfoil icing scenarios. The results are in good agreement and confirm that PCE methods are much more efficient for the canonical airfoil icing un...
Reynolds number effects on mixing due to topological chaos
Smith, Spencer A
2016-01-01
Topological chaos has emerged as a powerful tool to investigate fluid mixing. While this theory can guarantee a lower bound on the stretching rate of certain material lines, it does not indicate what fraction of the fluid actually participates in this minimally mandated mixing. Indeed, the area in which effective mixing takes place depends on physical parameters such as the Reynolds number. To help clarify this dependency, we numerically simulate the effects of a batch stirring device on a 2D incompressible Newtonian fluid in the laminar regime. In particular, we calculate the finite time Lyapunov exponent (FTLE) field for three different stirring protocols, one topologically complex (pseudo-Anosov) and two simple (finite-order), over a range of viscosities. After extracting appropriate measures indicative of both the amount of mixing and the area of effective mixing from the FTLE field, we see a clearly defined Reynolds number range in which the relative efficacy of the pseudo-Anosov protocol over the finite...
Design and Implementation of Image Encryption Algorithm Using Chaos
Directory of Open Access Journals (Sweden)
Sandhya Rani M.H.
2014-06-01
Full Text Available Images are widely used in diverse areas such as medical, military, science, engineering, art, advertising, entertainment, education as well as training, increasing the use of digital techniques for transmitting and storing images. So maintaining the confidentiality and integrity of images has become a major concern. This makes encryption necessary. The pixel values of neighbouring pixels in a plain image are strongly correlated. The proposed algorithm breaks this correlation increasing the entropy. Correlation is reduced by changing the pixel position this which is called confusion. Histogram is equalized by changing the pixel value this which is called diffusion. The proposed method of encryption algorithm is based on chaos theory. The plain-image is divided into blocks and then performs three levels of shuffling using different chaotic maps. In the first level the pixels within the block are shuffled. In the second level the blocks are shuffled and in the third level all the pixels in an image are shuffled. Finally the shuffled image is diffused using a chaotic sequence generated using symmetric keys, to produce the ciphered image for transmission. The experimental result demonstrates that the proposed algorithm can be used successfully to encrypt/decrypt the images with the secret keys. The analysis of the algorithm also shows that the algorithm gives larger key space and a high key sensitivity. The encrypted image has good encryption effect, information entropy and low correlation coefficient.
2011-07-01
WE RECOMMEND Fun Fly Stick Science Kit Fun fly stick introduces electrostatics to youngsters Special Relativity Text makes a useful addition to the study of relativity as an undergraduate LabVIEWTM 2009 Education Edition LabVIEW sets industry standard for gathering and analysing data, signal processing, instrumentation design and control, and automation and robotics Edison and Ford Winter Estates Thomas Edison's home is open to the public The Computer History Museum Take a walk through technology history at this computer museum WORTH A LOOK Fast Car Physics Book races through physics Beautiful Invisible The main subject of this book is theoretical physics Quantum Theory Cannot Hurt You A guide to physics on the large and small scale Chaos: The Science of Predictable Random Motion Book explores the mathematics behind chaotic behaviour Seven Wonders of the Universe A textual trip through the wonderful universe HANDLE WITH CARE Marie Curie: A Biography Book fails to capture Curie's science WEB WATCH Web clips to liven up science lessons
Spatial chaos-based image encryption design
Institute of Scientific and Technical Information of China (English)
LIU ShuTang; SUN FuYan
2009-01-01
In recent years, the chaos based cryptographic algorithms have suggested some new and efficient ways to develop secure image encryption techniques, but the drawbacks of small key space and weak security in one-dimensional chaotic cryptosystems are obvious. In this paper, permutation and sub-stitution methods are incorporated to present a stronger image encryption algorithm. Spatial chaotic maps are used to realize the position permutation, and to confuse the relationship between the ci-pher-image and the plain-image. The experimental results demonstrate that the suggested encryption scheme of image has the advantages of large key space and high security; moreover, the distribution of grey values of the encrypted image has a random-like behavior.
Food chain chaos due to transcritical point
Deng, Bo; Hines, Gwendolen
2003-06-01
Chaotic dynamics of a classical prey-predator-superpredator ecological model are considered. Although much is known about the behavior of the model numerically, very few results have been proven analytically. A new analytical result is obtained. It is demonstrated that there exists a subset on which a singular Poincaré map generated by the model is conjugate to the shift map on two symbols. The existence of such a Poincaré map is due to two conditions: the assumption that each species has its own time scale ranging from fast for the prey to slow for the superpredator, and the existence of transcritical points, leading to the classical mathematical phenomenon of Pontryagin's delay of loss of stability. This chaos generating mechanism is new, neither suspected in abstract form nor recognized in numerical experiments in the literature.
Mechanics From Newton's Laws to Deterministic Chaos
Scheck, Florian
2010-01-01
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 fifth edition is updated and revised with more explanations, additional examples and sections on Noether's theorem. 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 120 problems with complete solutions, as well as some practical exa...
Controlling chaos using an exponential control
Gadre, S D; Gadre, Sangeeta D; Varma, V S
1995-01-01
We demonstrate that chaos can be controlled using a multiplicative exponential feedback control. All three types of unstable orbits - unstable fixed points, limit cycles and chaotic trajectories can be stabilized using this control. The control is effective both for maps and flows. The control is significant, particularly for systems with several degrees of freedom, as knowledge of only one variable on the desired unstable orbit is sufficient to settle the system on to that orbit. We find, that in all the cases studied, the transient time is a decreasing function of the stiffness of control. But increasing the stiffness beyond an optimum value can increase the transient time. The control can also be used to create suitable new stable attractors in a map, which did not exist in the original system.
Chaos in body-vortex interactions
DEFF Research Database (Denmark)
Pedersen, Johan Rønby; Aref, Hassan
2010-01-01
The model of body–vortex interactions, where the fluid flow is planar, ideal and unbounded, and the vortex is a point vortex, is studied. The body may have a constant circulation around it. The governing equations for the general case of a freely moving body of arbitrary shape and mass density...... 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...... and an arbitrary number of point vortices are presented. The case of a body and a single vortex is then investigated numerically in detail. In this paper, the body is a homogeneous, elliptical cylinder. For large body–vortex separations, the system behaves much like a vortex pair regardless of body shape. The case...
Digital Communications Using Chaos and Nonlinear Dynamics
Larson, Lawrence E; Liu, Jia-Ming
2006-01-01
This book introduces readers to a new and exciting cross-disciplinary field of digital communications with chaos. This field was born around 15 years ago, when it was first demonstrated that nonlinear systems which produce complex non-periodic noise-like chaotic signals, can be synchronized and modulated to carry useful information. Thus, chaotic signals can be used instead of pseudo-random digital sequences for spread-spectrum and private communication applications. This deceptively simple idea spun hundreds of research papers, and many novel communication schemes based on chaotic signals have been proposed. However, only very recently researchers have begun to make a transition from academic studies toward practical implementation issues, and many "promising" schemes had to be discarded or re-formulated. This book describes the state of the art (both theoretical and experimental) of this novel field. The book is written by leading experts in the fields of Nonlinear Dynamics and Electrical Engineering who pa...
Stochastic chaos in a turbulent swirling flow
Faranda, Davide; Saint-Michel, Brice; Wiertel, Cecile; Padilla, Vincent; Dubrulle, Berengere; Daviaud, Francois
2016-01-01
We report the experimental evidence of the existence of a random attractor in a fully developed turbulent swirling flow. By defining a global observable which tracks the asymmetry in the flux of angular momentum imparted to the flow, we can first reconstruct the associated turbulent attractor and then follow its route towards chaos. We further show that the experimental attractor can be modeled by stochastic Duffing equations, that match the quantitative properties of the experimental flow, namely the number of quasi-stationary states and transition rates among them, the effective dimensions, and the continuity of the first Lyapunov exponents. Such properties can neither be recovered using deterministic models nor using stochastic differential equations based on effective potentials obtained by inverting the probability distributions of the experimental global observables. Our findings open the way to low dimensional modeling of systems featuring a large number of degrees of freedom and multiple quasi-station...
Spatial chaos-based image encryption design
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
In recent years, the chaos based cryptographic algorithms have suggested some new and efficient ways to develop secure image encryption techniques, but the drawbacks of small key space and weak security in one-dimensional chaotic cryptosystems are obvious. In this paper, permutation and sub- stitution methods are incorporated to present a stronger image encryption algorithm. Spatial chaotic maps are used to realize the position permutation, and to confuse the relationship between the ci- pher-image and the plain-image. The experimental results demonstrate that the suggested encryption scheme of image has the advantages of large key space and high security; moreover, the distribution of grey values of the encrypted image has a random-like behavior.
Complex Nonlinearity Chaos, Phase Transitions, Topology Change and Path Integrals
Ivancevic, Vladimir G
2008-01-01
Complex Nonlinearity: Chaos, Phase Transitions, Topology Change and Path Integrals is a book about prediction & control of general nonlinear and chaotic dynamics of high-dimensional complex systems of various physical and non-physical nature and their underpinning geometro-topological change. The book starts with a textbook-like expose on nonlinear dynamics, attractors and chaos, both temporal and spatio-temporal, including modern techniques of chaos–control. Chapter 2 turns to the edge of chaos, in the form of phase transitions (equilibrium and non-equilibrium, oscillatory, fractal and noise-induced), as well as the related field of synergetics. While the natural stage for linear dynamics comprises of flat, Euclidean geometry (with the corresponding calculation tools from linear algebra and analysis), the natural stage for nonlinear dynamics is curved, Riemannian geometry (with the corresponding tools from nonlinear, tensor algebra and analysis). The extreme nonlinearity – chaos – corresponds to th...
Filtering with Marked Point Process Observations via Poisson Chaos Expansion
International Nuclear Information System (INIS)
We study a general filtering problem with marked point process observations. The motivation comes from modeling financial ultra-high frequency data. First, we rigorously derive the unnormalized filtering equation with marked point process observations under mild assumptions, especially relaxing the bounded condition of stochastic intensity. Then, we derive the Poisson chaos expansion for the unnormalized filter. Based on the chaos expansion, we establish the uniqueness of solutions of the unnormalized filtering equation. Moreover, we derive the Poisson chaos expansion for the unnormalized filter density under additional conditions. To explore the computational advantage, we further construct a new consistent recursive numerical scheme based on the truncation of the chaos density expansion for a simple case. The new algorithm divides the computations into those containing solely system coefficients and those including the observations, and assign the former off-line.
Fractional Chaos Based Communication Systems-An Introduction
Institute of Scientific and Technical Information of China (English)
Juebang Yu
2008-01-01
As one of secure communication means, chaotic communication systems has been well-developed during the past three decades. Technical papers, both for theoretical and practical investigations, have reached a huge amount in number. On the other hand, fractional chaos, as a parallel ongoing research topic, also attracts many researchers to investigate. As far as the IT field is concerned, the research on control systems by using fractional chaos known as FOC (fractional order control) has been a hot issue for quite a long time. As a comparison, interesting enough, up to now we have not found any research result related to Fractional Chaos Communi cation (FCC) system, Le., a system based on fractional chaos. The motivation of the present article is to reveal the feasibility of realizing communication systems based upon FCC and their superiority over the conventional integer chaotic communication systems. Principles of FCC and its advantages over integer chaotic communication systems are also discussed.
Discrete chaos in fractional sine and standard maps
Energy Technology Data Exchange (ETDEWEB)
Wu, Guo-Cheng, E-mail: wuguocheng@gmail.com [Key Laboratory of Numerical Simulation of Sichuan Province, College of Mathematics and Information Science, Neijiang Normal University, Neijiang 641112 (China); College of Water Resource and Hydropower, Sichuan University, Chengdu 610065 (China); Baleanu, Dumitru, E-mail: dumitru@cankaya.edu.tr [Department of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, PO Box 80204, Jeddah 21589 (Saudi Arabia); Department of Mathematics and Computer Sciences, Faculty of Arts and Sciences, Cankaya University, 06530 Balgat, Ankara (Turkey); Institute of Space Sciences, Magurele-Bucharest (Romania); Zeng, Sheng-Da [School of Science, Guangxi University for Nationalities, Nanning 530006 (China)
2014-01-24
Fractional standard and sine maps are proposed by using the discrete fractional calculus. The chaos behaviors are then numerically discussed when the difference order is a fractional one. The bifurcation diagrams and the phase portraits are presented, respectively.
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 resource
WHAT DOES CHAOS HAVE TO DO WITH SYSTEMS AND CONTROL ENGINEERING?
Institute of Scientific and Technical Information of China (English)
CHEN Guanrong
2001-01-01
Chaos as a very special type of complex dynamical behaviors hasbeen studied for about four decades. Yet the traditional trend of analyzing and understanding chaos has evolved to controlling and utilizing chaos today. Research in the field of chaos modeling,control, and synchronization includes not only ordering chaos, which means to weaken or completely suppress chaos when it is harmful, but also chaotification, which refers to enhancing existing chaos or creating chaos purposely when it is useful, by any means of control technology. This article offers a brief overview about the potential impact of controlled chaos on beneficial applications in science and engineering, and introduces some recent progress in chaotification via feedback control methods.
Chaos and the quantum: how nonlinear effects can explain certain quantum paradoxes
McHarris, Wm C.
2011-07-01
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
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
Bifurcations and chaos control in discrete small-world networks
Institute of Scientific and Technical Information of China (English)
Li Ning; Sun Hai-Yi; Zhang Qing-Ling
2012-01-01
An impulsive delayed feedback control strategy to control period-doubling bifurcations and chaos is proposed.The control method is then applied to a discrete small-world network model.Qualitative analyses and simulations show that under a generic condition,the bifurcations and the chaos can be delayed or eliminated completely.In addition,the periodic orbits embedded in the chaotic attractor can be stabilized.
Secure Communication System Based on Chaos in Optical Fibre
Institute of Scientific and Technical Information of China (English)
Pak; L; Chu; Fan; Zhang; William; Mak; Robust; Lai
2003-01-01
1 IntroductionRecently, there have been intense research activities on the study of synchronized chaos generated by fibre lasers and its application to secure communication systems. So far, all studies concentrate on two aspects: (1) the effect of the transmission channel between the transmitter and the receiver has been neglected, and (2) the chaos and the signal are carried by one wavelength. Both theoretical and experimental investigations make
Chaos suppression in a spin-torque nano-oscillator
Xu, H. Z.; Chen, X.; Liu, J.-M.
2008-11-01
We propose a novel practicable self-control scheme to suppress chaos in a spin-torque nano-oscillator in the presence of spin-polarized dc and ac. The magnetization dynamics is investigated by performing micromagnetic simulation. A complete chaos control diagram is obtained, indicating that employment of this proper self-control scheme over a broad frequency range of the ac can greatly reduce the degree of chaoticity in the oscillator.
Relations between distributional, Li-Yorke and {omega} chaos
Energy Technology Data Exchange (ETDEWEB)
Guirao, Juan Luis Garcia [Departamento de Matematica Aplicada y Estadistica, Universidad Politecnica de Cartagena, C/Paseo Alfonso XIII, 30203-Cartagena (Region de Murcia) (Spain)]. E-mail: juan.garcia@upct.es; Lampart, Marek [Mathematical Institute at Opava, Silesian University at Opava, Na Rybnicku 1, 746 01 Opava (Czech Republic)]. E-mail: marek.lampart@math.slu.cz
2006-05-15
The forcing relations between notions of distributional, Li-Yorke and {omega} chaos were studied by many authors. In this paper we summarize all known connections between these three different types of chaos and fulfill the results for general compact metric spaces by the construction of a selfmap on a compact perfect set which is {omega} chaotic, not distributionally chaotic and has zero topological entropy.
Fluctuations of Spatial Patterns as a Measure of Classical Chaos
Cao, Z J; Cao, Zhen; Hwa, Rudolph C.
1997-01-01
In problems where the temporal evolution of a nonlinear system cannot be followed, a method for studying the fluctuations of spatial patterns has been developed. That method is applied to well-known problems in deterministic chaos (the logistic map and the Lorenz model) to check its effectiveness in characterizing the dynamical behaviors. It is found that the indices $\\mu _q$ are as useful as the Lyapunov exponents in providing a quantitative measure of chaos.
Universal quantification for deterministic chaos in dynamical systems
Selvam, A. Mary
2000-01-01
A cell dynamical system model for deterministic chaos enables precise quantification of the round-off error growth,i.e., deterministic chaos in digital computer realizations of mathematical models of continuum dynamical systems. The model predicts the following: (a) The phase space trajectory (strange attractor) when resolved as a function of the computer accuracy has intrinsic logarithmic spiral curvature with the quasiperiodic Penrose tiling pattern for the internal structure. (b) The unive...
OnN Kac's Chaos and Related Problems
Hauray, Maxime
2012-01-01
This paper is devoted to establish quantitative and qualitative estimates related to the notion of chaos as firstly formulated by M. Kac [37] in his study of mean-field limit for systems of N undistinguishable particles as N \\rightarrow \\infty. First, we quantitatively liken three usual measures of Kac's chaos, some involving the all N variables, other involving a finite fixed number of variables. The cornerstone of the proof is a new representation of the Monge-Kantorovich-Wasserstein (MKW) distance for symmetric N-particle probabilities in terms of the distance between the law of the associated empirical measures on the one hand, and a new estimate on some MKW distance on probability spaces endowed with a suitable Hilbert norm taking advantage of the associated good algebraic structure. Next, we define the notion of entropy chaos and Fisher information chaos in a similar way as defined by Carlen et al [17]. We show that Fisher information chaos is stronger than entropy chaos, which in turn is stronger than ...
Chaos Suppression in a Sine Square Map through Nonlinear Coupling
Institute of Scientific and Technical Information of China (English)
Eduardo L. Brugnago; Paulo C. Rech
2011-01-01
We study a pair of nonlinearly coupled identical chaotic sine square maps.More specifically,we investigate the chaos suppression associated with the variation of two parameters.Two-dimensional parameter-space regions where the chaotic dynamics of the individual chaotic sine square map is driven towards regular dynamics are delimited.Additionally,the dynamics of the coupled system is numerically characterized as the parameters are changed.In recent years,many efforts have been devoted to chaos suppression in a nonlinear dynamics field.Iglesias et al.[1] reported a chaos suppression method through numerical truncation and rounding errors,with applications in discrete-time systems.Hénon map[2] and the Burgers map[3] were used to illustrate the method.A method of feedback impulsive chaos suppression was introduced by Osipov et al.[4]It is an algorithm of suppressing chaos in continuoustime dissipative systems with an external impulsive force,whose necessary condition is a reduction of the continuous flow to a discrete-time one-dimensional map.%We study a pair of nonlinearly coupled identical chaotic sine square maps. More specifically, we investigate the chaos suppression associated with the variation of two parameters. Two-dimensional parameter-space regions where the chaotic dynamics of the individual chaotic sine square map is driven towards regular dynamics are delimited. Additionally, the dynamics of the coupled system is numerically characterized as the parameters are changed.
Staircase functions, spectral regidity and a rule for quantizing chaos
International Nuclear Information System (INIS)
Considering the Selberg trace formula as an exact version of Gutzwiller's semiclassical periodic-orbit theory in the case of the free motion on compact Riemann surfaces with constant negative curvature (Hadamard-Gutzwiller model), we study two complementary basic problems in quantum chaology: the computation of the calssical staircase N(l), the number of periodic orbits with length shorter than l, in terms of the quantal energy spectrum {En}, the computation of the spectral staircase N (E), the number of quantal energies below the energy E, in terms of the length spectrum {ln} of the classical periodic orbits. A formulation of the periodic-orbit theory is presented which is intrinsically unsmoothed, but for which an effective smoothing arises from the limited 'input data', i.e. from the limited knowledge of the periodic orbits in the case of N(E) and the limited knowledge of quantal energies in the case of N(l). Based on the periodic-orbit formula for N(E), we propose a new rule for quantizing chaos, which simply states that the quantal energies are determined by the zeros of the function ξ1(E) = cos (πN(E)). The formulas for N(l) and N(E) as well as the new quantization condition are tested numerically. Furthermore, it is shown that the staircase N(E) computed from the length spectrum yields (up to a constant) a good description of the spectral rigidity Δ3(L), being the first numerical attempt to compute a statistical property of the quantal energy spectrum of a chaotic system from classical periodic orbits. (orig.)
Forgotten and neglected theories of Poincare
International Nuclear Information System (INIS)
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)
'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.
Advanced prerequisite for E-infinity theory
Energy Technology Data Exchange (ETDEWEB)
El Naschie, M. Saladin [Department of Physics, University of Alexandria, Alexandria (Egypt); Department of Astrophysics, Cairo University (Egypt); Department of Physics, Mansura University (Egypt)
2006-11-15
This is the third of a series of papers written with the primary aim of communicating necessary theoretical background knowledge required for an in-depth study of E-infinity theory. Compared to the previous two papers [El Naschie MS. Elementary prerequisites for E-infinity (Recommended background readings in nonlinear dynamics, geometry and topology). Chaos, Solitons and Fractals 2006;30(3):579-605; El Naschie MS. Intermediate prerequisites for E-infinity theory. Chaos, Solitons and Fractals 2006;30(3):622-8], the present one may be described as advanced.
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The analytic criteria for the local activity theory in one-port cellular neural network (CNN) with five local state variables are presented. The application to a Hyper-chaos synchronization Chua's circuit (HCSCC) CNN with 1125 variables is studied. The bifurcation diagrams of the HCSCC CNN show that they are slightly different from the smoothed CNN with one or two ports and four state variables calculated earlier. The evolution of the patterns of the state variables of the HCSCC CNN is stimulated. Oscillatory patterns, chaotic patterns, convergent or divergent patterns may emerge if the selected cell parameters are located in the locally active domains but nearby or in the edge of chaos domain.
Chaos in the Showalter-Noyes-Bar-Eli model of the Belousov-Zhabotinskii reaction
Lindberg, David; Turner, Jack S.; Barkley, Dwight
1990-03-01
The observation of robust, large-scale chaos in the Showalter-Noyes-Bar-Eli model of the Belousov-Zhabotinskii reaction is reported. The chaos observed is comparable to that found in CSTR experiments at low flow rates.
Attractors, bifurcations, & chaos nonlinear phenomena in economics
Puu, Tönu
2003-01-01
The present book relies on various editions of my earlier book "Nonlinear Economic Dynamics", first published in 1989 in the Springer series "Lecture Notes in Economics and Mathematical Systems", and republished in three more, successively revised and expanded editions, as a Springer monograph, in 1991, 1993, and 1997, and in a Russian translation as "Nelineynaia Economicheskaia Dinamica". The first three editions were focused on applications. The last was differ ent, as it also included some chapters with mathematical background mate rial -ordinary differential equations and iterated maps -so as to make the book self-contained and suitable as a textbook for economics students of dynamical systems. To the same pedagogical purpose, the number of illus trations were expanded. The book published in 2000, with the title "A ttractors, Bifurcations, and Chaos -Nonlinear Phenomena in Economics", was so much changed, that the author felt it reasonable to give it a new title. There were two new math ematics ch...
Chaos Synchronization in Navier-Stokes Turbulence
Lalescu, Cristian; Meneveau, Charles; Eyink, Gregory
2013-03-01
Chaos synchronization (CS) has been studied for some time now (Pecora & Carroll 1990), for systems with only a few degrees of freedom as well as for systems described by partial differential equations (Boccaletti et al 2002). CS in general is said to be present in coupled dynamical systems when a specific property of each system has the same time evolution for all, even though the evolution itself is chaotic. The Navier-Stokes (NS) equations describe the velocity for a wide range of fluids, and their solutions are usually called turbulent if fluctuation amplitudes decrease as a power of their wavenumber. There have been some studies of CS for continuous systems (Kocarev et al 1997), but CS for NS turbulence seems not to have been investigated so far. We focus on the synchronization of the small scales of a turbulent flow for which the time history of large scales is prescribed. Our DNS results show that high-wavenumbers in turbulence are fully slaved to modes with wavenumbers up to a critical fraction of the Kolmogorov dissipation wavenumber. The motivation for our work is to study deeply sub-Kolmogorov scales in fully developed turbulence (Schumacher 2007), which we found to be recoverable even at very high Reynolds number from simulations with moderate resolutions. This work is supported by the National Science Foundation's CDI-II program, project CMMI-0941530
Disentangling Complexity from Randomness and Chaos
Directory of Open Access Journals (Sweden)
Lena C. Zuchowski
2012-02-01
Full Text Available This study aims to disentangle complexity from randomness and chaos, and to present a definition of complexity that emphasizes its epistemically distinct qualities. I will review existing attempts at defining complexity and argue that these suffer from two major faults: a tendency to neglect the underlying dynamics and to focus exclusively on the phenomenology of complex systems; and linguistic imprecisions in describing these phenomenologies. I will argue that the tendency to discuss phenomenology removed from the underlying dynamics is the main root of the difficulties in distinguishing complex from chaotic or random systems. In my own definition, I will explicitly try to avoid these pitfalls. The theoretical contemplations in this paper will be tested on a sample of five models: the random Kac ring, the chaotic CA30, the regular CA90, the complex CA110 and the complex Bak-Sneppen model. Although these modelling studies are restricted in scope and can only be seen as preliminary, they still constitute on of the first attempts to investigate complex systems comparatively.
Genotoxicity of drinking water from Chao Lake
Energy Technology Data Exchange (ETDEWEB)
Liu, Q.; Jiao, Q.C. [Nanjing Univ. (China). Dept. of Biological Science and Technology; Huang, X.M.; Jiang, J.P.; Cui, S.Q.; Yao, G.H.; Jiang, Z.R.; Zhao, H.K.; Wang, N.Y. [Anhui Antiepidemic Station, Hefei (China)
1999-02-01
Genotoxic activity appears to originate primarily from reactions of chlorine with humic substances in the source waters. Comparisons of extracts of settled versus chlorinated water have confirmed that chlorinating during water treatment produces mutagenic activity in the mutagenicity tests. Present work on XAD-2 extracts of raw, chlorinated (treated), and settled water from the Chao Lake region of China has involved a battery of mutagenicity assays for various genetic endpoints: the Salmonella test, the sister-chromatid exchange (SCE) induction in Chinese hamster lung (CHL) cells, and the micronucleus (MN) induction in the peripheral blood erythrocytes of silver carp. Extracts of raw and treated water but not the settled water are mutagenic in the Salmonella assay. On the other hand, extracts of three water samples show activity in the SCE and MN assays, especially the raw and treated water. These data show that contamination and chlorinating contribute mutagens to drinking water and suggest that the mammalian assays may be more sensitive for detecting mutagenicity in aquatic environment than the Salmonella test.
Stability Analysis of Nonlinear Feedback Control Methods for Beam Halo-chaos
Institute of Scientific and Technical Information of China (English)
WANGZhong-sheng; FANGJin-qing; CHENGuan-rong
2003-01-01
Control of beam halo-chaos has been a more challenge subject in recent years, in which nonlinear feedback method for beam halo-chaos has been developed for control of beam halo-chaos in high-current proton linear accelerators. However, stability analysis of nonlinear feedback control methods for beam halo-chaos has still been an open and important topic in this field. In this letter.
Controlling Chaos Probability of a Bose-Einstein Condensate in a Weak Optical Superlattice
Institute of Scientific and Technical Information of China (English)
XU Jun; LUO Xiao-Bing
2009-01-01
@@ The spatial chaos probability of a Bose-Einstein condensate perturbed by a weak optical superlattice is studied. It is demonstrated that the spatial chaotic solution appears with a certain probability in a given parameter region under a random boundary condition. The effects of the lattice depths and wave vectors on the chaos probability are illustrated, and different regions associated with different chaos probabilities are found. This suggests a feasible scheme for suppressing and strengthening chaos by adjusting the optical superlattice experimentally.
Experimental study of chaos synchronization in the Belousov-Zhabotinsky chemical system
International Nuclear Information System (INIS)
Employing self-adaptive parameter regulation scheme, chaos synchronization in the Belousov-Zhabotinsky-CSTR chemical system has been studied experimentally. By optimizing the combination of regulation parameters, the trend of chaos synchronization is observed and the prediction of chaos synchronization from numerical simulation is thus verified by the experiment. In addition, the difference of sensitivity to noise with the mass coupling scheme and the self-adaptive parameter regulation scheme in chaos synchronization has also been discussed
Uncovering Oscillations, Complexity, and Chaos in Chemical Kinetics Using Mathematica
Ferreira, M. M. C.; Ferreira, W. C., Jr.; Lino, A. C. S.; Porto, M. E. G.
1999-06-01
Unlike reactions with no peculiar temporal behavior, in oscillatory reactions concentrations can rise and fall spontaneously in a cyclic or disorganized fashion. In this article, the software Mathematica is used for a theoretical study of kinetic mechanisms of oscillating and chaotic reactions. A first simple example is introduced through a three-step reaction, called the Lotka model, which exhibits a temporal behavior characterized by damped oscillations. The phase plane method of dynamic systems theory is introduced for a geometric interpretation of the reaction kinetics without solving the differential rate equations. The equations are later numerically solved using the built-in routine NDSolve and the results are plotted. The next example, still with a very simple mechanism, is the Lotka-Volterra model reaction, which oscillates indefinitely. The kinetic process and rate equations are also represented by a three-step reaction mechanism. The most important difference between this and the former reaction is that the undamped oscillation has two autocatalytic steps instead of one. The periods of oscillations are obtained by using the discrete Fourier transform (DFT)-a well-known tool in spectroscopy, although not so common in this context. In the last section, it is shown how a simple model of biochemical interactions can be useful to understand the complex behavior of important biological systems. The model consists of two allosteric enzymes coupled in series and activated by its own products. This reaction scheme is important for explaining many metabolic mechanisms, such as the glycolytic oscillations in muscles, yeast glycolysis, and the periodic synthesis of cyclic AMP. A few of many possible dynamic behaviors are exemplified through a prototype glycolytic enzymatic reaction proposed by Decroly and Goldbeter. By simply modifying the initial concentrations, limit cycles, chaos, and birhythmicity are computationally obtained and visualized.
Quantum signatures of chaos in a kicked top.
Chaudhury, S; Smith, A; Anderson, B E; Ghose, S; Jessen, P S
2009-10-01
Chaotic behaviour is ubiquitous and plays an important part in most fields of science. In classical physics, chaos is characterized by hypersensitivity of the time evolution of a system to initial conditions. Quantum mechanics does not permit a similar definition owing in part to the uncertainty principle, and in part to the Schrödinger equation, which preserves the overlap between quantum states. This fundamental disconnect poses a challenge to quantum-classical correspondence, and has motivated a long-standing search for quantum signatures of classical chaos. Here we present the experimental realization of a common paradigm for quantum chaos-the quantum kicked top- and the observation directly in quantum phase space of dynamics that have a chaotic classical counterpart. Our system is based on the combined electronic and nuclear spin of a single atom and is therefore deep in the quantum regime; nevertheless, we find good correspondence between the quantum dynamics and classical phase space structures. Because chaos is inherently a dynamical phenomenon, special significance attaches to dynamical signatures such as sensitivity to perturbation or the generation of entropy and entanglement, for which only indirect evidence has been available. We observe clear differences in the sensitivity to perturbation in chaotic versus regular, non-chaotic regimes, and present experimental evidence for dynamical entanglement as a signature of chaos. PMID:19812668
Fuzzy controller based on chaos optimal design and its application
Institute of Scientific and Technical Information of China (English)
邹恩; 李祥飞; 张泰山
2004-01-01
In order to overcome difficulty of tuning parameters of fuzzy controller, a chaos optimal design method based on annealing strategy is proposed. First, apply the chaotic variables to search for parameters of fuzzy controller, and transform the optimal variables into chaotic variables by carrier-wave method. Making use of the intrinsic stochastic property and ergodicity of chaos movement to escape from the local minimum and direct optimization searching within global range, an approximate global optimal solution is obtained. Then, the chaos local searching and optimization based on annealing strategy are cited, the parameters are optimized again within the limits of the approximate global optimal solution, the optimization is realized by means of combination of global and partial chaos searching, which can converge quickly to global optimal value. Finally, the third order system and discrete nonlinear system are simulated and compared with traditional method of fuzzy control. The results show that the new chaos optimal design method is superior to fuzzy control method, and that the control results are of high precision, with no overshoot and fast response.
When chaos meets hyperchaos: 4D Rössler model
Energy Technology Data Exchange (ETDEWEB)
Barrio, Roberto, E-mail: rbarrio@unizar.es [Departamento de Matemática Aplicada and IUMA, University of Zaragoza, E-50009 Zaragoza (Spain); Computational Dynamics group, University of Zaragoza, E-50009 Zaragoza (Spain); Angeles Martínez, M., E-mail: gelimc@unizar.es [Computational Dynamics group, University of Zaragoza, E-50009 Zaragoza (Spain); Serrano, Sergio, E-mail: sserrano@unizar.es [Departamento de Matemática Aplicada and IUMA, University of Zaragoza, E-50009 Zaragoza (Spain); Computational Dynamics group, University of Zaragoza, E-50009 Zaragoza (Spain); Wilczak, Daniel, E-mail: wilczak@ii.uj.edu.pl [Faculty of Mathematics and Computer Science, Jagiellonian University, Łojasiewicza 6, 30-348 Kraków (Poland)
2015-10-09
Chaotic behavior is a common feature of nonlinear dynamics, as well as hyperchaos in high-dimensional systems. In numerical simulations of these systems it is quite difficult to distinguish one from another behavior in some situations, as the results are frequently quite “noisy”. We show that in such systems a global hyperchaotic invariant set is present giving rise to long hyperchaotic transient behaviors. This fact provides a mechanism for these noisy results. The coexistence of chaos and hyperchaos is proved via Computer-Assisted Proofs techniques. - Highlights: • The coexistence of chaos and hyperchaos in the 4D Rössler system is proved via Computer-Assisted Proofs techniques. • A global hyperchaotic invariant set is present giving rise to long hyperchaotic transient behaviors. • The long transient behaviors make difficult in numerical simulations to distinguish chaos from hyperchaos in some situations.
A novel image encryption scheme based on spatial chaos map
Energy Technology Data Exchange (ETDEWEB)
Sun Fuyan [College of Control Science and Engineering, Shandong University, Jinan 250061 (China)], E-mail: fuyan.sun@gmail.com; Liu Shutang [College of Control Science and Engineering, Shandong University, Jinan 250061 (China); Li Zhongqin [HeiLongJiang Institute of Science and Technology, Harbin 150027 (China); Lue Zongwang [Information and Communication College, Guilin University of Electronic and Technology, Guilin 541004 (China); Corporate Engineering Department, Johnson Electric Co. Ltd., Shenzhen 518125 (China)
2008-11-15
In recent years, the chaos-based cryptographic algorithms have suggested some new and efficient ways to develop secure image encryption techniques, but the drawbacks of small key space and weak security in one-dimensional chaotic cryptosystems are obvious. In this paper, spatial chaos system are used for high degree security image encryption while its speed is acceptable. The proposed algorithm is described in detail. The basic idea is to encrypt the image in space with spatial chaos map pixel by pixel, and then the pixels are confused in multiple directions of space. Using this method one cycle, the image becomes indistinguishable in space due to inherent properties of spatial chaotic systems. Several experimental results, key sensitivity tests, key space analysis, and statistical analysis show that the approach for image cryptosystems provides an efficient and secure way for real time image encryption and transmission from the cryptographic viewpoint.
Polymer additives in fluid turbulence and distributed chaos
Bershadskii, A
2016-01-01
The fluids and polymers have different fundamental symmetries. Namely, the Lagrangian relabeling symmetry of fluids is absent for polymers (while the translational and rotational symmetries are still present). This fact results in spontaneous breaking of the relabeling symmetry in fluid turbulence even at a tiny polymer addition. Since helicity conservation in inviscid fluid motions is a consequence of the relabeling symmetry (due to the Noether's theorem) violation of this conservation by the polymer additives results in the strong effects in the distributed chaos. The distributed chaos in turbulence with the spontaneously broken relabeling symmetry is characterized by stretched exponential spectra $\\propto \\exp(-k/k_{\\beta})^{\\beta}$ with $\\beta =2/5$. The spectral range of this distributed chaos is extended in direction of the small wavenumbers and $k_{\\beta}$ becomes much larger in comparison with the pure fluid (Newtonian) case. This results in substantial suppression of small-scale turbulence and large-...
When chaos meets hyperchaos: 4D Rössler model
International Nuclear Information System (INIS)
Chaotic behavior is a common feature of nonlinear dynamics, as well as hyperchaos in high-dimensional systems. In numerical simulations of these systems it is quite difficult to distinguish one from another behavior in some situations, as the results are frequently quite “noisy”. We show that in such systems a global hyperchaotic invariant set is present giving rise to long hyperchaotic transient behaviors. This fact provides a mechanism for these noisy results. The coexistence of chaos and hyperchaos is proved via Computer-Assisted Proofs techniques. - Highlights: • The coexistence of chaos and hyperchaos in the 4D Rössler system is proved via Computer-Assisted Proofs techniques. • A global hyperchaotic invariant set is present giving rise to long hyperchaotic transient behaviors. • The long transient behaviors make difficult in numerical simulations to distinguish chaos from hyperchaos in some situations
Color image authentication based on spatiotemporal chaos and SVD
Energy Technology Data Exchange (ETDEWEB)
Peng Zhenni [College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016 (China)], E-mail: jennyp8201@yahoo.com.cn; Liu Wenbo [College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016 (China)], E-mail: wenboliu@nuaa.edu.cn
2008-05-15
In this paper, a new semi-fragile watermarking scheme for color image authentication is proposed based on spatiotemporal chaos and SVD (singular value decomposition). Wavelet transform is applied to watermarking. In contrast to conventional approaches where the watermark is embedded directly on the wavelet coefficients, we embed the watermark onto the SVs (singular values) of the blocks within wavelet subband. In order to enhance the security, spatiotemporal chaos is employed to select the embedding positions for each watermark bit as well as for watermark encryption. The experiment results show that the proposed scheme is able to identify malicious attacks to the image, while is robust to JPEG compression. And due to the sensitivity to the initial conditions of the spatiotemporal chaos, the security of the scheme is greatly improved.
A novel image encryption scheme based on spatial chaos map
International Nuclear Information System (INIS)
In recent years, the chaos-based cryptographic algorithms have suggested some new and efficient ways to develop secure image encryption techniques, but the drawbacks of small key space and weak security in one-dimensional chaotic cryptosystems are obvious. In this paper, spatial chaos system are used for high degree security image encryption while its speed is acceptable. The proposed algorithm is described in detail. The basic idea is to encrypt the image in space with spatial chaos map pixel by pixel, and then the pixels are confused in multiple directions of space. Using this method one cycle, the image becomes indistinguishable in space due to inherent properties of spatial chaotic systems. Several experimental results, key sensitivity tests, key space analysis, and statistical analysis show that the approach for image cryptosystems provides an efficient and secure way for real time image encryption and transmission from the cryptographic viewpoint
Dynamical topology and statistical properties of spatiotemporal chaos.
Zhuang, Quntao; Gao, Xun; Ouyang, Qi; Wang, Hongli
2012-12-01
For spatiotemporal chaos described by partial differential equations, there are generally locations where the dynamical variable achieves its local extremum or where the time partial derivative of the variable vanishes instantaneously. To a large extent, the location and movement of these topologically special points determine the qualitative structure of the disordered states. We analyze numerically statistical properties of the topologically special points in one-dimensional spatiotemporal chaos. The probability distribution functions for the number of point, the lifespan, and the distance covered during their lifetime are obtained from numerical simulations. Mathematically, we establish a probabilistic model to describe the dynamics of these topologically special points. In spite of the different definitions in different spatiotemporal chaos, the dynamics of these special points can be described in a uniform approach.
Color image authentication based on spatiotemporal chaos and SVD
International Nuclear Information System (INIS)
In this paper, a new semi-fragile watermarking scheme for color image authentication is proposed based on spatiotemporal chaos and SVD (singular value decomposition). Wavelet transform is applied to watermarking. In contrast to conventional approaches where the watermark is embedded directly on the wavelet coefficients, we embed the watermark onto the SVs (singular values) of the blocks within wavelet subband. In order to enhance the security, spatiotemporal chaos is employed to select the embedding positions for each watermark bit as well as for watermark encryption. The experiment results show that the proposed scheme is able to identify malicious attacks to the image, while is robust to JPEG compression. And due to the sensitivity to the initial conditions of the spatiotemporal chaos, the security of the scheme is greatly improved
Energy Technology Data Exchange (ETDEWEB)
Serletis, Apostolos [Department of Economics, University of Calgary, Calgary, Alta., T2N 1N4 (Canada)]. E-mail: Serletis@ucalgary.ca; Shahmoradi, Asghar [Faculty of Economics, University of Tehran, Tehran (Iran, Islamic Republic of)
2007-08-15
This paper uses monthly observations for the real exchange rate between Canada and the United States over the recent flexible exchange rate period (from January 1, 1973 to August 1, 2004) to test purchasing power parity between Canada and the United States using unit root and stationarity tests. Moreover, given the apparent random walk behavior in the real exchange rate, various tests from dynamical systems theory, such as for example, the Nychka et al. [Nychka DW, Ellner S, Ronald GA, McCaffrey D. Finding chaos in noisy systems. J Roy Stat Soc B 1992;54:399-426] chaos test, the Li [Li W. Absence of 1/f spectra in Dow Jones average. Int J Bifurcat Chaos 1991;1:583-97] self-organized criticality test, and the Hansen [Hansen, B.E. Inference when a nuisance parameter is not identified under the null hypothesis. Econometrica 1996;64:413-30] threshold effects test are used to distinguish between stochastic and deterministic origin for the real exchange rate.
Multistability, chaos, and random signal generation in semiconductor superlattices
Ying, Lei; Huang, Danhong; Lai, Ying-Cheng
2016-06-01
Historically, semiconductor superlattices, artificial periodic structures of different semiconductor materials, were invented with the purpose of engineering or manipulating the electronic properties of semiconductor devices. A key application lies in generating radiation sources, amplifiers, and detectors in the "unusual" spectral range of subterahertz and terahertz (0.1-10 THz), which cannot be readily realized using conventional radiation sources, the so-called THz gap. Efforts in the past three decades have demonstrated various nonlinear dynamical behaviors including chaos, suggesting the potential to exploit chaos in semiconductor superlattices as random signal sources (e.g., random number generators) in the THz frequency range. We consider a realistic model of hot electrons in semiconductor superlattice, taking into account the induced space charge field. Through a systematic exploration of the phase space we find that, when the system is subject to an external electrical driving of a single frequency, chaos is typically associated with the occurrence of multistability. That is, for a given parameter setting, while there are initial conditions that lead to chaotic trajectories, simultaneously there are other initial conditions that lead to regular motions. Transition to multistability, i.e., the emergence of multistability with chaos as a system parameter passes through a critical point, is found and argued to be abrupt. Multistability thus presents an obstacle to utilizing the superlattice system as a reliable and robust random signal source. However, we demonstrate that, when an additional driving field of incommensurate frequency is applied, multistability can be eliminated, with chaos representing the only possible asymptotic behavior of the system. In such a case, a random initial condition will lead to a trajectory landing in a chaotic attractor with probability 1, making quasiperiodically driven semiconductor superlattices potentially as a reliable
Multistability, chaos, and random signal generation in semiconductor superlattices.
Ying, Lei; Huang, Danhong; Lai, Ying-Cheng
2016-06-01
Historically, semiconductor superlattices, artificial periodic structures of different semiconductor materials, were invented with the purpose of engineering or manipulating the electronic properties of semiconductor devices. A key application lies in generating radiation sources, amplifiers, and detectors in the "unusual" spectral range of subterahertz and terahertz (0.1-10 THz), which cannot be readily realized using conventional radiation sources, the so-called THz gap. Efforts in the past three decades have demonstrated various nonlinear dynamical behaviors including chaos, suggesting the potential to exploit chaos in semiconductor superlattices as random signal sources (e.g., random number generators) in the THz frequency range. We consider a realistic model of hot electrons in semiconductor superlattice, taking into account the induced space charge field. Through a systematic exploration of the phase space we find that, when the system is subject to an external electrical driving of a single frequency, chaos is typically associated with the occurrence of multistability. That is, for a given parameter setting, while there are initial conditions that lead to chaotic trajectories, simultaneously there are other initial conditions that lead to regular motions. Transition to multistability, i.e., the emergence of multistability with chaos as a system parameter passes through a critical point, is found and argued to be abrupt. Multistability thus presents an obstacle to utilizing the superlattice system as a reliable and robust random signal source. However, we demonstrate that, when an additional driving field of incommensurate frequency is applied, multistability can be eliminated, with chaos representing the only possible asymptotic behavior of the system. In such a case, a random initial condition will lead to a trajectory landing in a chaotic attractor with probability 1, making quasiperiodically driven semiconductor superlattices potentially as a reliable
Structured chaos shapes spike-response noise entropy in balanced neural networks
Directory of Open Access Journals (Sweden)
Guillaume eLajoie
2014-10-01
Full Text Available Large networks of sparsely coupled, excitatory and inhibitory cells occur throughout the brain. For many models of these networks, a striking feature is that their dynamics are chaotic and thus, are sensitive to small perturbations. How does this chaos manifest in the neural code? Specifically, how variable are the spike patterns that such a network produces in response to an input signal? To answer this, we derive a bound for a general measure of variability -- spike-train entropy. This leads to important insights on the variability of multi-cell spike pattern distributions in large recurrent networks of spiking neurons responding to fluctuating inputs. The analysis is based on results from random dynamical systems theory and is complemented by detailed numerical simulations. We find that the spike pattern entropy is an order of magnitude lower than what would be extrapolated from single cells. This holds despite the fact that network coupling becomes vanishingly sparse as network size grows -- a phenomenon that depends on ``extensive chaos, as previously discovered for balanced networks without stimulus drive. Moreover, we show how spike pattern entropy is controlled by temporal features of the inputs. Our findings provide insight into how neural networks may encode stimuli in the presence of inherently chaotic dynamics.
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.
Chaos tool implementation for non-singer and singer voice comparison (preliminary study)
Energy Technology Data Exchange (ETDEWEB)
Dajer, Me; Pereira, Jc; Maciel, Cd [Department of Electric Engineering, School of Engineering of Sao Carlos, University of Sao Paulo, Sao Carlos (Brazil); Av. Trabalhador Sao-Carlesnse, 400. CEP 13566-590. Sao Carlos. SP (Brazil)
2007-11-15
Voice waveform is linked to the stretch, shorten, widen or constrict vocal tract. The articulation effects of the singer's vocal tract modify the voice acoustical characteristics and differ from the non-singer voices. In the last decades, Chaos Theory has shown the possibility to explore the dynamic nature of voice signals from a different point of view. The purpose of this paper is to apply the chaos technique of phase space reconstruction to analyze non- singers and singer voices in order to explore the signal nonlinear dynamic, and correlate them with traditional acoustic parameters. Eight voice samples of sustained vowel /i/ from non-singers and eight from singers were analyzed with 'ANL' software. The samples were also acoustically analyzed with 'Analise de Voz 5.0' in order to extract acoustic perturbation measures jitter and shimmer, and the coefficient of excess - (EX). The results showed different visual patterns for the two groups correlated with different jitter, shimmer, and coefficient of excess values. We conclude that these results clearly indicate the potential of phase space reconstruction technique for analysis and comparison of non-singers and singer voices. They also show a promising tool for training voices application.
Messaoudi, Imen; Elloumi-Oueslati, Afef; Lachiri, Zied
2014-01-01
Investigating the roles and functions of DNA within genomes is becoming a primary focus of genomic research. Thus, the research works are moving towards cooperation between different scientific disciplines which aims at facilitating the interpretation of genetic information. In order to characterize the DNA of living organisms, signal processing tools appear to be very suitable for such study. However, a DNA sequence must be converted into a numerical sequence before processing; which defines the concept of DNA coding. In line with this, we propose a new one dimensional model based on the chaos game representation theory called Frequency Chaos Game Signal: FCGS. Then, we perform a Smoothed Fourier Transform to enhance hidden periodicities in the C.elegans DNA sequences. Through this study, we demonstrate the performance of our coding approach in highlighting characteristic periodicities. Indeed, several periodicities are shown to be involved in the 1D spectra and the 2D spectrograms of FCGSs. To investigate further about the contribution of our method in the enhancement of characteristic spectral attributes, a comparison with a range of binary indicators is established.
Quantum dissipative chaos in the statistics of excitation numbers
Kryuchkyan, G Y; Kryuchkyan, Gagik Yu.; Manvelyan, Suren B.
2002-01-01
A quantum manifestation of chaotic classical dynamics is found in the framework of oscillatory numbers statistics for the model of nonlinear dissipative oscillator. It is shown by numerical simulation of an ensemble of quantum trajectories that the probability distributions and variances of oscillatory number states are strongly transformed in the order-to-chaos transition. The nonclassical, sub-Poissonian statistics of oscillatory excitation numbers is established for chaotic dissipative dynamics in the framework of Fano factor and Wigner functions. These results are proposed for testing and experimental studing of quantum dissipative chaos.
Dynamic Ice-Water Interactions Form Europa's Chaos Terrains
Blankenship, D. D.; Schmidt, B. E.; Patterson, G. W.; Schenk, P.
2011-12-01
Unique to the surface of Europa, chaos terrain is diagnostic of the properties and dynamics of its icy shell. We present a new model that suggests large melt lenses form within the shell and that water-ice interactions above and within these lenses drive the production of chaos. This model is consistent with key observations of chaos, predicts observables for future missions, and indicates that the surface is likely still active today[1]. We apply lessons from ice-water interaction in the terrestrial cryosphere to hypothesize a dynamic lense-collapse model to for Europa's chaos terrain. Chaos terrain morphology, like that of Conamara chaos and Thera Macula, suggests a four-phase formation [1]: 1) Surface deflection occurs as ice melts over ascending thermal plumes, as regularly occurs on Earth as subglacial volcanoes activate. The same process can occur at Europa if thermal plumes cause pressure melt as they cross ice-impurity eutectics. 2) Resulting hydraulic gradients and driving forces produce a sealed, pressurized melt lense, akin to the hydraulic sealing of subglacial caldera lakes. On Europa, the water cannot escape the lense due to the horizontally continuous ice shell. 3) Extension of the brittle ice lid above the lense opens cracks, allowing for the ice to be hydrofractured by pressurized water. Fracture, brine injection and percolation within the ice and possible iceberg toppling produces ice-melange-like granular matrix material. 4) Refreezing of the melt lense and brine-filled pores and cracks within the matrix results in raised chaos. Brine soaking and injection concentrates the ice in brines and adds water volume to the shell. As this englacial water freezes, the now water-filled ice will expand, not unlike the process of forming pingos and other "expansion ice" phenomena on Earth. The refreezing can raise the surface and create the oft-observed matrix "domes" In this presentation, we describe how catastrophic ice-water interactions on Earth have
Research progress of chaos-based watermarking%混沌数字水印技术研究进展
Institute of Scientific and Technical Information of China (English)
刘竹松; 陈平华; 刘怡俊
2011-01-01
结合近几年混沌数字水印的研究成果,系统地从混沌数字水印研究分类和研究领域两个方面,综述了混沌数字水印的最新研究成果.介绍了混沌数字水印的定义及常见分类,从混沌序列数字水印、混沌映射数字水印和混沌系统数字水印三个方面介绍了国内外研究情况,从文本水印、图形水印、音频水印、视频水印等领域详细综述了混沌数字水印研究理论和算法,就混沌数字水印研究中存在的问题和未来的发展趋势进行了总结和展望.%This paper summarized the latest research results in both classification and research field.First of all, it introduced the definition of chaotic digital watermarking and its common classification.Discussed the research status of chaos sequence watermarking, chaos mapping watermarking and chaos system watermarking at home and abroad in the next.Then reviewed the research theories and algorithms in the field of text watermarking, graphics watermarking, audio watermarking and video watermarking in detail.Finally, pointed out some challenges and problems of chaos-based watermarking.
MPPT of PV array using stepped-up chaos optimization algorithm
Wang, Lihua; WEI, XUEYE; SHAO, YUQIN; ZHU, TIANLONG; ZHANG, JUNHONG
2015-01-01
In order to achieve maximum efficiency, a maximum power point tracking (MPPT) scheme should be applied in photovoltaic systems. Among all the MPPT schemes, the chaos optimization scheme is one of the hot topics in recent years. In this study, a novel stepped-up chaos optimization algorithm is presented. A chaos mapping $x_{n+1} =\\mu \\sin (\\pi x_{n} )$ is used as a chaos generator to produce a chaos variable. In the process of MPPT, a coarse search is done to find the current optimal solution ...
Experimental observation of a chaos-to-chaos transition in laser droplet generation
Krese, Blaz; Govekar, Edvard
2010-01-01
We examine the dynamics of laser droplet generation in dependence on the detachment pulse power. In the absence of the detachment pulse, undulating pendant droplets are formed at the end of a properly fed metal wire due to the impact of the primary laser pulse that induces melting. Eventually, these droplets detach, i.e. overcome the surface tension, because of their increasing mass. We show that this spontaneous dripping is deterministically chaotic by means of a positive largest Lyapunov exponent and a negative divergence. In the presence of the detachment pulse, however, the generation of droplets is fastened depending on the pulse power. At high powers, the spontaneity of dripping is completely overshadowed by the impact of the detachment pulse. Still, amplitude chaos can be detected, which similarly as the spontaneous dripping, is characterized by a positive largest Lyapunov exponent and a negative divergence, thus indicating that the observed dynamics is deterministically chaotic with an attractor as so...
Institute of Scientific and Technical Information of China (English)
FANG Jin-Qing; YU Xing-Huo
2004-01-01
@@ Study of beam halo-chaos has become a key issue of concern for many future important applications. Control of halo-chaos has been researched intensively. This is the first time that the synchronization of beam halo-chaos has been realized in this field so far. Two nonlinear feedback control methods are proposed for the cascading synchronizing halo-chaos in coupled lattices of a periodic focusing channel. The simulation results show that the methods are effective. The realization of the synchronization of beam halo-chaos is significant not only for halo-chaos control itself but also for halo-chaos-based secure communication which may become an innovative technique.
Chaos, Dissipation and Quantal Brownian Motion
Cohen, Doron
1999-01-01
Energy absorption by driven chaotic systems, the theory of energy spreading and quantal Brownian motion are considered. In particular we discuss the theory of a classical particle that interacts with quantal chaotic degrees of freedom, and try to relate it to the problem of quantal particle that interacts with an effective harmonic bath.
vs. a polynomial chaos-based MCMC
Siripatana, Adil
2014-08-01
Bayesian Inference of Manning\\'s n coefficient in a Storm Surge Model Framework: comparison between Kalman lter and polynomial based method Adil Siripatana Conventional coastal ocean models solve the shallow water equations, which describe the conservation of mass and momentum when the horizontal length scale is much greater than the vertical length scale. In this case vertical pressure gradients in the momentum equations are nearly hydrostatic. The outputs of coastal ocean models are thus sensitive to the bottom stress terms de ned through the formulation of Manning\\'s n coefficients. This thesis considers the Bayesian inference problem of the Manning\\'s n coefficient in the context of storm surge based on the coastal ocean ADCIRC model. In the first part of the thesis, we apply an ensemble-based Kalman filter, the singular evolutive interpolated Kalman (SEIK) filter to estimate both a constant Manning\\'s n coefficient and a 2-D parameterized Manning\\'s coefficient on one ideal and one of more realistic domain using observation system simulation experiments (OSSEs). We study the sensitivity of the system to the ensemble size. we also access the benefits from using an in ation factor on the filter performance. To study the limitation of the Guassian restricted assumption on the SEIK lter, 5 we also implemented in the second part of this thesis a Markov Chain Monte Carlo (MCMC) method based on a Generalized Polynomial chaos (gPc) approach for the estimation of the 1-D and 2-D Mannning\\'s n coe cient. The gPc is used to build a surrogate model that imitate the ADCIRC model in order to make the computational cost of implementing the MCMC with the ADCIRC model reasonable. We evaluate the performance of the MCMC-gPc approach and study its robustness to di erent OSSEs scenario. we also compare its estimates with those resulting from SEIK in term of parameter estimates and full distributions. we present a full analysis of the solution of these two methods, of the
2006-01-01
NASA's Spitzer and Hubble Space Telescopes have teamed up to expose the chaos that baby stars are creating 1,500 light-years away in a cosmic cloud called the Orion nebula. This striking infrared and visible-light composite indicates that four monstrously massive stars at the center of the cloud may be the main culprits in the familiar Orion constellation. The stars are collectively called the 'Trapezium.' Their community can be identified as the yellow smudge near the center of the image. Swirls of green in Hubble's ultraviolet and visible-light view reveal hydrogen and sulfur gas that have been heated and ionized by intense ultraviolet radiation from the Trapezium's stars. Meanwhile, Spitzer's infrared view exposes carbon-rich molecules called polycyclic aromatic hydrocarbons in the cloud. These organic molecules have been illuminated by the Trapezium's stars, and are shown in the composite as wisps of red and orange. On Earth, polycyclic aromatic hydrocarbons are found on burnt toast and in automobile exhaust. Together, the telescopes expose the stars in Orion as a rainbow of dots sprinkled throughout the image. Orange-yellow dots revealed by Spitzer are actually infant stars deeply embedded in a cocoon of dust and gas. Hubble showed less embedded stars as specks of green, and foreground stars as blue spots. Stellar winds from clusters of newborn stars scattered throughout the cloud etched all of the well-defined ridges and cavities in Orion. The large cavity near the right of the image was most likely carved by winds from the Trapezium's stars. Located 1,500 light-years away from Earth, the Orion nebula is the brightest spot in the sword of the Orion, or the 'Hunter' constellation. The cosmic cloud is also our closest massive star-formation factory, and astronomers believe it contains more than 1,000 young stars. The Orion constellation is a familiar sight in the fall and winter night sky in the northern hemisphere. The nebula is invisible to the unaided eye
Security problems with a chaos-based deniable authentication scheme
International Nuclear Information System (INIS)
Recently, a new scheme was proposed for deniable authentication. Its main originality lied on applying a chaos-based encryption-hash parallel algorithm and the semi-group property of the Chebyshev chaotic map. Although original and practicable, its insecurity and inefficiency are shown in this paper, thus rendering it inadequate for adoption in e-commerce
Review of Stephen Arons's "Short Route to Chaos."
Glenn, Charles L.
1998-01-01
"Short Route to Chaos" criticizes the Goals 2000 program, related educational reforms, and the agenda of the Religious Right from the viewpoint of the secular Left. Arons supports school choice, school and teacher independence from government regulation of instructional content, publicly funded schools, and equity in funding. (SLD)
Toward Therapeutic Autopoiesis: Chaos, Complexity, and Narrative Therapy.
Chen, Mei-whei
The paradigm of modern psychology has been the determinism of Newtonian physics. That model earns psychology status as a science yet tunnels it to a linear way of unraveling human functioning. Responding to demands for a more holistic approach to psychological practice, it is necessary to redefine the "self" and other terms. Chaos, complexity, and…
Confidential Communication Through Chaos Encryption in Wireless Sensor Network
Institute of Scientific and Technical Information of China (English)
CHEN Shuai; ZHONG Xian-xin
2007-01-01
A new byte block cipher algorithm with discrete chaos and Feistel structure has been studied for confidential communication in wireless sensor network to improve security. After permutation, the byte block was encrypted through a Feistel structure in multiple turns and afterwards replaced again. The child keys are the composite sequence of discrete chaos and linear congruence sequences. Both the plain text and cipher text are of 8 bits. The number of keys is alterable. A nonlinear encryption function in the Feistel structure with chaos was constructed. The cipher algorithm was realized in the Micaz node,and the confidential communication experiment in wireless sensor network was completed successfully. Additional ROM memory required for the cipher algorithm is 4144 bytes and an additional RAM memory 61 bytes. The cipher algorithm is nonlinear chaos and the Feistel structure holds the best of the RC6, DES and SKIPJACK cipher algorithms.The result shows that the algorithm needs a little memory and is safe at a high level.
Bifurcations, Period doubling and chaos in clarinet-like systems
Maganza, Christian; Caussé, René; Laloë, Franck
1986-01-01
Wind instruments provide interesting hydrodynamical systems where non-linearities are important but well localized. A simple analysis shows that these systems should undergo Feignebaum-type route to chaos, with a cascade of period doublings. Experiments have been performed fo confirm these predictions
Between order and chaos: The quest for meaningful information
P. Adriaans
2009-01-01
The notion of meaningful information seems to be associated with the sweet spot between order and chaos. This form of meaningfulness of information, which is primarily what science is interested in, is not captured by both Shannon information and Kolmogorov complexity. In this paper I develop a theo
Two-mode chaos and its synchronization properties
DEFF Research Database (Denmark)
Postnov, D E; Shishkin, A V; Sosnovtseva, Olga;
2005-01-01
Using a simple model with bimodal dynamics, we investigate the intra- and inter-system entrainment of the two different time scales involved in the chaotic oscillations. The transition between mode-locked and mode-unlocked chaos is analyzed for a single system. For coupled oscillators, we...
Chaos Synchronization on Parameters Adaptive Control for Chen Chaotic System
Institute of Scientific and Technical Information of China (English)
ZHOU Ping
2003-01-01
Chaos synchronization of Chen chaotic system for parameters unknown is discussed in this paper using a scalar output. Using the concept of conditional Lyapunov exponents, the negativity of all Lyapunov exponents shows the synchronization of transmitter systems with receiver systems even though system parametes are not known to receiver systems.
Suppressing Spatiotemporal Chaos via Non-feedback Pinning Method
Institute of Scientific and Technical Information of China (English)
WU Shun-Guang; SANG Hai-Bo; HE Kai-Fen
2001-01-01
The spatiotemporal chaos in the system described by a one-dimensional nonlinear drift-wave equation is suppressed by the non-feedback pinning method. By adding additive external noise to the controlled state, we find that the deviation from the target spacetime pattern increases in a power law with noise intensity. The possible controlling mechanism is discussed.
Optimal control for stochastic systems with polynomial chaos
Gallagher, David James
Assuring robustness of control system performance against model uncertainty is a significant component of control design. Current methods for developing a robust controller, however, are typically either too conservative or too computationally expensive. This thesis uses generalized polynomial chaos alongside finite-horizon optimal control as a new method of robust control design for a stochastic system. Since the equations for the mean and variance of the response can be expressed in terms of coefficients from a polynomial chaos expansion, optimizing a polynomial chaos expansion can be used to optimize the mean and variance, thus providing robust responses in a stochastic system. This thesis first provides a review of the concepts and literature then the rationale as well as the derivation of the proposed robust control method. Three examples are given to show the effectiveness of the new control method and are discussed. In particular, the final example demonstrates the applicability of using polynomial chaos to provide robust control for a stochastic soft landing problem.
Parametric resonance induced chaos in magnetic damped driven pendulum
Khomeriki, Giorgi
2016-07-01
A damped driven pendulum with a magnetic driving force, appearing from a solenoid, where ac current flows is considered. The solenoid acts on the magnet, which is located at a free end of the pendulum. In this system the existence and interrelation of chaos and parametric resonance is theoretically examined. Derived analytical results are supported by numerical simulations and conducted experiments.
Integrability and Quantum Chaos in Spin Glass Shards
Georgeot, B.; Shepelyansky, D. L.
1998-01-01
We study spin glass clusters ("shards") in a random transverse magnetic field, and determine the regime where quantum chaos and random matrix level statistics emerge from the integrable limits of weak and strong field. Relations with quantum phase transition are also discussed.
Bifurcation and chaos in multi-parallel-connected current-mode controlled boost DC-DC converters
Institute of Scientific and Technical Information of China (English)
CHEN Ming-liang; MA Wei-ming
2006-01-01
This paper studied the bifurcation and chaos phenomenon in a multi-parallel-connected current-mode controlled boost DC-DC converter system with the use of nonlinear mapping bifurcation theory of two dimensions,and the changing rules of the bifurcation charts with the increase of the control parallels and control parameters were concluded.The method of discrete mapping modeling was utilized to construct the difference equations of the system operating in continuous conduction mode (CCM).Analyses and computer emulations were made.
Study on Chaos Created by Hopf Bifurcation of One Kind of Financial System and Its Application
Institute of Scientific and Technical Information of China (English)
JunhaiMa; BiaoRen; YanGao
2004-01-01
From a mathematical model of one kind complicated financial system, corresponding local topological structures of such kind system on condition of certain parametercombination, unstable equilibrium point of the system, conditions on which Hopf bifurcation is created and stability of the limit circle corresponding to the Hopf bifurcation as well as condition on which the limit circle is stable have been studied. From relationship between each parameter and the Hopf bifurcation all the way to route which leads to chaos etc have been studied. Following the above, conditions on which complicated behaviors created locally in such kind system has been analyzed. By applying fractal dimension, Lyapunov index, the intrinsic complexity of the system on such condition has been studied, and result of the numerical simulation proves the theory of this paper correct.
Reithmeier, Eduard
1991-01-01
Limit cycles or, more general, periodic solutions of nonlinear dynamical systems occur in many different fields of application. Although, there is extensive literature on periodic solutions, in particular on existence theorems, the connection to physical and technical applications needs to be improved. The bifurcation behavior of periodic solutions by means of parameter variations plays an important role in transition to chaos, so numerical algorithms are necessary to compute periodic solutions and investigate their stability on a numerical basis. From the technical point of view, dynamical systems with discontinuities are of special interest. The discontinuities may occur with respect to the variables describing the configuration space manifold or/and with respect to the variables of the vector-field of the dynamical system. The multiple shooting method is employed in computing limit cycles numerically, and is modified for systems with discontinuities. The theory is supported by numerous examples, mainly fro...
Fractal space-time fluctuations: A signature of quantumlike chaos in dynamical systems
Selvam, A M
2004-01-01
Dynamical systems in nature such as fluid flows, heart beat patterns, rainfall variability, stock market price fluctuations, etc. exhibit selfsimilar fractal fluctuations on all scales in space and time. Power spectral analyses of fractal fluctuations exhibit inverse power law form indicating long-range space-time correlations, identified as self-organized criticality. The author has proposed a general systems theory, which predicts the observed self-organized criticality as signatures of quantumlike chaos. The model shows that (1) the fractal fluctuations result from an overall logarithmic spiral trajectory with the quasiperiodic Penrose tiling pattern for the internal structure. Conventional power spectral analysis of such a logarithmic spiral trajectory will show a continuum of eddies with progressive increase in phase. (2) Power spectral analyses of fractal fluctuations of dynamical systems exhibit the universal inverse power law form of the statistical normal distribution. Such a result indicates that th...
Directory of Open Access Journals (Sweden)
Dr. V. Sundarapandian
2011-06-01
Full Text Available In this paper, we apply adaptive control method to derive new results for the global chaos synchronization of identical hyperchaotic Lorenz systems (2007, identical hyperchaotic Chen systems (2010 and non-identical hyperchaotic Lorenz and hyperchaotic Chen systems. In this paper, we shall assume that the parameters of both master and slave systems are unknown and we devise adaptive synchronizing schemes using the estimates of parameters for both master and slave systems. Our adaptive synchronization results derived in this paper are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the adaptive control method is very effective and convenient to synchronize identical and non-identical hyperchaotic Lorenz and hyperchaotic Chensystems. Numerical simulations are shown to demonstrate the effectiveness of the proposed adaptive synchronization schemes for the hyperchaotic systems addressed in this paper.
Quantum chaos? Genericity and nongenericity in the MHD spectrum of nonaxisymmetric toroidal plasmas
Dewar, R L; Nührenberg, C; Tatsuno, T; McMillan, B F
2006-01-01
The eigenmode spectrum is a fundamental starting point for the analysis of plasma stability and the onset of turbulence, but the characterization of the spectrum even for the simplest plasma model, ideal magnetohydrodynamics (MHD), is not fully understood. This is especially true in configurations with no continuous geometric symmetry, such as a real tokamak when the discrete nature of the external magnetic field coils is taken into account, or the alternative fusion concept, the stellarator, where axisymmetry is deliberately broken to provide a nonzero winding number (rotational transform) on each invariant torus of the magnetic field line dynamics (assumed for present purposes to be an integrable Hamiltonian system). Quantum (wave) chaos theory provides tools for characterizing the spectrum statistically, from the regular spectrum of the separable case (integrable semiclassical dynamics) to that where the semiclassical ray dynamics is so chaotic that no simple classification of the individual eigenvalues is...
Rydberg atoms in external fields as an example of open quantum systems with classical chaos
International Nuclear Information System (INIS)
We examine the quantum spectra of hydrogen atoms in external magnetic and electric fields above the ionization threshold with respect to signatures of classical chaos characteristics of open systems. The spectra are obtained by calculating wavefunctions and photionization cross sections in the continuum region with the aid of the complex-coordinate-rotation method. We find that the photoionization cross sections exhibit strong Ericson fluctuations, a quantum feature characteristic of classically chaotic scattering, in energy-field regions where classical trajectory calculations reveal a fractal dependence of the classical ionization time on the initial conditions. We also compare the nearest-neighbour-spacing distributions of complex resonance energies with predictions of random-matrix theories and find that our results are well reproduced by a Ginibre distribution. (author)
Relation of chaos activity characteristics of the cardiac system with the evolution of species
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
According to the nonlinear theory, the experiments have been conducted on sample ECG (electrocardiogram) signals of healthy human beings, coronary heart disease patients and adult canines. On the basis of the analyses of the power spectra, the computation of the correlation dimension and the Lyapunov exponent to a large number of ECG signals, the following conclusions are shown: through the comparative research, (1( the analyses of the power spectra, the computation of the correlation dimension and the Lyapunov exponent to the ECG signals reflect the whole dynamic characteristics of the hearts, and they may become a new method of researching ECG quantitatively to an early diagnose of heart disease. (2( Under normal physiological conditions the cardiac activities are chaotic, while under pathologic conditions the cardiac activities approach regularity. (3( On the basis of the comparative research of human beings and canines, it is revealed that chaos may be a quantitative index to measure the evolution of species. This conclusion would supply a new cut-in point to elaborate the Darwin theory, and it would enable us to explain the life theory renewably using the basic principle of nonlinear theory.
Difference equations from rabbits to chaos
Cull, Paul; Robson, Robby
2005-01-01
In this new text, designed for sophomores studying mathematics and computer science, the authors cover the basics of difference equations and some of their applications in computing and in population biology. Each chapter leads to techniques that can be applied by hand to small examples or programmed for larger problems. Along the way, the reader will use linear algebra and graph theory, develop formal power series, solve combinatorial problems, visit Perron-Frobenius theory, discuss pseudorandom number generation and integer factorization, and apply the Fast Fourier Transform to multiply poly
Outflow channel sources, reactivation, and chaos formation, Xanthe Terra, Mars
Rodriguez, J.A.P.; Sasaki, S.; Kuzmin, R.O.; Dohm, J.M.; Tanaka, K.L.; Miyamoto, H.; Kurita, K.; Komatsu, G.; Fairen, A.G.; Ferris, J.C.
2005-01-01
The undulating, warped, and densely fractured surfaces of highland regions east of Valles Marineris (located north of the eastern Aureum Chaos, east of the Hydraotes Chaos, and south of the Hydaspis Chaos) resulted from extensional surface warping related to ground subsidence, caused when pressurized water confined in subterranean caverns was released to the surface. Water emanations formed crater lakes and resulted in channeling episodes involved in the excavation of Ares, Tiu, and Simud Valles of the eastern part of the circum-Chryse outflow channel system. Progressive surface subsidence and associated reduction of the subsurface cavernous volume, and/or episodes of magmatic-driven activity, led to increases of the hydrostatic pressure, resulting in reactivation of both catastrophic and non-catastrophic outflow activity. Ancient cratered highland and basin materials that underwent large-scale subsidence grade into densely fractured terrains. Collapse of rock materials in these regions resulted in the formation of chaotic terrains, which occur in and near the headwaters of the eastern circum-Chryse outflow channels. The deepest chaotic terrain in the Hydaspis Chaos region resulted from the collapse of pre-existing outflow channel floors. The release of volatiles and related collapse may have included water emanations not necessarily linked to catastrophic outflow. Basal warming related to dike intrusions, thermokarst activity involving wet sediments and/or dissected ice-enriched country rock, permafrost exposed to the atmosphere by extensional tectonism and channel incision, and/or the injection of water into porous floor material, may have enhanced outflow channel floor instability and subsequent collapse. In addition to the possible genetic linkage to outflow channel development dating back to at least the Late Noachian, clear disruption of impact craters with pristine ejecta blankets and rims, as well as preservation of fine tectonic fabrics, suggest that
DEFF Research Database (Denmark)
Rennison, Betina Wolfgang
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...
Laser dynamical reservoir computing with consistency: an approach of a chaos mask signal.
Nakayama, Joma; Kanno, Kazutaka; Uchida, Atsushi
2016-04-18
We numerically investigate reservoir computing based on the consistency of a semiconductor laser subjected to optical feedback and injection. We introduce a chaos mask signal as an input temporal mask for reservoir computing and perform a time-series prediction task. We compare the errors of the task obtained from the chaos mask signal with those obtained from other digital and analog masks. The performance of the prediction task can be improved by using the chaos mask signal due to complex dynamical response.
The design and research of anti-color-noise chaos M-ary communication system
Yongqing Fu; Xingyuan Li; Yanan Li; Lin Zhang
2016-01-01
Previously a novel chaos M-ary digital communication method based on spatiotemporal chaos Hamilton oscillator has been proposed. Without chaos synchronization circumstance, it has performance improvement in bandwidth efficiency, transmission efficiency and anti-white-noise performance compared with traditional communication method. In this paper, the channel noise influence on chaotic modulation signals and the construction problem of anti-color-noise chaotic M-ary communication system are st...
Recursive proportional feedback and its use to control chaos in an electrochemical system
Rollins, R W; Sherard, P; Dewald, H D
1995-01-01
The recursive proportional feedback (RPF) algorithm for controlling chaos is described and applied to control chemical chaos observed during the electrodissolution of a rotating copper disk in a sodium acetate/acetic acid buffer. Experimental evidence is presented to indicate why the RPF method was used and the theoretical robustness of the algorithm is discussed. (This paper appears in the "Proceedings of the 2nd Conference on EXPERIMENTAL CHAOS," World Scientific Press, River Ridge, NJ, 1995)
Institute of Scientific and Technical Information of China (English)
吴敏; 赵文礼; 周芳
2013-01-01
为解决工程实际中因待测信号常常被淹没在噪声背景中而传统信号检测方法难以检测等问题,将基于混沌理论的非线性信号检测技术应用到实际工程故障诊断中,开展了基于Duffing振子的微弱信号检测原理的分析,建立了混沌振子与微弱信号检测之间的关系,提出了基于Duffing振子的微弱信号检测方法,利用混沌系统相变对周期小信号的敏感性和对噪声具有免疫力的特点,设计制作了基于Duffing振子的微弱信号检测电路；对微弱信号检测的自适应进行了研究,利用AVR单片机及AD9850等芯片实现了信号检测电路的自动跟踪扫频功能,最后开展了该信号检测电路对不同频率微弱信号的检测试验.研究结果表明,用该电路可以实现在工程中常见的噪声背景下的中、低频率微弱周期信号的检测.%Aiming at the problems of weak signal generally hidden in the background of strong noise and it is difficult to be detected by the traditional signal detection methods,chaos detection technology in the fault diagnosis of nonlinear to practical engineering was used,the principle of weak signal detection of Duffing oscillator was investigated.After the analysis of principle of chaos detection,the system state equation which was used to design the electronic circuit was established.The method of auto-tracking and sweep-frequency to detect arbitrarily weak signal under strong noise background was studied and the electronic circuit was designed.The self-adaption of weak signal detection was investigated,the automatic tracking frequency sweep function of the signal detection circuit was realized using by AVR MCU and AD9850 chip.The different frequency of weak signal detection was tested.The results indicate that the weak medium-low frequency signals can be detected from the background of noise by using the circuit.
Catastrophic ice lake collapse in Aram Chaos, Mars
Roda, Manuel; Zegers, Tanja E; Oosthoek, Jelmer H P
2014-01-01
Hesperian chaotic terrains have been recognized as the source of outflow channels formed by catastrophic outflows. Four main scenarios have been proposed for the formation of chaotic terrains that involve different amounts of water and single or multiple outflow events. Here, we test these scenarios with morphological and structural analyses of imagery and elevation data for Aram Chaos in conjunction with numerical modeling of the morphological evolution of the catastrophic carving of the outflow valley. The morphological and geological analyses of Aram Chaos suggest large-scale collapse and subsidence (1500 m) of the entire area, which is consistent with a massive expulsion of liquid water from the subsurface in one single event. The combined observations suggest a complex process starting with the outflow of water from two small channels, followed by continuous groundwater sapping and headward erosion and ending with a catastrophic lake rim collapse and carving of the Aram Valley, which is synchronous with ...
Intermittency and chaos in intracavity doubled lasers. II
Energy Technology Data Exchange (ETDEWEB)
James, G.E.; Harrell, E.M. II (School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332 (USA)); Roy, R. (School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332 (USA))
1990-03-01
We describe the nonlinear dynamics of intracavity doubled multimode lasers. Baer (J. Opt. Soc. Am. B 3, 1175 (1986)) observed irregular amplitude fluctuations in a multimode yttrium aluminum garnet laser with an intracavity potassium titanyl phosphate frequency-doubling crystal; we identify type-III intermittency as the route to chaos. Subsequently, Oka and Kubota (Opt. Lett. 13, 805 (1988)) demonstrated the stabilization of such a laser by the introduction of a quarter wave plate into the cavity. A generalized model of rate equations for this case is introduced. It is shown that a second route to chaos through a Hopf bifurcation, synchronization, and period-doubling sequence occurs on rotation of the quarter wave plate within the cavity. In addition, we predict that the laser output may be stable for particular lengths of the doubling crystal.
Randomness versus deterministic chaos: Effect on invasion percolation clusters
Peng, Chung-Kang; Prakash, Sona; Herrmann, Hans J.; Stanley, H. Eugene
1990-10-01
What is the difference between randomness and chaos \\? Although one can define randomness and one can define chaos, one cannot easily assess the difference in a practical situation. Here we compare the results of these two antipodal approaches on a specific example. Specifically, we study how well the logistic map in its chaotic regime can be used as quasirandom number generator by calculating pertinent properties of a well-known random process: invasion percolation. Only if λ>λ*1 (the first reverse bifurcation point) is a smooth extrapolation in system size possible, and percolation exponents are retrieved. If λ≠1, a sequential filling of the lattice with the random numbers generates a measurable anisotropy in the growth sequence of the clusters, due to short-range correlations.
Granular chaos and mixing: Whirled in a grain of sand
Energy Technology Data Exchange (ETDEWEB)
Shinbrot, Troy, E-mail: shinbrot@rutgers.edu [Department of Biomedical Engineering, Rutgers University, Piscataway, New Jersey 08854 (United States)
2015-09-15
In this paper, we overview examples of chaos in granular flows. We begin by reviewing several remarkable behaviors that have intrigued researchers over the past few decades, and we then focus on three areas in which chaos plays an intrinsic role in granular behavior. First, we discuss pattern formation in vibrated beds, which we show is a direct result of chaotic scattering combined with dynamical dissipation. Next, we consider stick-slip motion, which involves chaotic scattering on the micro-scale, and which results in complex and as yet unexplained peculiarities on the macro-scale. Finally, we examine granular mixing, which we show combines micro-scale chaotic scattering and macro-scale stick-slip motion into behaviors that are well described by dynamical systems tools, such as iterative mappings.
Climate predictions: the chaos and complexity in climate models
Mihailović, Dragutin T; Arsenić, Ilija
2013-01-01
Some issues which are relevant for the recent state in climate modeling have been considered. A detailed overview of literature related to this subject is given. The concept in modeling of climate, as a complex system, seen through Godel's Theorem and Rosen's definition of complexity and predictability is discussed. It is pointed out to occurrence of chaos in computing the environmental interface temperature from the energy balance equation given in a difference form. A coupled system of equations, often used in climate models is analyzed. It is shown that the Lyapunov exponent mostly has positive values allowing presence of chaos in this systems. The horizontal energy exchange between environmental interfaces, which is described by the dynamics of driven coupled oscillators, is analyzed. Their behavior and synchronization, when a perturbation is introduced in the system, as a function of the coupling parameters, the logistic parameter and the parameter of exchange, was studied calculating the Lyapunov expone...
Polynomial chaos expansion with random and fuzzy variables
Jacquelin, E.; Friswell, M. I.; Adhikari, S.; Dessombz, O.; Sinou, J.-J.
2016-06-01
A dynamical uncertain system is studied in this paper. Two kinds of uncertainties are addressed, where the uncertain parameters are described through random variables and/or fuzzy variables. A general framework is proposed to deal with both kinds of uncertainty using a polynomial chaos expansion (PCE). It is shown that fuzzy variables may be expanded in terms of polynomial chaos when Legendre polynomials are used. The components of the PCE are a solution of an equation that does not depend on the nature of uncertainty. Once this equation is solved, the post-processing of the data gives the moments of the random response when the uncertainties are random or gives the response interval when the variables are fuzzy. With the PCE approach, it is also possible to deal with mixed uncertainty, when some parameters are random and others are fuzzy. The results provide a fuzzy description of the response statistical moments.
Comparative study of variational chaos indicators and ODEs' numerical integrators
Darriba, Luciano A; Cincotta, Pablo M; Giordano, Claudia M
2012-01-01
The reader can find in the literature a lot of different techniques to study the dynamics of a given system and also, many suitable numerical integrators to compute them. Notwithstanding the recent work of Maffione et al. (2011a) for mappings, a detailed comparison among the widespread indicators of chaos in a general system is still lacking. Such a comparison could lead to select the most efficient algorithms given a certain dynamical problem. Furthermore, in order to choose the appropriate numerical integrators to compute them, more comparative studies among numerical integrators are also needed. This work deals with both problems. We first extend the work of Maffione et al. (2011) for mappings to the 2D H\\'enon & Heiles (1964) potential, and compare several variational indicators of chaos: the Lyapunov Indicator (LI); the Mean Exponential Growth Factor of Nearby Orbits (MEGNO); the Smaller Alignment Index (SALI) and its generalized version, the Generalized Alignment Index (GALI); the Fast Lyapunov Indi...
Chaos control and taming of turbulence in plasma devices
DEFF Research Database (Denmark)
Klinger, T.; Schröder, C.; Block, D.;
2001-01-01
Chaos and turbulence are often considered as troublesome features of plasma devices. In the general framework of nonlinear dynamical systems, a number of strategies have been developed to achieve active control over complex temporal or spatio-temporal behavior. Many of these techniques apply to...... plasma instabilities. In the present paper we discuss recent progress in chaos control and taming of turbulence in three different plasma "model" experiments: (1) Chaotic oscillations in simple plasma diodes, (2) ionization wave turbulence in the positive column of glow discharges, and (3) drift wave...... turbulence in a magnetized plasma column. Depending on the physical mechanism of the specific instability in each case, an appropriate control strategy is chosen out of a variety of different approaches; in particular discrete feedback, continuous feedback, or spatio-temporal open-loop synchronization...
Quantum mechanics with chaos correspondence principle, measurement and complexity
Kirilyuk, A P
1995-01-01
The true dynamical randomness is obtained as a natural fundamental property of deterministic quantum systems. It provides quantum chaos passing to the classical dynamical chaos under the ordinary semiclassical transition, which extends the correspondence principle to chaotic systems. In return one should accept the modified form of quantum formalism (exemplified by the Schrodinger equation) which, however, does not contradict the ordinary form, and the main postulates, of quantum mechanics. It introduces the principle of the fundamental dynamic multivaluedness extending the quantum paradigm to complex dynamical behaviour. Moreover, a causal solution to the well-known problems of the foundations of quantum mechanics, those of quantum indeterminacy and wave reduction, is also found using the same method. The concept of the fundamental dynamic uncertainty thus established is universal in character and provides a unified scheme of the complete description of arbitrary complex system of any origin. This scheme inc...
Intermittency and transient chaos from simple frequency-dependent selection.
Gavrilets, S; Hastings, A
1995-08-22
Frequency-dependent selection is an important determinant of the evolution of gametophytic self-incompatibility systems in plants, aposematic (warning) and cryptic coloration, systems of mimicry, competitive interactions among members of a population, mating preferences, predator-prey and host-parasite interactions, aggression and other behavioural traits. Past theoretical studies of frequency-dependent selection have shown it to be a plausible mechanism for the maintenance of genetic variability in natural populations. Here, through an analysis of a simple deterministic model for frequency-dependent selection, we demonstrate that complex dynamic behaviour is possible under a broad range of parameter values. In particular we show that the model exhibits not only cycles and chaos but also, for a more restricted set of parameters, transient chaos and intermittency: alterations between an apparently deterministic behaviour and apparently chaotic fluctuations. This behaviour, which has not been stressed within the population genetics literature, provides an explanation for erratic dynamics of gene frequencies.
Control of complex dynamics and chaos in distributed parameter systems
Energy Technology Data Exchange (ETDEWEB)
Chakravarti, S.; Marek, M.; Ray, W.H. [Univ. of Wisconsin, Madison, WI (United States)
1995-12-31
This paper discusses a methodology for controlling complex dynamics and chaos in distributed parameter systems. The reaction-diffusion system with Brusselator kinetics, where the torus-doubling or quasi-periodic (two characteristic incommensurate frequencies) route to chaos exists in a defined range of parameter values, is used as an example. Poincare maps are used for characterization of quasi-periodic and chaotic attractors. The dominant modes or topos, which are inherent properties of the system, are identified by means of the Singular Value Decomposition. Tested modal feedback control schemas based on identified dominant spatial modes confirm the possibility of stabilization of simple quasi-periodic trajectories in the complex quasi-periodic or chaotic spatiotemporal patterns.
Universality in Chaos of Particle Motion near Black Hole Horizon
Hashimoto, Koji
2016-01-01
Motion of a particle near a horizon of a spherically symmetric black hole is shown to possess a universal Lyapunov exponent of a chaos provided by its surface gravity. To probe the horizon, we introduce electromagnetic or scalar force to the particle so that it does not fall into the horizon. There appears an unstable maximum of the total potential where the evaluated maximal Lyapunov exponent is found to be independent of the external forces and the particle mass. The Lyapunov exponent is universally given by the surface gravity of the black hole. Unless there are other sources of a chaos, the Lyapunov exponent is subject to an inequality $\\lambda \\leq 2\\pi T_{\\rm BH}/\\hbar$, which is identical to the bound recently discovered by Maldacena, Shenker and Stanford.
From Hamiltonian chaos to complex systems a nonlinear physics approach
Leonetti, Marc
2013-01-01
From Hamiltonian Chaos to Complex Systems: A Nonlinear Physics Approach collects contributions on recent developments in non-linear dynamics and statistical physics with an emphasis on complex systems. This book provides a wide range of state-of-the-art research in these fields. The unifying aspect of this book is a demonstration of how similar tools coming from dynamical systems, nonlinear physics, and statistical dynamics can lead to a large panorama of research in various fields of physics and beyond, most notably with the perspective of application in complex systems. This book also: Illustrates the broad research influence of tools coming from dynamical systems, nonlinear physics, and statistical dynamics Adopts a pedagogic approach to facilitate understanding by non-specialists and students Presents applications in complex systems Includes 150 illustrations From Hamiltonian Chaos to Complex Systems: A Nonlinear Physics Approach is an ideal book for graduate students and researchers working in applied...
Impulse-induced localized control of chaos in starlike networks
Chacón, Ricardo; Palmero, Faustino; Cuevas-Maraver, Jesús
2016-06-01
Locally decreasing the impulse transmitted by periodic pulses is shown to be a reliable method of taming chaos in starlike networks of dissipative nonlinear oscillators, leading to both synchronous periodic states and equilibria (oscillation death). Specifically, the paradigmatic model of damped kicked rotators is studied in which it is assumed that when the rotators are driven synchronously, i.e., all driving pulses transmit the same impulse, the networks display chaotic dynamics. It is found that the taming effect of decreasing the impulse transmitted by the pulses acting on particular nodes strongly depends on their number and degree of connectivity. A theoretical analysis is given explaining the basic physical mechanism as well as the main features of the chaos-control scenario.
Texture features from Chaos Game Representation Images of Genomes
Directory of Open Access Journals (Sweden)
Vrinda V. Nair
2013-04-01
Full Text Available The proposed work investigates the effectiveness of coarse measures of the Chaos Game Representation (CGR images in differentiating genomes of various organisms. Major work in this area is seen to focus on feature extraction using Frequency Chaos Game Representation (FCGR matrices. Although it is biologically significant, FCGR matrix has an inherent error which is associated with the insufficient computing as well as the screen resolutions. Hence the CGR image is converted to a texture image and corresponding feature vectors extracted. Features such as the texture properties and the subsequent wavelet coefficients of the texture image are used. Our work suggests that texture features characterize genomes well further; their wavelet coefficients yield better distinguishing capabilities.
Is there chaos in the Spanish labour market?
International Nuclear Information System (INIS)
Highlights: We consider Spanish unemployment time series. We apply a number of nonlinearity tests and chaoticity measures. We establish the presence of nonlinearity and chaos, which disappears when the data are shuffled. Abstract: One could argue that there is a resurgence of the non-linear modelling in economics. Some instruments have been developed to measure the complexity or instability of the analysed systems. At the present work some of these developed techniques are applied to verify the non-linearity present in the time series of Spanish unemployment, as well as to quantify the degree of complexity of the system that has generated the series. Using these techniques we find evidence of chaos in Spanish unemployment time series.
Hypersensitivity and chaos signatures in the quantum baker's maps
Scott, A J; Caves, C M; Schack, R; Brun, Todd A.; Caves, Carlton M.; Schack, Ruediger
2006-01-01
Classical chaotic systems are distinguished by their sensitive dependence on initial conditions. The absence of this property in quantum systems has lead to a number of different criteria being proposed for quantum chaos, including linear growth of entropy, exponential decay of fidelity, and hypersensitivity to perturbation. All of these accurately predict chaos in the classical limit, but it is not clear that they behave the same far from the classical realm. We investigate the dynamics of a family of quantizations of the baker's map, which range from a highly entangling unitary transformation to an essentially trivial shift map. Linear entropy growth and fidelity decay are exhibited by this entire family of maps, but hypersensitivity distinguishes between the simple dynamics of the trivial shift map and the more complicated dynamics of the other quantizations. This is supported by an analytical argument for short times and numerical evidence at later times.
INTRODUCTION: The Physics of Chaos and Related Problems: Proceedings of the 59th Nobel Symposium
Lundqvist, Stig
1985-01-01
The physics of non-linear phenomena has developed in a remarkable way over the last couple of decades and has accelerated over the last few years, in particular because of the recent progress in the study of chaotic behaviour. In particular the discovery of the universal properties of the transition into chaos for certain classes of systems has stimulated much recent work in different directions both theoretically and experimentally. Chaos theory has become a real challenge to physicists in many different fields and also in many other disciplines such as astronomy, chemistry, medicine, meteorology and economics and social theory. The study of chaos-related phenomena has a truly interdisciplinary character and makes use of important concepts and methods from other disciplines. For the description of chaotic structures one needs a new, recently developed geometry called fractal geometry. For the discussion of the enormous richness of ordered structures which appear, one uses the theory of pattern recognition. In order to study even the simplest theoretical models describing chaos, a computer is essential. It should finally be mentioned that important aspects of computer science are related to the theory of order and chaos. A Nobel Symposium provides an excellent opportunity to bring together a group of prominent scientists for a stimulating exchange of new ideas and results. The Nobel Symposia are very small meetings by invitation only and the number of key participants is typically in the range 20-40. These symposia are organized through a special Nobel Symposium Committee after proposals from individuals. This symposium was sponsored by the Nobel Foundation through its Nobel Symposium Fund with grants from The Tercentenary Fund of the Bank of Sweden and The Knut Alice Wallenberg Foundation. Additional support was obtained from the Royal Academy of Sciences, The Nordic Institute for Theoretical Atomic Physics (NORDITA), Chalmers University of Technology and
INTRODUCTION: The Physics of Chaos and Related Problems: Proceedings of the 59th Nobel Symposium
Lundqvist, Stig
1985-01-01
The physics of non-linear phenomena has developed in a remarkable way over the last couple of decades and has accelerated over the last few years, in particular because of the recent progress in the study of chaotic behaviour. In particular the discovery of the universal properties of the transition into chaos for certain classes of systems has stimulated much recent work in different directions both theoretically and experimentally. Chaos theory has become a real challenge to physicists in many different fields and also in many other disciplines such as astronomy, chemistry, medicine, meteorology and economics and social theory. The study of chaos-related phenomena has a truly interdisciplinary character and makes use of important concepts and methods from other disciplines. For the description of chaotic structures one needs a new, recently developed geometry called fractal geometry. For the discussion of the enormous richness of ordered structures which appear, one uses the theory of pattern recognition. In order to study even the simplest theoretical models describing chaos, a computer is essential. It should finally be mentioned that important aspects of computer science are related to the theory of order and chaos. A Nobel Symposium provides an excellent opportunity to bring together a group of prominent scientists for a stimulating exchange of new ideas and results. The Nobel Symposia are very small meetings by invitation only and the number of key participants is typically in the range 20-40. These symposia are organized through a special Nobel Symposium Committee after proposals from individuals. This symposium was sponsored by the Nobel Foundation through its Nobel Symposium Fund with grants from The Tercentenary Fund of the Bank of Sweden and The Knut Alice Wallenberg Foundation. Additional support was obtained from the Royal Academy of Sciences, The Nordic Institute for Theoretical Atomic Physics (NORDITA), Chalmers University of Technology and