Sample records for chaos theory

  1. Chaos theory in politics

    Erçetin, Şefika; Tekin, Ali


    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.

  2. Chaos Theory and Post Modernism

    Snell, Joel


    Chaos theory is often associated with post modernism. However, one may make the point that both terms are misunderstood. The point of this article is to define both terms and indicate their relationship. Description: Chaos theory is associated with a definition of a theory dealing with variables (butterflies) that are not directly related to a…

  3. Ancient and Current Chaos Theories

    Güngör Gündüz


    Full Text Available Chaos theories developed in the last three decades have made very important contributions to our understanding of dynamical systems and natural phenomena. The meaning of chaos in the current theories and in the past is somewhat different from each other. In this work, the properties of dynamical systems and the evolution of chaotic systems were discussed in terms of the views of ancient philosophers. The meaning of chaos in Anaximenes’ philosophy and its role in the Ancient natural philosophy has been discussed in relation to other natural philosophers such as of Anaximander, Parmenides, Heraclitus, Empedocles, Leucippus (i.e. atomists and Aristotle. In addition, the fundamental concepts of statistical mechanics and the current chaos theories were discussed in relation to the views in Ancient natural philosophy. The roots of the scientific concepts such as randomness, autocatalysis, nonlinear growth, information, pattern, etc. in the Ancient natural philosophy were investigated.

  4. "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…

  5. Advances in chaos theory and intelligent control

    Vaidyanathan, Sundarapandian


    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...

  6. Chaos and gauge field theory

    Biro, TS; Mueller, B


    This book introduces a rapidly growing new research area - the study of dynamical properties of elementary fields. The methods used in this field range from algebraic topology to parallel computer programming. The main aim of this research is to understand the behavior of elementary particles and fields under extreme circumstances, first of all at high temperature and energy density generated in the largest accelerators of the world and supposed to be present in the early evolution of our Universe shortly after the Big Bang.In particular, chaos is rediscovered in a new appearance in these stud

  7. Chaos theory: A fascinating concept for oncologists

    The oncologist is confronted daily by questions related to the fact that any patient presents a specific evolution for his cancer: he is challenged by very different, unexpected and often unpredictable outcomes, in some of his patients. The mathematical approach used today to describe this evolution has recourse to statistics and probability laws: such an approach does not ultimately apply to one particular patient, but to a given more or less heterogeneous population. This approach therefore poorly characterizes the dynamics of this disease and does not allow to state whether a patient is cured, to predict if he will relapse and when this could occur, and in what form, nor to predict the response to treatment and, in particular, to radiation therapy. Chaos theory, not well known by oncologists, could allow a better understanding of these issues. Developed to investigate complex systems producing behaviours that cannot be predicted due to a great sensitivity to initial conditions, chaos theory is rich of suitable concepts for a new approach of cancer dynamics. This article is three-fold: to provide a brief introduction to chaos theory, to clarify the main connecting points between chaos and carcinogenesis and to point out few promising research perspectives, especially in radiotherapy. (authors)

  8. Chaos Theory and Literature from an Existentialist Perspective

    Khamees Ragab Aman, Yasser


    Yasser Khamees Ragab Aman proposes in his article "Chaos Theory and Literature from an Existentialist Perspective" that in literature the relation, principles, and processes of chaos and order can be analyzed from an existentialist perspective. Chaos lies at the heart of nothingness and order is the appearance of the achievement it tries to realize, temporary it may seem. Aman argues that with the application of chaos theory to works of literature may yield new insight and applies in his pape...

  9. Chaos theory perspective for industry clusters development

    Yu, Haiying; Jiang, Minghui; Li, Chengzhang


    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.

  10. Chaos Theory for Evolutionary Algorithms Researchers

    Čelikovský, Sergej; Zelinka, I.

    Berlin : Springer-Verlag, 2010 - (Zelinka, I.; Čelikovský, S.; Richter, H.; Chen, G.), s. 89-143 ISBN 978-3-642-10706-1. - (Studies in Computational Intelligence. 267) R&D Projects: GA ČR(CZ) GA102/08/0186 Institutional research plan: CEZ:AV0Z10750506 Keywords : Complex Systems * Computational Intelligence * Deterministic Chaos * Evolutionary Computation Subject RIV: BC - Control Systems Theory

  11. 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

  12. 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.…

  13. Major open problems in chaos theory and nonlinear dynamics

    Li, Y Charles


    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.

  14. Strategic leadership: a view from quantum and chaos theories.

    McDaniel, R R


    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


    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.


    K. Thamizhchelvy


    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.

  17. Predicting vibration signals of automobile engine using chaos theory

    LIU Chun; ZHANG Laibin; WANG Zhaohui


    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.

  18. Theory of Secular Chaos and Mercury's Orbit

    Lithwick, Yoram


    We study the chaotic orbital evolution of planetary systems, focusing on secular (i.e., orbit-averaged) interactions, because these often dominate on long timescales. We first focus on the evolution of a test particle that is forced by multiple massive planets. To linear order in eccentricity and inclination, its orbit precesses with constant frequencies. But nonlinearities can shift the frequencies into and out of secular resonance with the planets' eigenfrequencies, or with linear combinations of those frequencies. The overlap of these nonlinear secular resonances drive secular chaos in planetary systems. We quantify the resulting dynamics for the first time by calculating the locations and widths of nonlinear secular resonances. When results from both analytical calculations and numerical integrations are displayed together in a newly developed "map of the mean momenta" (MMM), the agreement is excellent. This map is particularly revealing for non-coplanar planetary systems and demonstrates graphically that...

  19. The butterfly and the tornado: chaos theory and climate change

    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

  20. Chaos theory and its application in the atmosphere

    Zeng, Xubin


    Chaos theory, including the bifurcation and route to turbulence, and the characterization of chaos, is thoroughly reviewed. A practical method without adjustable free parameters was developed to compute the Lyapunov-exponent spectrum from short time series of low precision. The application of chaos is divided into three categories: observational data analysis, new ideas or insights inspired by chaos, and numerical model output analysis. Corresponding with these categories, three subjects are studied. First, the fractal dimension, Lyapunov-exponent spectrum, Kolmogorov entropy, and predictability are quantitatively evaluated from observed daily data of surface temperature and pressure over regions of different climate signal/noise ratios. No low-dimensional attractors can be obtained from these observational data. The error-doubling time is 2 to 8 days at different locations. Second, chaos in daisyworld, which is an idealized ecosystem/atmosphere interactive model, was studied. Periodic and chaotic states are found when the parameter controlling the feedback between biota and their environment is changed. This raises important questions regarding the validity and interpretation of the Gaia hypothesis. Finally, two-and three-dimensional mesoscale and large-eddy simulations are performed to study in detail the initial adjustment process and error growth dynamics of surface thermally-induced circulations, including the sensitivity to initial and boundary conditions as well as to model parameters. The predictability as a function of the size of surface heat patches under calm synoptic wind is quantitatively evaluated. Two-and three-dimensional simulations yield close or similar results regarding the predictability. The predictability and the coherent circulations modulated by the surface inhomogeneities are also studied by computing the autocorrelations and power spectra. A low (less than 5)-dimensional attractor is obtained from the model output. Possible physical

  1. The chaos avant-garde memories of the early days of chaos theory

    Abraham, Ralph H


    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

  2. Application of Chaos Theory in Trucks' Overloading Enforcement

    Abbas Mahmoudabadi


    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.

  3. Chaos theory: a new paradigm for psychotherapy?

    Lonie, I


    Thomas Kuhn's concept of paradigm as central to the functioning of a mature science is linked with Johnson-Abercrombie's recognition that perception itself is shaped by the schemata available to the subject. The rapidly advancing field of non-linear mathematics, in offering conceptual forms to represent complex events, may provide a useful framework in which to place various psychodynamic formulations about the development of the personality, and suggests the possibility of a new approach to research concerning the efficacy of psychotherapy. Dan Stern's latest concept of "moments" as the basic unit in structuring the personality, leading to the complex representational patterns and feed-back loops he terms "RIGS" may be viewed in this context. The paradigm may be extended to include such concepts as Peterfreund's linkage of psychodynamic theorising with aspects of information theory generated by the study of computers, and with Sullivan's concepts of repetitive patterns of behaviour recognisable, and changing, throughout the course of a therapy. PMID:1793425

  4. Models and applications of chaos theory in modern sciences

    Zeraoulia, Elhadj


    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

  5. What Can We Learn from Chaos Theory? An Alternative Approach to Instructional Systems Design.

    You, Yeongmahn


    Explains chaos theory; compares a conventional instructional systems design (ISD) approach with chaos theory and dynamic nonlinear systems, including deterministic predictability and indeterministic unpredictability and negative and positive feedback; explores theoretical implications for developing an alternative ISD model; and recommends future…

  6. Chaos and order in non-integrable model field theories

    We illustrate the presence of chaos and order in non-integrable, classical field theories, which we view as many-degree-of-freedom Hamiltonian nonlinear dynamical systems. For definiteness, we focus on the χ4 theory and compare and contrast it with the celebrated integrable sine-Gordon equation. We introduce and investigate two specific problems: the interactions of solitary ''kink''-like waves in non-integrable theories; and the existence of stable ''breather'' solutions -- spatially-localized, time-periodic nonlinear waves -- in the χ4 theory. For the former problem we review the rather well developed understanding, based on a combination of computational simulations and heuristic analytic models, of the presence of a sequence of resonances in the kink-antikink interactions as a function of the relative velocity of the interaction. For the latter problem we discuss first the case of the continuum χ4 theory. We discuss the multiple-scale asymptotic perturbation theory arguments which first suggested the existence of χ4 breathers, then the subsequent discovery of terms ''beyond-all-orders'' in the perturbation expansion which destroy the putative breather, and finally, the recent rigorous proofs of the non-existence of breathers in the continuum theory. We then present some very recent numerical results on the existence of breathers in discrete χ4 theories which show an intricate interweaving of stable and unstable breather solutions on finite discrete lattices. We develop a heuristic theoretical explanation of the regions of stability and instability

  7. Viewing Eye Movements During Reading through the Lens of Chaos Theory: How Reading Is Like the Weather

    Paulson, Eric J.


    This theoretical article examines reading processes using chaos theory as an analogy. Three principles of chaos theory are identified and discussed, then related to reading processes as revealed through eye movement research. Used as an analogy, the chaos theory principle of sensitive dependence contributes to understanding the difficulty in…

  8. Complexity and Chaos Theories as Potential Paradigms for Understanding and Treating Dissociative Disorders.

    Drinkard, Lynne Bradford


    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.

  9. Chaotic Feedback Loops within Decision Making Groups: Towards an Integration of Chaos Theory and Cybernetics.

    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…

  10. Radiotherapy and chaos theory: The tit and the butterfly..

    Although the same simple laws govern cancer outcome (cell division repeated again and again), each tumour has a different outcome before as well as after irradiation therapy. The linear-quadratic radiosensitivity model allows an assessment of tumor sensitivity to radiotherapy. This model presents some limitations in clinical practice because it does not take into account the interactions between tumour cells and non-tumoral bystander cells (such as endothelial cells, fibroblasts, immune cells...) that modulate radiosensitivity and tumor growth dynamics. These interactions can lead to non-linear and complex tumor growth which appears to be random but that is not since there is not so many tumors spontaneously regressing. In this paper we propose to develop a deterministic approach for tumour growth dynamics using chaos theory. Various characteristics of cancer dynamics and tumor radiosensitivity can be explained using mathematical models of competing cell species. (authors)

  11. Chaos and order in non-integrable model field theories

    Campbell, D.K.; Peyrard, M.


    We illustrate the presence of chaos and order in non-integrable, classical field theories, which we view as many-degree-of-freedom Hamiltonian nonlinear dynamical systems. For definiteness, we focus on the {chi}{sup 4} theory and compare and contrast it with the celebrated integrable sine-Gordon equation. We introduce and investigate two specific problems: the interactions of solitary kink''-like waves in non-integrable theories; and the existence of stable breather'' solutions -- spatially-localized, time-periodic nonlinear waves -- in the {chi}{sup 4} theory. For the former problem we review the rather well developed understanding, based on a combination of computational simulations and heuristic analytic models, of the presence of a sequence of resonances in the kink-antikink interactions as a function of the relative velocity of the interaction. For the latter problem we discuss first the case of the continuum {chi}{sup 4} theory. We discuss the multiple-scale asymptotic perturbation theory arguments which first suggested the existence of {chi}{sup 4} breathers, then the subsequent discovery of terms beyond-all-orders'' in the perturbation expansion which destroy the putative breather, and finally, the recent rigorous proofs of the non-existence of breathers in the continuum theory. We then present some very recent numerical results on the existence of breathers in discrete {chi}{sup 4} theories which show an intricate interweaving of stable and unstable breather solutions on finite discrete lattices. We develop a heuristic theoretical explanation of the regions of stability and instability.

  12. James Ellroy’s American Tabloid: Conspiracy Theory and Chaos Theory

    Boof-Vermesse, Isabelle


    As Ellroy himself suggests it in his introduction to American Tabloid, small causes can have portentous effects. Applying determinist chaos theory to the conspiracy that led to the JFK assassination as it is revisited by what is, after all, a fictional text, this essay draws some conclusions as to the opposition between “compartmentalisation” and “connectionism”, on the one hand, and as to the turbulent relationship between history and fiction, on the other.

  13. Theory of the nucleus as applied to quantum chaos

    Bunakov, V. E., E-mail: [St. Petersburg State University, Petersburg Nuclear Physics Institute, National Research Center Kurchatov Institute (Russian Federation)


    A critical analysis of the present-day concept of chaos in quantum systems as nothing but a quantum signature of chaos in classical mechanics is given. It is proposed to specify a regular versus a chaotic behavior on the basis of symmetries of the system being considered and global integrals of motion that are associated with these symmetries in accordance with the Liouville-Arnold theorem rather than on the basis of the concept of Lyapunov’s instability of trajectories. Numerical criteria of quantum chaos that follow from the proposed concept are analyzed.

  14. On Philosophical Problems in the Foundations of Chaos Theory

    Belanger, Christopher Armand

    This dissertation examines several philosophical issues in the foundations of chaos theory and fractal geometry. In Chapter 1, I argue that our epistemological and ontological investigations would be better served by looking at the particular successes and failures of individual chaotic models, rather than focussing on broad questions of approximate truth. Thee rest of the dissertation can then be seen as a set of attempts to put this program into practice. In Chapter 2 I consider the prospects for instrumental fractal models of non-fractal physical objects. Although philosophers have contended that such models must always be inferior to non-fractal models, I argue that in some cases fractal models can be vastly epistemologically superior to their non-fractal rivals. In Chapter 3 I take up questions of ontology, and consider the prospects for the existence of fractals in physical space. Although philosophers have argued that physical fractals are an impossibility, I argue that classical mechanics and chaotic models could entail the existence of interesting fractal regions of space. In Chapter 4 I consider two definitions of observational equivalence for chaotic models, and ague that they fail to meet acceptability criteria.

  15. Application of Theories of Complexity and Chaos to Economic Misgovernance

    Partha Gangopadhyay


    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.

  16. The Value of Failing in Career Development: A Chaos Theory Perspective

    Pryor, Robert G. L.; Bright, James E. H.


    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…

  17. [Dynamic paradigm in psychopathology: "chaos theory", from physics to psychiatry].

    Pezard, L; Nandrino, J L


    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

  18. Borrowed knowledge chaos theory and the challenge of learning across disciplines

    Kellert, Stephen H


    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...

  19. Riemannian theory of Hamiltonian chaos and Lyapunov exponents

    Casetti, L; Pettini, M; Casetti, Lapo; Clementi, Cecilia; Pettini, Marco


    This paper deals with the problem of analytically computing the largest Lyapunov exponent for many degrees of freedom Hamiltonian systems. This aim is succesfully reached within a theoretical framework that makes use of a geometrization of newtonian dynamics in the language of Riemannian geometry. A new point of view about the origin of chaos in these systems is obtained independently of homoclinic intersections. Chaos is here related to curvature fluctuations of the manifolds whose geodesics are natural motions and is described by means of Jacobi equation for geodesic spread. Under general conditions ane effective stability equation is derived; an analytic formula for the growth-rate of its solutions is worked out and applied to the Fermi-Pasta-Ulam beta model and to a chain of coupled rotators. An excellent agreement is found the theoretical prediction and the values of the Lyapunov exponent obtained by numerical simulations for both models.

  20. Asymptotic chaos expansions in finance theory and practice

    Nicolay, David


    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...

  1. Chaos and Crisis: Propositions for a General Theory of Crisis Communication.

    Seeger, Matthew W.


    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…

  2. Final report on the application of chaos theory to an alumina sensor for aluminum reduction cells

    Williford, R.E.; Windisch, C.F. Jr.


    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.

  3. Estimation of Daily Discharge of Baranduz River via Chaos Theory

    Ahmad Pour Mohammad Aghdam


    Full Text Available The chaotic behavior of monthly precipitation time series is investigated using the phasespace reconstruction technique and the principal component analysis method. To reconstruct phase space, the time delay and embedding dimension are needed and for this purpose, average mutual information and algorithm of false nearest neighbors are used. The delay time for Baranduz River is calculated via the average mutual information method which is equal to 66. The most suitable inscribed dimension, by use of false nearest neighbors approach, is about 28. The correlation in time series of water flow is equal to 3.1 which require at least 3 variables to describe the system. The low value of correlation in daily scale is an indication of the existence of chaos in the water flow of Baranduz Chay River.

  4. Text Steganography using LSB insertion method along with Chaos Theory

    S., Bhavana


    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.

  5. The Implication of Chaos/Complexity Theory into Second Language Acquisition

    Minoo Alemi


    Full Text Available With the advances in Quantum physics and meteorology, science has moved towards more uncertainty and unpredictability (Larsen-Freeman, 2002 [12]. This has resulted in the emergence of Chaos/Complexity Science (Valle, 2000 [20], or Theory (Larsen-Freeman, 1997 [11], and Dynamic System Theory (De Bot, Lowie, & Verspoor, 2007 [3]. As Larsen-Freeman (1997 [11] states the name of chaos/complexity science is paradoxical terminology in that the word science means order as well as complexity but in Ch/C this complexity is achieved through chaotic situation. In science we are searching for cause and effect connection while in Ch/C such a connection is not that much straightforward. Efforts have been invested to apply the concept into Second Language Acquisition (SLA (Larsen-Freeman, 1997 [11] due to incommensurable issues in SLA Larsen-Freeman (1997 [11], especially, introduced the concept into SLA in detail, however, we think more works and speculations on the topic are required on all aspects which are related to SLA. To this end, this article is a critical review of the implication of Chaos/Complexity theory into SLA from three perspectives: the Nature of Language Complexity, SLA Incommensurable Theories, and the Complex Nature of Classroom.

  6. Complexity Theory of Beam Halo-Chaos and Its Control Methods With Prospective Applications


    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

  7. Application of Chaos Theory in the Prediction of Motorised Traffic Flows on Urban Networks

    Aderemi Adewumi; Jimmy Kagamba; Alex Alochukwu


    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. No...




    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 ...

  9. A New Technique in saving Fingerprint with low volume by using Chaos Game and Fractal Theory

    Maryam Ashourzadeh


    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

  10. A new electricity price forecasting method based on chaos theory and data mining

    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.

  11. Common prescriptions for psychology derived from dialectical materialism and chaos theory.

    Gilgen, A R


    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

  12. Important theories of the 20th century. Relativity, cosmology, quantum mechanics and chaos theory. 3. corr. ed.

    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.

  13. The reasons for the application of chaos theory to the analysis of catastrophes.

    Valery, Kudin


    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.

  14. Final report on the application of chaos theory to an alumina sensor for aluminum reduction cells. Inert Electrodes Program

    Williford, R.E.; Windisch, C.F. Jr.


    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.

  15. Prediction of regional seasonal fluctuations in precipitation based on chaos theory

    LuValle, M


    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...

  16. Predictive Control Using Short-Term Prediction Method Based on chaos theory

    In this paper, an active vibration control method for nonlinear mechanical systems is discussed. The control forces are determined by using the future values of the system obtained by the short-term prediction method based on chaos theory. The authors call such a control method a predictive control method. This method is applied to a pendulum system forced by a sinusoidal torque at the supported point as a numerical example here. The equation of motion for the system becomes nonlinear one when the swing angle is large. The angular displacements near future are used to calculate the control forces. Particularly, the methods to get the optimal sampling period, the forward horizon and the backward horizon are presented here and the effectiveness of the methods are examined numerically

  17. A unified theory of chaos linking nonlinear dynamics and statistical physics

    Poon, Chi-Sang; Wu, Guo-Qiang


    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...

  18. To explore the prevention and treatment of Tai Chi Chuan Exercise on hypertension based on the theory of chaos

    Xiang-Lin CHI


    Full Text Available In this paper,review and analysis of  the fluctuations of blood pressure and pathogenesis of hypertension were presented a review and analysed based on chaos theory. At the same time, we interpreted philosophically the special concept of Tai Chi Chuan Exercise. Furthermore, the possible mechanisms of prevention and treatment of Tai Chi Chuan on hypertension was reviewed on the basis of clinical research literature.

  19. Understanding Chaos via Nuclei

    Cejnar, Pavel; Stránský, Pavel


    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.

  20. Cultural planning and Chaos Theory in Cyberspace: some notes on a Digital Cultural Atlas Project for Western Sydney

    Elaine Lally


    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.


    Matthew O’Lemmon


    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.

  2. Paths to chaos

    Rapid growth in the study of nonlinear dynamics and chaos in classical mechanics, has led physicists to reappraise their abandonment of this definition of atomic theory in favour of quantum mechanics adopted earlier this century. The concept of chaos in classical mechanics is examined in this paper and manifestations of chaos in quantum mechanics are explored. While quantum mechanics teaches that atomic particles must not be pictured as moving sharply in defined orbits, these precise orbits can be used to describe essential features of the measurable quantum mechanical spectra. (UK)

  3. Chaos applications in telecommunications

    Stavroulakis, Peter


    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

  4. 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.

  5. Cardiac interbeat interval dynamics from childhood to senescence : comparison of conventional and new measures based on fractals and chaos theory

    Pikkujamsa, S. M.; Makikallio, T. H.; Sourander, L. B.; Raiha, I. J.; Puukka, P.; Skytta, J.; Peng, C. K.; Goldberger, A. L.; Huikuri, H. V.


    BACKGROUND: New methods of R-R interval variability based on fractal scaling and nonlinear dynamics ("chaos theory") may give new insights into heart rate dynamics. The aims of this study were to (1) systematically characterize and quantify the effects of aging from early childhood to advanced age on 24-hour heart rate dynamics in healthy subjects; (2) compare age-related changes in conventional time- and frequency-domain measures with changes in newly derived measures based on fractal scaling and complexity (chaos) theory; and (3) further test the hypothesis that there is loss of complexity and altered fractal scaling of heart rate dynamics with advanced age. METHODS AND RESULTS: The relationship between age and cardiac interbeat (R-R) interval dynamics from childhood to senescence was studied in 114 healthy subjects (age range, 1 to 82 years) by measurement of the slope, beta, of the power-law regression line (log power-log frequency) of R-R interval variability (10(-4) to 10(-2) Hz), approximate entropy (ApEn), short-term (alpha(1)) and intermediate-term (alpha(2)) fractal scaling exponents obtained by detrended fluctuation analysis, and traditional time- and frequency-domain measures from 24-hour ECG recordings. Compared with young adults (60 years, n=29). CONCLUSIONS: Cardiac interbeat interval dynamics change markedly from childhood to old age in healthy subjects. Children show complexity and fractal correlation properties of R-R interval time series comparable to those of young adults, despite lower overall heart rate variability. Healthy aging is associated with R-R interval dynamics showing higher regularity and altered fractal scaling consistent with a loss of complex variability.

  6. 2012 Symposium on Chaos, Complexity and Leadership

    Erçetin, Şefika


    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.

  7. Colored chaos

    Mueller, B.


    The report contains viewgraphs on the following: ergodicity and chaos; Hamiltonian dynamics; metric properties; Lyapunov exponents; KS entropy; dynamical realization; lattice formulation; and numerical results.

  8. A modified artificial bee colony based on chaos theory for solving non-convex emission/economic dispatch

    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

  9. Patterns in chaos

    Classification of chaotic patterns in classical Hamiltonian systems is given as a series of levels with increasing disorder. Hamiltonian dynamics is presented, including the renormalization chaos, based upon the fairly simple resonant theory. First estimates for the critical structure and related statistical anomalies in arbitrary dimensions are discussed. 49 refs




    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.

  11. Recent Developments on Chaos in Mechanical Systems

    Mohammad Sajid


    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...

  12. Organizational Change at the Edge of Chaos: A Complexity Theory Perspective of Autopoietic Systems

    Susini, Domenico, III.


    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…

  13. Effect of metal oxide arrester on the chaotic oscillations in the voltage transformer with nonlinear core loss model using chaos theory

    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)

  14. Chaos a very short introduction

    Smith, Leonard


    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.

  15. Spatial chaos in weakly dispersive and viscous media a nonperturbative theory of the driven KdV-Burgers equation

    Malkov, M A


    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...

  16. Chaos on hyperspace

    Beran, Zdeněk; Čelikovský, Sergej


    Roč. 23, č. 5 (2013), 1350084-1-1350084-9. ISSN 0218-1274 R&D Projects: GA ČR GA13-20433S Institutional support: RVO:67985556 Keywords : Hyperspace * chaos * shadowing * Bernoulli shift Subject RIV: BC - Control Systems Theory Impact factor: 1.017, year: 2013

  17. Chaos the science of predictable random motion

    Kautz, Richard


    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.

  18. Chaos and fractals. Applications to nuclear engineering

    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)

  19. 2nd International Symposium on Chaos, Complexity and Leadership

    Banerjee, Santo


    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.

  20. Teaching and Learning in a Student Success Course: A Discussion Concerning the Development of the Internal Locus of Control Using Fuzzy Logic, TQM, and the Chaos Theory of Education.

    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…

  1. Fractals and chaos

    Earnshow, R; Jones, H


    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...


    A. Bonatto


    Full Text Available Chaos is based on nonlinear phenomena occurring everywhere, but it brings stability and its own structure. Many are the linear realities, but there are phenomena to which mathematical systems do not describe acceptably. Charting these relationships is challenging to obtain a representative model of reality. In the chaos, a small disturbance will amplify, and initially close trajectories diverge. The instability leads to new aspects. This helps in the process of modeling for the study of simulations that are applied in the financial and economic fields, showing that the market continues to disorder in an organized manner. Research in the last 25 years focus on the risk and volatility of the behavior of commodity prices. The analysis and forecast of price behavior in commodity markets are relevant both for producers, cooperatives and industries and for global financial markets. These applications aim to enable projections of future commodity prices, improving decision-making in the future. In modeling commodity time series we must take into account several factors such as seasonality in prices due to fluctuations in supply and demand during periods of crop and season. The analysis of the behavior of prices of an asset is important for predicting future revenue, past behavior analysis of a series of prices and study of the historical price of a product. That's one reason the applicability of chaos theory: the ability to identify and explain fluctuations in the markets that appear to be random, but actually are not.

  3. Chaos in hadrons

    In the last decade quantum chaos has become a well established discipline with outreach to different fields, from condensed-matter to nuclear physics. The most important signature of quantum chaos is the statistical analysis of the energy spectrum, which distinguishes between systems with integrable and chaotic classical analogues. In recent years, spectral statistical techniques inherited from quantum chaos have been applied successfully to the baryon spectrum revealing its likely chaotic behaviour even at the lowest energies. However, the theoretical spectra present a behaviour closer to the statistics of integrable systems which makes theory and experiment statistically incompatible. The usual statement of missing resonances in the experimental spectrum when compared to the theoretical ones cannot account for the discrepancies. In this communication we report an improved analysis of the baryon spectrum, taking into account the low statistics and the error bars associated with each resonance. Our findings give a major support to the previous conclusions. Besides, analogue analyses are performed in the experimental meson spectrum, with comparison to theoretical models.

  4. Geodesics deviation equation approach to chaos

    Dobrowolski, Tomasz; Szczesny, Jerzy


    Geodesics deviation equation (GDE) is itroduced. In "adiabatic" approximation exact solution of the GDE if found. Perturbation theory in general case is formulated. Geometrical criterion of local instability which may lead to chaos is formulated.

  5. Chaos Behaviour of Molecular Orbit

    LIU Shu-Tang; SUN Fu-Yan; SHEN Shu-Lan


    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.

  6. Chaos Synthesis by Evolutionary Algorithms

    Zelinka, I.; Chen, G.; Čelikovský, Sergej

    Berlin : Springer-Verlag, 2010 - (Zelinka, I.; Čelikovský, S.; Richter, H.; Chen, G.), s. 345-382 ISBN 978-3-642-10706-1. - (Studies in Computational Intelligence. 267) Institutional research plan: CEZ:AV0Z10750506 Keywords : chaos synthesis * evolutionary algorithms * self organizingmigrating * evolutionary computing Subject RIV: BC - Control Systems Theory

  7. 4th international interdisciplinary chaos symposium

    Banerjee, Santo; Caglar, Suleyman; Ozer, Mehmet; Chaos and complex systems


    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...

  8. Semiconductor Lasers Stability, Instability and Chaos

    Ohtsubo, Junji


    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...

  9. Chaos, decoherence and quantum cosmology

    In this topical review we discuss the connections between chaos, decoherence and quantum cosmology. We understand chaos as classical chaos in systems with a finite number of degrees of freedom, decoherence as environment induced decoherence and quantum cosmology as the theory of the Wheeler-DeWitt equation or else the consistent history formulation thereof, first in mini super spaces and later through its extension to midi super spaces. The overall conclusion is that consideration of decoherence is necessary (and probably sufficient) to sustain an interpretation of quantum cosmology based on the wavefunction of the Universe adopting a Wentzel-Kramers-Brillouin form for large Universes, but a definitive account of the semiclassical transition in classically chaotic cosmological models is not available in the literature yet. (topical review)

  10. Physics and Applications of Laser Diode Chaos

    Sciamanna, Marc


    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.

  11. Chaos dynamic characteristics during mine fires


    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

  12. Embrace the Chaos

    Huwe, Terence K.


    "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…

  13. Polynomial chaos representation of a stochastic preconditioner

    Desceliers, Christophe; Ghanem, R; Soize, Christian


    A method is developed in this paper to accelerate the convergence in computing the solution of stochastic algebraic systems of equations. The method is based on computing, via statistical sampling, a polynomial chaos decomposition of a stochastic preconditioner to the system of equations. This preconditioner can subsequently be used in conjunction with either chaos representations of the solution or with approaches based on Monte Carlo sampling. In addition to presenting the supporting theory...

  14. Decoherence, determinism and chaos

    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

  15. Decoherence, determinism and chaos

    Noyes, H.P.


    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.

  16. Hamiltonian Chaos and Fractional Dynamics

    This book provides an introduction and discussion of the main issues in the current understanding of classical Hamiltonian chaos, and of its fractional space-time structure. It also develops the most complex and open problems in this context, and provides a set of possible applications of these notions to some fundamental questions of dynamics: complexity and entropy of systems, foundation of classical statistical physics on the basis of chaos theory, and so on. Starting with an introduction of the basic principles of the Hamiltonian theory of chaos, the book covers many topics that can be found elsewhere in the literature, but which are collected here for the readers' convenience. In the last three parts, the author develops topics which are not typically included in the standard textbooks; among them are: - the failure of the traditional description of chaotic dynamics in terms of diffusion equations; - he fractional kinematics, its foundation and renormalization group analysis; - 'pseudo-chaos', i.e. kinetics of systems with weak mixing and zero Lyapunov exponents; - directional complexity and entropy. The purpose of this book is to provide researchers and students in physics, mathematics and engineering with an overview of many aspects of chaos and fractality in Hamiltonian dynamical systems. In my opinion it achieves this aim, at least provided researchers and students (mainly those involved in mathematical physics) can complement this reading with comprehensive material from more specialized sources which are provided as references and 'further reading'. Each section contains introductory pedagogical material, often illustrated by figures coming from several numerical simulations which give the feeling of what's going on, and thus is very useful to the reader who is not very familiar with the topics presented. Some problems are included at the end of most sections to help the reader to go deeper into the subject. My one regret is that the book does not

  17. Scrambling without chaos in RCFT

    Caputa, Pawel; Veliz-Osorio, Alvaro


    In this letter we investigate measures of chaos and entanglement scrambling in rational conformal field theories in 1+1 dimensions. First, we derive a formula for the late time value of the out-of-time-order correlators for these class of theories. Our universal result can be expressed as a particular combination of the modular S-matrix elements known as anyon monodromy scalar. Next, in the explicit setup of a $SU(N)_k$ WZW model, we compare the late time behaviour of the out-of-time correlators and the purity. Interestingly, in the large-c limit, the purity grows logarithmically but the out-of-time-order correlators remain constant. Therefore, we find that some systems may display entanglement scrambling in the absence of chaos.

  18. Chaos in the library environment

    Κατσιρίκου, Ανθή


    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...

  19. Chaos in electric drive systems analysis control and application

    Chau, K T


    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...

  20. Toward a definition of chaos for general relativity

    Witt, Donald; Schleich, Kristin


    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.

  1. Master Teachers: Making a Difference on the Edge of Chaos

    Chapin, Dexter


    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…

  2. 混沌理论对城市规划的启示%Enlightenment Of Chaos Theory On Urban Planning

    徐岩; 宋伟轩


    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.

  3. Hamiltonian chaos and fractional dynamics

    Zaslavsky, George M


    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 ...

  4. Physical white chaos generation

    Wang, Anbang; Wang, Bingjie; Li, Lei; Zhang, Mingjiang; Zhang, Wendong


    Physical chaos is a fascinating prospect for high-speed data security by serving as a masking carrier or a key source, but suffers from a colored spectrum that divulges system's intrinsic oscillations and degrades randomness. Here, we demonstrate that physical chaos with a white spectrum can be achieved by the optical heterodyning of two delayed-feedback lasers. A white chaotic spectrum with 1-dB fluctuation in a band of 11 GHz is experimentally obtained. The white chaos also has a perfect delta-like autocorrelation function and a high dimensionality of greater than 10, which makes chaos reconstruction extremely difficult and thus improves security.

  5. Quantum Chaos and Statistical Mechanics

    Srednicki, Mark


    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.

  6. A General Systems Theory for Chaos, Quantum Mechanics and Gravity for Dynamical Systems of all Space-Time Scales

    Selvam, A. M.


    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...

  7. Chaos of chiral condensate

    Hashimoto, Koji; Yoshida, Kentaroh


    Assigning a chaos index for vacua of generic quantum field theories is a challenging problem. We find chaotic behavior of chiral condensates of a quantum gauge theory at strong coupling limit, by using the AdS/CFT correspondence. We evaluate the time evolution of homogeneous quark condensates and in an N=2 supersymmetric QCD with the SU(N_c) gauge group at large N_c and at large 't Hooft coupling lambda. At an equivalent classical gravity picture, a Lyapunov exponent is readily defined. We show that the condensates exhibit chaotic behavior for energy density E > (6x10^2) (N_c/lambda^2) (m_q)^4 where m_q is the quark mass. The energy region of the chaotic vacua of the N=2 supersymmetric QCD increases for smaller N_c or larger lambda. The Lyapunov exponent is calculated as a function of the theory (N_c,lambda,E), showing that the N=2 supersymmetric QCD is more chaotic for smaller N_c.

  8. Replication of chaos in neural networks, economics and physics

    Akhmet, Marat


    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.


    Sang Tao; Wang Ruli; Yan Yixun


    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.

  10. The transition to chaos conservative classical systems and quantum manifestations

    Reichl, Linda E


    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...

  11. Contributions of plasma physics to chaos and nonlinear dynamics

    Escande, Dominique


    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

  12. The chaos machine: analogue computing rediscovered (1)

    Ambaum, Maarten H. P.; Harrison, R. Giles


    Analogue computers provide actual rather than virtual representations of model systems. They are powerful and engaging computing machines that are cheap and simple to build. This two-part Retronics article helps you build (and understand!) your own analogue computer to simulate the Lorenz butterfly that's become iconic for Chaos theory.

  13. Chaos synthesis by means of evolutionary algorithms

    Zelinka, I.; Chen, G.; Čelikovský, Sergej


    Roč. 18, č. 4 (2008), s. 911-942. ISSN 0218-1274 R&D Projects: GA ČR(CZ) GA102/08/0186 Institutional research plan: CEZ:AV0Z10750506 Keywords : Chaos * evolution * synthesis Subject RIV: BC - Control Systems Theory Impact factor: 0.870, year: 2008

  14. X-ray Digital Image Encryption Algorithm Based on Chaos Theory and Arnold Transformation%基于混沌理论和Arnold变换的X射线数字图像加密算法

    陶亮; 张运楚; 同玉洁


    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。

  15. Science of Chaos or Chaos in Science?

    Bricmont, Jean


    I try to clarify several confusions in the popular literature concerning chaos, determinism, the arrow of time, entropy and the role of probability in physics. Classical ideas going back to Laplace and Boltzmann are explained and defended while some recent views on irreversibility, due to Prigogine, are criticized.

  16. A bound on chaos

    Maldacena, Juan; Stanford, Douglas


    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.

  17. Nonlinear dynamics and quantum chaos an introduction

    Wimberger, Sandro


    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.

  18. Polynomial chaos functions and stochastic differential equations

    The Karhunen-Loeve procedure and the associated polynomial chaos expansion have been employed to solve a simple first order stochastic differential equation which is typical of transport problems. Because the equation has an analytical solution, it provides a useful test of the efficacy of polynomial chaos. We find that the convergence is very rapid in some cases but that the increased complexity associated with many random variables can lead to very long computational times. The work is illustrated by exact and approximate solutions for the mean, variance and the probability distribution itself. The usefulness of a white noise approximation is also assessed. Extensive numerical results are given which highlight the weaknesses and strengths of polynomial chaos. The general conclusion is that the method is promising but requires further detailed study by application to a practical problem in transport theory

  19. Chaos and Preheating

    Jorás, S E; Jor\\'as, Sergio E.


    We show evidence for a relationship between chaos and parametric resonance both in a classical system and in the semiclassical process of particle creation. We apply our considerations in a toy model for preheating after inflation.

  20. Exploiting chaos for applications

    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

  1. Chaos in quantum channels

    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.)


    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...

  2. Exploiting chaos for applications

    Ditto, William L., E-mail: [Department of Physics and Astronomy, University of Hawaii at Mānoa, Honolulu, Hawaii 96822 (United States); Sinha, Sudeshna, E-mail: [Indian Institute of Science Education and Research (IISER), Mohali, Knowledge City, Sector 81, SAS Nagar, PO Manauli 140306, Punjab (India)


    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.

  3. Quantifying chaos for ecological stoichiometry

    Duarte, Jorge; Januário, Cristina; Martins, Nuno; Sardanyés, Josep


    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.

  4. Chaos-based hash function (CBHF) for cryptographic applications

    As the core of cryptography, hash is the basic technique for information security. Many of the hash functions generate the message digest through a randomizing process of the original message. Subsequently, a chaos system also generates a random behavior, but at the same time a chaos system is completely deterministic. In this paper, an algorithm for one-way hash function construction based on chaos theory is introduced. Theoretical analysis and computer simulation indicate that the algorithm can satisfy all performance requirements of hash function in an efficient and flexible manner and secure against birthday attacks or meet-in-the-middle attacks, which is good choice for data integrity or authentication.

  5. Narrative and Chaos Acknowledging the Novelty of Lives-in-Time

    Randall, William L.


    In this paper I propose that interest in "narrative" within the human sciences is comparable to interest in "chaos" within the natural sciences. In their respective ways, theories on narrative and theories on chaos are aimed at appreciating the dynamics of complex, multi-dimensional systems which otherwise resist our attempts to predict, measure,…

  6. Chaos-assisted, broadband trapping of light in optical resonators

    Liu, C; Molinari, D; Khan, Y; Ooi, B S; Krauss, T F; Fratalocchi, A


    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.

  7. Study on chaos in short circuit gas metal arc welding process

    Lü Xiaoqing; Cao Biao; Zeng Min; Wang Zhenmin; Huang Shisheng


    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.

  8. Chaos and Nonlinear Dynamics in a Quantum Artificial Economy

    Gonçalves, Carlos Pedro


    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.

  9. Quantum Graphs: Applications to Quantum Chaos and Universal Spectral Statistics

    Gnutzmann, Sven; Smilansky, Uzy


    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...

  10. Competitive coexistence in stoichiometric chaos

    Deng, Bo; Loladze, Irakli


    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.

  11. Nuclear collective dynamics and chaos

    The present status and future problems in both the classical-level theory and full quantum theory of nuclear collective dynamics are discussed by putting special emphasis on their relation to the classical and quantum order-to-chaos transition dynamics, respectively. The nonlinear dynamics between the collective and single-particle excitation modes of motion specific for the finite, self-sustained and self-organizing system as the nucleus is discussed within the time-dependent Hartree-Fock (TDHF) theory, the basic equation of which is shown to be formally equivalent to the Hamilton's canonical equations of motion in the classical nonlinear dynamical system. An importance to relate the structure of the TDHF symplectic manifold with an inexhaustible rich structure of the classical phase space in the nonlinear system is stressed. A full quantum theory of nuclear collective dynamics is proposed under a dictation of what has been developed in the classical-level TDHF theory. It is shown that the proposed quantum theory enables us to explore exceeding complexity of the Hilbert space. It is discussed that a resonant denominator known as a source of the extraordinary rich structure of the phase space trajectories, also plays a decisive role in generating a rich structure of the quantum Hilbert space. (author) 87 refs

  12. Deterministic chaos an introduction

    Schuster, Heinz Georg


    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

  13. Chaos in Magnetoplasmas

    B. Buti


    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.

  14. Morphogenesis of Chaos

    Akhmet, Marat; Fen, Mehmet Onur


    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...

  15. Dissipative structures and chaos

    Mori, Hazime


    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.

  16. Efficient chaos shift keying method based on the second error derivative anti-synchronization detection

    Čelikovský, Sergej; Lynnyk, Volodymyr

    Vol. Library Catalog Number: CFP09537-CDR. Christchurch: IEEE, 2009, s. 530-535. ISBN 978-1-4244-4707-7. [Seventh IEEE International Conference on Control and Automation. Christchurch (NZ), 09.12.2009-11.12.2009] R&D Projects: GA ČR(CZ) GA102/08/0186 Institutional research plan: CEZ:AV0Z10750506 Keywords : chaos shift keying * chaos synchronization * efficient chaos Subject RIV: BC - Control Systems Theory

  17. An exploration of dynamical systems and chaos

    Argyris, John H; Haase, Maria; Friedrich, Rudolf


    This book is conceived as a comprehensive and detailed text-book on non-linear dynamical systems with particular emphasis on the exploration of chaotic phenomena. The self-contained introductory presentation is addressed both to those who wish to study the physics of chaotic systems and non-linear dynamics intensively as well as those who are curious to learn more about the fascinating world of chaotic phenomena. Basic concepts like Poincaré section, iterated mappings, Hamiltonian chaos and KAM theory, strange attractors, fractal dimensions, Lyapunov exponents, bifurcation theory, self-similarity and renormalisation and transitions to chaos are thoroughly explained. To facilitate comprehension, mathematical concepts and tools are introduced in short sub-sections. The text is supported by numerous computer experiments and a multitude of graphical illustrations and colour plates emphasising the geometrical and topological characteristics of the underlying dynamics. This volume is a completely revised and enlar...

  18. Frozen spatial chaos induced by boundaries

    Eguiluz, V M; Piro, O; Balle, S; Eguiluz, Victor M.; Hernandez-Garcia, Emilio; Piro, Oreste; Balle, Salvador


    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.

  19. Complex motions and chaos in nonlinear systems

    Machado, José; Zhang, Jiazhong


    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.

  20. Chaos in drive systems

    Kratochvíl C.


    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.

  1. Neural chaos and schizophrenia

    Bob, P.; Chládek, Jan; Šusta, M.; Glaslová, K.; Jagla, F.; Kukleta, M.


    Roč. 26, č. 4 (2007), s. 298-305. ISSN 0231-5882 Institutional research plan: CEZ:AV0Z20650511 Keywords : EDA * Lyapunov exponent * schizophrenia * chaos Subject RIV: FL - Psychiatry, Sexuology Impact factor: 1.286, year: 2007

  2. Chaos in GDP

    R. Kříž


    Full Text Available 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.

  3. Chaos in GDP

    R. Kříž


    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.

  4. Regularity and chaos in nuclear structure

    The BSC pairing gap, obtained from nuclear masses, shows large structural effects. A periodic orbit theory for the pairing gap has been developed, and generic expressions for the pairing gap fluctuations are derived, stressing the role of regularity/chaos. Results from the theory are compared to pairing gaps obtained from nuclear masses, calculated as well as measured. The comparison provides another quality control of nuclear mass formula, and gives additional insight in the nuclear pairing phenomenon. The theory can be applied to pairing fluctuations in other finite-size Fermi systems, as ultracold atomic gases or small metallic grains

  5. Chaos analysis and chaotic EMI suppression of DC-DC converters

    Zhang, Bo


    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

  6. Quantitative Research Methods in Chaos and Complexity: From Probability to Post Hoc Regression Analyses

    Gilstrap, Donald L.


    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…

  7. A Structure behind Primitive Chaos

    Ogasawara, Yoshihito


    Recently, a new concept, primitive chaos, has been proposed as a concept closely related to the fundamental problems of physics itself such as determinism, causality, free will, predictability, and irreversibility [J. Phys. Soc. Jpn. 79, 015002 (2010)]. This paper reveals a structure hidden behind the primitive chaos; under some conditions, a new primitive chaos is constructed from the original primitive chaos, this procedure can be repeated, and the hierarchical structure of the primitive chaos is obtained. This implies such a picture that new events and causality are constructed from the old ones, with the aid of the concept of a coarse graining. As an application of this structure, interesting facts are revealed for the essential condition of the primitive chaos and for chaotic behaviors.

  8. Quantum Correlations, Chaos and Information

    Madhok, Vaibhav

    Quantum chaos is the study of quantum systems whose classical description is chaotic. How does chaos manifest itself in the quantum world? In this spirit, we study the dynamical generation of entanglement as a signature of chaos in a system of periodically kicked coupled-tops, where chaos and entanglement arise from the same physical mechanism. The long-time entanglement as a function of the position of an initially localized wave packet very closely correlates with the classical phase space surface of section - it is nearly uniform in the chaotic sea, and reproduces the detailed structure of the regular islands. The uniform value in the chaotic sea is explained by the random state conjecture. As classically chaotic dynamics take localized distributions in phase space to random distributions, quantized versions take localized coherent states to pseudo-random states in Hilbert space. Such random states are highly entangled, with an average value near that of the maximally entangled state. For a map with global chaos, we derive that value based on new analytic results for the entropy of random states. For a mixed phase space, we use the Percival conjecture to identify a "chaotic subspace" of the Hilbert space. The typical entanglement, averaged over the unitarily invariant Haar measure in this subspace, agrees with the long-time averaged entanglement for initial states in the chaotic sea. In all cases the dynamically generated entanglement is that of a random complex vector, even though the system is time-reversal invariant, and the Floquet operator is a member of the circular orthogonal ensemble. Continuing on our journey to find the footprints of chaos in the quantum world, we explore quantum signatures of classical chaos by studying the rate of information gain in quantum tomography. The measurement record is obtained as a sequence of expectation values of a Hermitian operator evolving under repeated application of the Floquet operator of the quantum kicked top on

  9. The joy of transient chaos

    Tél, Tamás [Institute for Theoretical Physics, Eötvös University, and MTA-ELTE Theoretical Physics Research Group, Pázmány P. s. 1/A, Budapest H-1117 (Hungary)


    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.

  10. Chaos detection and predictability

    Gottwald, Georg; Laskar, Jacques


    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...

  11. Chaos in quantum channels

    Hosur, Pavan; Roberts, Daniel A; Yoshida, Beni


    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.

  12. Chaos A Program Collection for the PC

    Korsch, Hans Jürgen; Hartmann, Timo


    This new edition strives yet again to provide readers with a working knowledge of chaos theory and dynamical systems through parallel introductory explanations in the book and interaction with carefully-selected programs supplied on the accompanying diskette. The programs enable readers, especially advanced-undergraduate students in physics, engineering, and math, to tackle relevant physical systems quickly on their PCs, without distraction from algorithmic details. For the third edition of Chaos: A Program Collection for the PC, each of the previous twelve programs is polished and rewritten in C++ (both Windows and Linux versions are included). A new program treats kicked systems, an important class of two-dimensional problems, which is introduced in Chapter 13. Each chapter follows the structure: theoretical background; numerical techniques; interaction with the program; computer experiments; real experiments and empirical evidence; reference. Interacting with the many numerical experiments have proven to h...

  13. Recent Progress in Controlling Chaos

    Sanjuan, Miguel AF


    This book provides a collection of research papers on one of the topics where the applications of chaos have been more fruitful: controlling chaos. Here, new theoretical ideas, as experimental implementations of controlling chaos, are included, while the applications contained in this volume can be referred to turbulent magnetized plasmas, chaotic neural networks, modeling city traffic and models of interest in celestial mechanics. "Recent Progress in Controlling Chaos" will provide an overview of the recent progress in this field, which will be very useful for students and researche

  14. Robust chaos and its applications

    Zeraoulia, Elhadj


    Robust chaos is defined by the absence of periodic windows and coexisting attractors in some neighborhoods in the parameter space of a dynamical system. This unique book explores the definition, sources, and roles of robust chaos. The book is written in a reasonably self-contained manner and aims to provide students and researchers with the necessary understanding of the subject. Most of the known results, experiments, and conjectures about chaos in general and about robust chaos in particular are collected here in a pedagogical form. Many examples of dynamical systems, ranging from purely mat

  15. Martingales, Nonlinearity, and Chaos

    Barnett, William A.; Apostolos Serletis


    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...

  16. Enlightening complexity: making energy with chaos

    Molinari, D


    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.

  17. Application of chaos and fractals to computer vision

    Farmer, Michael E


    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

  18. 混沌理论视角下旅游目的地危机管理体系的构建%Study on Tourism Destination Crisis Management System with the Perspective of Chaos Theory



    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。

  19. The Origin of Chaos in the Outer Solar System

    Murray, N; Holman, M.


    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...

  20. The Retentivity of Chaos under Topological Conjugation

    Tianxiu Lu; Peiyong Zhu; Xinxing Wu


    The definitions of Devaney chaos (DevC), exact Devaney chaos (EDevC), mixing Devaney chaos (MDevC), and weak mixing Devaney chaos (WMDevC) are extended to topological spaces. This paper proves that these chaotic properties are all preserved under topological conjugation. Besides, an example is given to show that the Li-Yorke chaos is not preserved under topological conjugation if the domain is extended to a general metric space.

  1. Predicting Storm Surges: Chaos, Computational Intelligence, Data Assimilation, Ensembles

    Siek, M.B.L.A.


    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

  2. Does the transition to chaos determine the dynamic aperture?

    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

  3. Topological organization of (low-dimensional) chaos

    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

  4. Chaos in Multi-Valued Dynamical Systems

    Beran, Zdeněk; Čelikovský, S.

    Vegazana Campus of the University of León: Universidad de León, 2011, s. 1-5. [Physcon 2011 - 5th International Scientific Conference on Physics and Control. León (ES), 05.09.2011-08.09.2011] R&D Projects: GA ČR(CZ) GAP103/10/0628 Institutional research plan: CEZ:AV0Z10750506 Keywords : Multi-valued dynamical systems * chaos * differential inclusions Subject RIV: BC - Control Systems Theory

  5. generating topological chaos in lid-driven cavity flow

    Stremler, M. A.; Chen, J


    Periodic motion of three stirrers in a two-dimensional flow can lead to chaotic transport of the surrounding fluid. For certain stirrer motions, the generation of chaos is guaranteed solely by the topology of that motion and continuity of the fluid. Work in this area has focused largely on using physical rods as stirrers, but the theory also applies when the "stirrers" are passive fluid particles. We demonstrate the occurrence of topological chaos for Stokes flow in a two-dimensional lid-driv...

  6. The edge of chaos: A nonlinear view of psychoanalytic technique.

    Galatzer-Levy, Robert M


    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

  7. In the Wake of Chaos Unpredictable Order in Dynamical Systems

    Kellert, Stephen H


    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

  8. Chaos and The Changing Nature of Science and Medicine. Proceedings

    These proceedings represent the lectures given at the workshop on chaos and the changing nature of science and medicine. The workshop was sponsored by the University of South Alabama and the American Association of Physicists in Medicine. The topics discussed covered nonlinear dynamical systems, complexity theory, fractals, chaos in biology and medicine and in fluid dynamics. Applications of chaotic dynamics in climatology were also discussed. There were 8 lectures at the workshop and all 8 have been abstracted for the Energy Science and Technology database

  9. Observer-based chaos synchronization and its application to multi-valued alphabet chaos shift keying secure encryption

    Čelikovský, Sergej; Lynnyk, Volodymyr

    Bali: ASCC, 2006. s. 76-77. ISBN 979-15017-0. [Asian Control Conference ASCC 2006 /6./. 18.07.2006-21.07.2006, Bali] R&D Projects: GA ČR GA102/05/0011 Institutional research plan: CEZ:AV0Z10750506 Keywords : nonlinear observer * chaos synchronization * secure encryption Subject RIV: BC - Control Systems Theory

  10. Observer-based chaos synchronization and its application to multi-valued alphabet chaos shift keying secure encryption

    Čelikovský, Sergej; Lynnyk, Volodymyr

    Bali: ASCC, 2006, s. 52-57. ISBN 979-15017-0. [Asian Control Conference ASCC 2006 /6./. Bali (ID), 18.07.2006-21.07.2006] R&D Projects: GA ČR GA102/05/0011 Institutional research plan: CEZ:AV0Z10750506 Keywords : nonlinear observer * chaos synchronization * secure encryption Subject RIV: BC - Control Systems Theory

  11. 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...

  12. A Chaos Conveyor Belt

    Schmidt, Britney E.


    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


    Milan TASIĆ


    Socrates Protagoras' dilemma: the subjective or objective truth about the world, and ourselves, historically, has been ''resolved'' in favor of the ''knowledge as a necessary and general one'' (Socrates), and whose typical expression in our time is, for example, ''theory of everything'' (Einstein et al.), on which Stephen Hawking will say that it begins to speak of what God had in mind when creating the world. But more than two millennia after Protagoras, Kant will find that in every knowledg...

  14. On the optimal allocation of assets in investment portfolio with application of modern portfolio and nonlinear dynamic chaos theories in investment, commercial and central banks

    Ledenyov, Dimitri O.; Ledenyov, Viktor O.


    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 ...

  15. Cryptography with chaos and shadowing

    Smaoui, Nejib [Department of Mathematics and Computer Science, Kuwait University, P.O. Box 5969, Safat 13060 (Kuwait)], E-mail:; Kanso, Ali [Department of Mathematics and Computer Science, Kuwait University, P.O. Box 5969, Safat 13060 (Kuwait)], E-mail:


    In this paper, we present a novel approach to encrypt a message (a text composed by some alphabets) using chaos and shadowing. First, we generate a numerical chaotic orbit based on the logistic map, and use the shadowing algorithm of Smaoui and Kostelich [Smaoui N, Kostelich E. Using chaos to shadow the quadratic map for all time. Int J Comput Math 1998;70:117-29] to show that there exists a finite number of true orbits that shadow the numerical orbit. Then, the finite number of maps generated is used in Baptista's algorithm [Baptista MS. Cryptography with chaos. Phys Lett A 1998;240:50-4] to encrypt each character of the message. It is shown that the use of chaos and shadowing in the encryption process enhances the security level.

  16. Quantum Instantons and Quantum Chaos

    Jirari, H.; Kröger, H.; Luo, X. Q.; Moriarty, K. J. M.; Rubin, S. G.


    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.

  17. Cryptography with chaos and shadowing

    In this paper, we present a novel approach to encrypt a message (a text composed by some alphabets) using chaos and shadowing. First, we generate a numerical chaotic orbit based on the logistic map, and use the shadowing algorithm of Smaoui and Kostelich [Smaoui N, Kostelich E. Using chaos to shadow the quadratic map for all time. Int J Comput Math 1998;70:117-29] to show that there exists a finite number of true orbits that shadow the numerical orbit. Then, the finite number of maps generated is used in Baptista's algorithm [Baptista MS. Cryptography with chaos. Phys Lett A 1998;240:50-4] to encrypt each character of the message. It is shown that the use of chaos and shadowing in the encryption process enhances the security level.

  18. Quantum Chaos and Quantum Computers

    Shepelyansky, D L


    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...

  19. Ergodic cobweb chaos

    Akio Matsumoto


    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.

  20. Partially predictable chaos

    Wernecke, Hendrik; Gros, Claudius


    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.

  1. The Chaos Within Sudoku

    Ercsey-Ravasz, Maria


    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 $\\eta > 4$.

  2. Chaos in Partial Differential Equations

    Li, Y. Charles


    This is a survey on Chaos in Partial Differential Equations. First we classify soliton equations into three categories: 1. (1+1)-dimensional soliton equations, 2. soliton lattices, 3. (1+n)-dimensional soliton equations (n greater than 1). A systematic program has been established by the author and collaborators, for proving the existence of chaos in soliton equations under perturbations. For each category, we pick a representative to present the results. Then we review some initial results o...

  3. Chaos in circuits and systems

    Chen, Guanrong


    In this volume, leading experts present current achievements in the forefront of research in the challenging field of chaos in circuits and systems, with emphasis on engineering perspectives, methodologies, circuitry design techniques, and potential applications of chaos and bifurcation. A combination of overview, tutorial and technical articles, the book describes state-of-the-art research on significant problems in this field. It is suitable for readers ranging from graduate students, university professors, laboratory researchers and industrial practitioners to applied mathematicians and phy

  4. The Theoretical Overview of "the Human Nature Hypothesis" in Economics Based on Atomic Theory and Chaos Theory Perspective%经济学中关于“人性假定”的理论综述——基于原子论和混沌论视角

    柴国君; 李文豪; 魏晶国


    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。

  5. Lecture notes on Gaussian multiplicative chaos and Liouville Quantum Gravity

    Rhodes, Rémi; Vargas, Vincent


    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 ...

  6. Chaos, brain and divided consciousness.

    Bob, Petr


    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

  7. From Cool Cash to Coded Chaos

    Rennison, Betina Wolfgang

    Communication makes a difference. The manner in which we communicate creates the phenomena we communicate about. It can seem obvious, but we are nevertheless seldom aware of the complexity this constructivist assumption implies. Through an analysis of a new salary system in the public sector 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 of...... management differently. In this chaos of codes the managerial challenge is to take a second order position in order to strategically manage the communication that manages management itself. Key words: Management; personnel management; human-relations; pay-system; communication; system-theory; discursive...

  8. Chaos: A Very Short Introduction

    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

  9. Chaos: A Very Short Introduction

    Klages, R [School of Mathematical Sciences, Mile End Road, London, E1 4NS (United Kingdom)


    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

  10. Chaos synchronization and parameter identification of three time scales brushless DC motor system

    Ge, Z.-M. [Department of Mechanical Engineering, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu 300, Taiwan (China)]. E-mail:; Cheng, J.-W. [Department of Mechanical Engineering, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu 300, Taiwan (China)


    Chaotic anticontrol and chaos synchronization of brushless DC motor system are studied in this paper. Nondimensional dynamic equations of three time scale brushless DC motor system are presented. Using numerical results, such as phase diagram, bifurcation diagram, and Lyapunov exponent, periodic and chaotic motions can be observed. Then, chaos synchronization of two identical systems via additional inputs and Lyapunov stability theory are studied. And further, the parameter of the system is traced via adaptive control and random optimization method.

  11. Anti-synchronization chaos shift keying method: error derivative detection improvement

    Čelikovský, Sergej; Lynnyk, Volodymyr

    London: IFAC, 2009, s. 1-6. [Chaos 09. Londýn (GB), 22.06.2009-24.06.2009] R&D Projects: GA ČR(CZ) GA102/08/0186; GA MŠk LA09026 Institutional research plan: CEZ:AV0Z10750506 Keywords : Nonlinear system * chaos shift keying * generalized Lorenz system Subject RIV: BC - Control Systems Theory

  12. Chaos synchronization and parameter identification of three time scales brushless DC motor system

    Chaotic anticontrol and chaos synchronization of brushless DC motor system are studied in this paper. Nondimensional dynamic equations of three time scale brushless DC motor system are presented. Using numerical results, such as phase diagram, bifurcation diagram, and Lyapunov exponent, periodic and chaotic motions can be observed. Then, chaos synchronization of two identical systems via additional inputs and Lyapunov stability theory are studied. And further, the parameter of the system is traced via adaptive control and random optimization method

  13. Transition to Chaos in Random Neuronal Networks

    Kadmon, Jonathan; Sompolinsky, Haim


    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

  14. On CFT and Quantum Chaos

    Turiaci, Gustavo


    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.

  15. Quantum chaos in multiwell potentials

    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)

  16. The dream's navel between chaos and thought.

    Scalzone, F; Zontini, G


    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

  17. Role of nonlinear dynamics and chaos in applied sciences

    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)

  18. Deterministic polarization chaos from a laser diode

    Virte, Martin; Thienpont, Hugo; Sciamanna, Marc


    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.

  19. Transition to chaos in externally modulated hydrodynamic systems

    An amplitude equation associated with externally modulated hydrodynamic systems is considered. A simple physical model to evaluate analytically the Melnikov function is proposed. The onset of chaos is studied numerically through a computation of the largest Lyapunov exponent, a construction of the bifurcation diagram, and an analysis of the phase space trajectories. Theory predicts the regions of chaotic behavior of the system in good agreement with computer calculations. (author)

  20. On a functional lasalle principle with application to chaos synchronization

    Chen, G.; Čelikovský, Sergej; Zhou, J.


    Roč. 19, č. 12 (2009), s. 4253-4261. ISSN 0218-1274 R&D Projects: GA ČR(CZ) GA102/08/0186; GA MŠk LA09026 Institutional research plan: CEZ:AV0Z10750506 Keywords : Chaos synchronization * LaSalle invariance principle * Lineared equation Subject RIV: BC - Control Systems Theory Impact factor: 0.918, year: 2009

  1. On Some False Chaos Indicators When Analyzing Sampled Data

    Augustová, Petra; Beran, Zdeněk; Čelikovský, Sergej

    Vol. Part III. Cham : Springer, 2014 - (Sanayei, A.; Rossler, E.; Zelinka, I.), s. 249-258 ISBN 978-3-319-10758-5. ISSN 2194-7287. - (Emergence, Complexity and Computation ECC. 14). [ISCS 2014: The Interdisciplinary Symposium on Complex Systems. Florencie (IT), 15.09.2014-18.09.2014] R&D Projects: GA ČR GA13-20433S Institutional support: RVO:67985556 Keywords : Chaos * Lorenz systems * Lyapunov exponent Subject RIV: BC - Control Systems Theory

  2. Propagation of chaos for interacting particles subject to environmental noise

    Coghi, Michele; Flandoli, Franco


    A system of interacting particles described by stochastic differential equations is considered. Opposite to the usual scheme, where the noise perturbations acting on different particles are independent, here the particles are subject to the same space-dependent noise, similarly to the (non-interacting) particles of the theory of diffusion of passive scalars. We prove a result of propagation of chaos and show that the limit PDE is stochastic and of inviscid type, opposite to the case when inde...

  3. Controlled institutional chaos: development of conceptual approaches to the study

    Dyatlov Sergei Alexeevich


    Full Text Available The article is devoted to the methodological principles of the organization of the global economic system, the crisis of the industrial and market paradigms, reviewing the evolution of views and critical analysis of the main provisions of the concept of controlled chaos and entropy logic theory. Introduced into the scientific circulation a number of new concepts. Formulated the new concept of "creative order".

  4. Synchronization of chaos in non-identical parametrically excited systems

    Idowu, B.A. [Department of Physics, Lagos State University, Ojo (Nigeria)], E-mail:; Vincent, U.E. [Department of Physics, Olabisi Onabanjo University, P.M.B 2002, Ago-Iwoye (Nigeria)], E-mail:; Njah, A.N. [Department of Physics, University of Agriculture, Abeokuta (Nigeria)


    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.

  5. Notions of Chaotic Cryptography: Sketch of a Chaos based Cryptosystem

    Carmen, Pellicer-Lostao; Ricardo, López-Ruiz


    Chaotic cryptography describes the use of chaos theory (in particular physical dynamical systems working in chaotic regime as part of communication techniques and computation algorithms) to perform different cryptographic tasks in a cryptographic system. In the end, the question is, can chaotic systems provide alternative techniques able to enhance cryptographic algorithms?. This chapter can be a worthy material to guide the reader in order to answer himself this question. Thus, the objective...

  6. Generalized Semiflows and Chaos in Multivalued Dynamical Systems

    Beran, Zdeněk; Čelikovský, Sergej


    Roč. 26, č. 25 (2012), 1246016-1-1246016-11. ISSN 0217-9792 R&D Projects: GA ČR(CZ) GAP103/12/1794 Institutional support: RVO:67985556 Keywords : Multivalued dynamical systems * chaos * differential inclusions Subject RIV: BC - Control Systems Theory Impact factor: 0.358, year: 2012

  7. Solitons and chaos in plasma

    Plasma exhibits a full of variety of nonlinear phenomena. Active research in nonlinear plasma physics contributed to explore the concepts of soliton and chaos. Structure of soliton equations and dynamics of low dimensional Hamiltonian systems are discussed to emphasize the universality of these novel concepts in the wide branch of science and engineering. (author) 52 refs

  8. Distributed chaos in turbulent wakes

    Bershadskii, A


    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 ...

  9. MHD turbulence and distributed chaos

    Bershadskii, A


    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 $\\beta=4/7$.

  10. Chaos and remedial investigations

    Current research into the nature of chaos indicates that even for systems that are well known and easily modeled, slight changes in the scale used to measure the input have unpredictable results in the model output. The conduct of a remedial investigation (RI) is dictated by well-established rules of investigation and management, yet small changes in project orientation, regulatory environment, or site conditions have unpredictable consequences to the project. The consequences can lead to either brilliant success or utter failure. The chaotic effect of a change in scale is most often illustrated by an exercise in measuring the length of the coast of Great Britain. If a straight ruler 10-kilometers long is used, the sum of the 10-kilometer increments gives the length of the coast. If the ruler is changed to five kilometers long and the exercise is repeated, the sum of the five-kilometer increments will not be the same as the sum of the 10-kilometer increments. Nor is there a way to predict what the length of the coast will be using any other scale. Several examples from the Fernald Project RI are used to illustrate open-quotes changes in scaleclose quotes in both technical and management situations. Given that there is no way to predict the outcome of scale changes in a RI, technical and project management must be alert to the fact that a scale has changed and the investigation is no longer on the path it was thought to be on. The key to success, therefore, is to develop specific units of measure for a number of activities, in addition to cost and schedule, and track them regularly. An example for tracking a portion of the field investigation is presented. The determination of effective units of measure is perhaps the most difficult aspect of any project. Changes in scale sometimes go unnoticed until suddenly the budget is expended and only a portion of the work is completed. Remedial investigations on large facilities provide new and complex challenges

  11. Quantum chaos, thermalization and dissipation in nuclear systems

    Sudhir R Jain


    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.

  12. An Improved Chaos Genetic Algorithm for T-Shaped MIMO Radar Antenna Array Optimization

    Xin Fu


    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.

  13. Chaos, Dirac observables and constraint quantization

    Dittrich, Bianca; Koslowski, Tim A; Nelson, Mike I


    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...

  14. Time reversibility, computer simulation, algorithms, chaos

    Hoover, William Graham


    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...

  15. Urban chaos and replacement dynamics in nature and society

    Chen, Yanguang


    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.

  16. A Quantum Correction To Chaos

    Fitzpatrick, A Liam


    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.

  17. Spatiotemporal chaos from bursting dynamics

    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)


    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.

  18. On the definition of 'chaos'

    A new definition of a chaotic invariant set is given for a continuous semiflow in a metric space. It generalizes the well-known definition due to Devaney and allows one to take into account a special feature occurring in the non-compact infinite-dimensional case: so-called turbulent chaos. The paper consists of two sections. The first contains several well-known facts from chaotic dynamics, together with new definitions and results. The second presents a concrete example demonstrating that our definition of chaos is meaningful. Namely, an infinite-dimensional system of ordinary differential equations is investigated having an attractor that is chaotic in the sense of the new definition but not in the sense of Devaney or Knudsen. Bibliography: 65 titles.

  19. Chaos, turbulence and strange attractors

    Using the turbulence example, the author recalls the two different conceptions of the nature of an erratic regime: the one in which a great number of elementary events are concerned (Landau) and the other one in which, on the contrary, a few number of elementary events are concerned (Ruelle and Takens). The last type of erratic comportment has a deterministic origin and is pointed by the adjective chaotic. Phase space for a dynamic system is presented and so the attractor nation. Chaos and notion of sensitiveness to initial conditions are defined. In scrutining the geometry of an attractor corresponding to a chaotic regime, the notion of strange attractor is shown. Some experiments results are given as illustration. Application field is recalled: for example, studies on hamiltonian chaos are made at DRFC (Department of research on controlled fusion at CEA) in relation with plasma instabilities

  20. Nonlinear Spatio-Temporal Dynamics and Chaos in Semiconductors

    Schöll, Eckehard


    Nonlinear transport phenomena are an increasingly important aspect of modern semiconductor research. This volume deals with complex nonlinear dynamics, pattern formation, and chaotic behavior in such systems. It bridges the gap between two well-established fields: the theory of dynamic systems and nonlinear charge transport in semiconductors. This unified approach helps reveal important electronic transport instabilities. The initial chapters lay a general framework for the theoretical description of nonlinear self-organized spatio-temporal patterns, such as current filaments, field domains, fronts, and analysis of their stability. Later chapters consider important model systems in detail: impact ionization induced impurity breakdown, Hall instabilities, superlattices, and low-dimensional structures. State-of-the-art results include chaos control, spatio-temporal chaos, multistability, pattern selection, activator-inhibitor kinetics, and global coupling, linking fundamental issues to electronic device applications. This book will be of great value to semiconductor physicists and nonlinear scientists alike.

  1. Master stability analysis in transient spatiotemporal chaos.

    Wackerbauer, Renate


    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

  2. The chaos cookbook a practical programming guide

    Pritchard, Joe


    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

  3. Relative chaos in stellar systems

    Statistical properties of many-dimensional dynamical system -s tellar systems of different types, are investigated by means of estimation of Ricci curvature in the direction of the velocity of geodesics. Numerical experiment is performed to calculate the Ricci and scalar curvatures for systems with equal total energy. The results of calculations enable one to obtain schematic classification of stellar systems by increasing degree of chaos

  4. Analysis of FBC deterministic chaos

    Daw, C.S.


    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.

  5. Chaos and multiple photon absorption

    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

  6. Model for Shock Wave Chaos

    Kasimov, Aslan R.


    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.

  7. Quantum chaos inside space-temporal Sinai billiards

    Addazi, Andrea


    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.

  8. Stochastic Chaos with Its Control and Synchronization

    Zhang Ying; Xu Wei; Zhang Tianshu; Yang Xiaoli; Wu Cunli; Fang Tong


    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

  9. Discretization chaos - Feedback control and transition to chaos

    Grantham, Walter J.; Athalye, Amit M.


    Problems in the design of feedback controllers for chaotic dynamical systems are considered theoretically, focusing on two cases where chaos arises only when a nonchaotic continuous-time system is discretized into a simpler discrete-time systems (exponential discretization and pseudo-Euler integration applied to Lotka-Volterra competition and prey-predator systems). Numerical simulation results are presented in extensive graphs and discussed in detail. It is concluded that care must be taken in applying standard dynamical-systems methods to control systems that may be discontinuous or nondifferentiable.


    Maistrenko, V.; Vasylenko, A.; Maistrenko, Y.; Mosekilde, Erik


    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 inter...

  11. Chaos in nonlinear oscillations controlling and synchronization

    Lakshamanan, M


    This book deals with the bifurcation and chaotic aspects of damped and driven nonlinear oscillators. The analytical and numerical aspects of the chaotic dynamics of these oscillators are covered, together with appropriate experimental studies using nonlinear electronic circuits. Recent exciting developments in chaos research are also discussed, such as the control and synchronization of chaos and possible technological applications.

  12. The CHAOS-4 geomagnetic field model

    Olsen, Nils; Lühr, H.; Finlay, Chris;


    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...

  13. The CHAOS-4 Geomagnetic Field Model

    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 resolut...

  14. Kinematic dynamo, supersymmetry breaking, and chaos

    Ovchinnikov, Igor V.; Enßlin, Torsten A.


    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.

  15. Geology and Origin of Europa's Mitten Feature (Murias Chaos)

    Figueredo, P. H.; Chuang, F. C.; Rathbun, J.; Kirk, R. L.; Greeley, R.


    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.

  16. Chaos M-ary modulation and demodulation method based on Hamilton oscillator and its application in communication

    Fu, Yongqing; Li, Xingyuan; Li, Yanan; Yang, Wei; Song, Hailiang


    Chaotic communication has aroused general interests in recent years, but its communication effect is not ideal with the restriction of chaos synchronization. In this paper a new chaos M-ary digital modulation and demodulation method is proposed. By using region controllable characteristics of spatiotemporal chaos Hamilton map in phase plane and chaos unique characteristic, which is sensitive to initial value, zone mapping method is proposed. It establishes the map relationship between M-ary digital information and the region of Hamilton map phase plane, thus the M-ary information chaos modulation is realized. In addition, zone partition demodulation method is proposed based on the structure characteristic of Hamilton modulated information, which separates M-ary information from phase trajectory of chaotic Hamilton map, and the theory analysis of zone partition demodulator's boundary range is given. Finally, the communication system based on the two methods is constructed on the personal computer. The simulation shows that in high speed transmission communications and with no chaos synchronization circumstance, the proposed chaotic M-ary modulation and demodulation method has outperformed some conventional M-ary modulation methods, such as quadrature phase shift keying and M-ary pulse amplitude modulation in bit error rate. Besides, it has performance improvement in bandwidth efficiency, transmission efficiency and anti-noise performance, and the system complexity is low and chaos signal is easy to generate.

  17. Decoherence, determinism and chaos revisited

    Noyes, H.P.


    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.

  18. Quelques aspects de Chaos Quantique

    Nonnenmacher, Stéphane


    Ce mémoire résume mes travaux dans 3 domaines reliés au "chaos quantique". J'y aborde tout d'abord les questions de répartition spatiale des fonctions propres de systèmes quantiques classiquement chaotiques. Dans une seconde partie, je résume mes travaux sur la distribution des résonances pour les systèmes de diffusion dont l'ensemble des trajectoires captées est fractal, et supporte une dynamique chaotique. Enfin, je mentionne des résultats obtenus sur les transformations chaotiques bruitées...

  19. Periodic orbits in arithmetical chaos

    Length spectra of periodic orbits are investigated for some chaotic dynamical systems whose quantum energy spectra show unexpected statistical properties and for which the notion of arithmetical chaos has been introduced recently. These systems are defined as the unconstrained motions of particles on two dimensional surfaces of constant negative curvature whose fundamental groups are given by number theoretical statements (arithmetic Fuchsian groups). It is shown that the mean multiplicity of lengths l of periodic orbits grows asymptotically like c x el/2/l, l → ∞. Moreover, the constant c (depending on the arithmetic group) is determined. (orig.)

  20. Decoherence, determinism and chaos revisited

    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

  1. An Experimental Investigation of Secure Communication With Chaos Masking

    Dhar, Sourav


    The most exciting recent development in nonlinear dynamics is realization that chaos can be useful. One application involves "Secure Communication". Two piecewise linear systems with switching nonlinearities have been taken as chaos generators. In the present work the phenomenon of secure communication with chaos masking has been investigated experimentally. In this investigation chaos which is generated from two chaos generators is masked with the massage signal to be transmitted, thus makes communication is more secure.

  2. Chaos suppression through asymmetric coupling

    Bragard, J.; Vidal, G.; Mancini, H.; Mendoza, C.; Boccaletti, S.


    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.

  3. Structure of the channeling electrons wave functions under dynamical chaos conditions

    Shul'ga, N F; Tarnovsky, A I; Isupov, A Yu


    The stationary wave functions of fast electrons axially channeling in the silicon crystal near [110] direction have been found numerically for integrable and non-integrable cases, for which the classical motion is regular and chaotic, respectively. The nodal structure of the wave functions in the quasi-classical region, where the energy levels density is high, is agreed with quantum chaos theory predictions.

  4. Controlling Chaos in Permanent Magnet Synchronous Motor Control System via Fuzzy Guaranteed Cost Controller

    Yi-You Hou


    This paper investigates the guaranteed cost control of chaos problem in permanent magnet synchronous motor (PMSM) via Takagi-Sugeno (T-S) fuzzy method approach. Based on Lyapunov stability theory and linear matrix inequality (LMI) technique, a state feedback controller is proposed to stabilize the PMSM systems. An illustrative example is provided to verify the validity of the results developed in this paper.

  5. Controlling chaos (OGY) implemented on a reconstructed ecological two-dimensional map

    We numerically demonstrate a way to stabilize an unstable equilibrium in the ecological dynamics reconstructed from real-world time series data, namely, alternate bearing of citrus trees. The reconstruction of deterministic dynamics from short and noisy ecological time series has been a crucial issue since May's historical work [May RM. Biological populations with nonoverlapping generations: stable points, stable cycles and chaos. Science 1974;186:645-7; Hassell MP, Lawton JH, May RM. Patterns of dynamical behavior in single species populations. J Anim Ecol 1976;45:471-86]. Response surface methodology, followed by the differential equation approach is recognized as a promising method of reconstruction [Turchin P. Rarity of density dependence or population with lags? Nature 1990;344:660-3; Turchin P, Taylor AD. Complex dynamics in ecological time series. Ecology 1992;73:289-305; Ellner S, Turchin P. Chaos in a noisy world: new method and evidence from time series analysis. Am Nat 1995;145(3):343-75; Turchin P, Ellner S. Living on the edge of chaos: population dynamics of fennoscandian voles. Ecology 2000;8(11):3116]. Here, the reconstructed ecological dynamics was described by a two-dimensional map derived from the response surface created by the data. The response surface created was experimentally validated in four one-year forward predictions in 2001, 2002, 2003 and 2004. Controlling chaos is very important when applying chaos theory to solving real-world problems. The OGY method is the first and most popular methodology for controlling chaos and can be used as an algorithm to stabilize an unstable fixed point by putting the state on a stable manifold [Ott E, Grebogi C, York JA. Controlling chaos. Phys Rev Lett 1990;64:1996-9]. We applied the OGY method to our reconstructed two-dimensional map and as a result were able to control alternate bearing in numerical simulations.

  6. Chaos of radiative heat-loss-induced flame front instability

    Kinugawa, Hikaru; Ueda, Kazuhiro; Gotoda, Hiroshi


    We are intensively studying the chaos via the period-doubling bifurcation cascade in radiative heat-loss-induced flame front instability by analytical methods based on dynamical systems theory and complex networks. Significant changes in flame front dynamics in the chaotic region, which cannot be seen in the bifurcation diagrams, were successfully extracted from recurrence quantification analysis and nonlinear forecasting and from the network entropy. The temporal dynamics of the fuel concentration in the well-developed chaotic region is much more complicated than that of the flame front temperature. It exhibits self-affinity as a result of the scale-free structure in the constructed visibility graph.

  7. Chaos Transfer in Fluidized Beds Accompanied with Biomass Pyrolysis

    唐松涛; 李定凯; 吕子安; 沈幼庭


    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.

  8. Elimination of spiral waves and spatiotemporal chaos by the synchronization transmission technology of network signals

    Zhang Qing-Ling; Lu Ling; Zhang Yi


    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.

  9. Symbolic dynamics-based error analysis on chaos synchronization via noisy channels

    Lin, Da; Zhang, Fuchen; Liu, Jia-Ming


    In this study, symbolic dynamics is used to research the error of chaos synchronization via noisy channels. The theory of symbolic dynamics reduces chaos to a shift map that acts on a discrete set of symbols, each of which contains information about the system state. Using this transformation, a coder-decoder scheme is proposed. A model for the relationship among word length, region number of a partition, and synchronization error is provided. According to the model, the fundamental trade-off between word length and region number can be optimized to minimize the synchronization error. Numerical simulations provide support for our results.

  10. Spatiotemporal chaos synchronization of an uncertain network based on sliding mode control

    The sliding mode control method is used to study spatiotemporal chaos synchronization of an uncertain network. The method is extended from synchronization between two chaotic systems to the synchronization of complex network composed of N spatiotemporal chaotic systems. The sliding surface of the network and the control input are designed. Furthermore, the effectiveness of the method is analysed based on the stability theory. The Burgers equation with spatiotemporal chaos behavior is taken as an example to simulate the experiment. It is found that the synchronization performance of the network is very stable