Control and Chaos

The articles in this Control and Chaos volume are an outgrowth of a US-Australia workshop held in Hawaii in 1995. Experts in dynamical systems theory and control theory from the US and Australia, as well as England and Japan, focused on the problem of controlling nonlinear and potentially chaotic systems using limited control effort. The formal contributions take into account the discussions and commentaries of the participants and are reflected at the end of each article. Part I contains papers dealing with modeling, behavior, reconstruction, prediction and numerics. Part II deals with controlling complex systems by means of embedding unstable periodic orbits, targeting, filtering, optimization and adaptive methods. Part III contains four applications papers including the control of a bouncing ball, evolutionary stability, chaos in ecosystems, and neural networks. Contents and Contributors: Understanding Complex Dynamics Triangulating Noisy Dynamical Systems S. Allie, A. Mees, K. Judd, D. Watson Attractor Reconstruction and Control Using Interspike Intervals T. Sauer Modeling Chaos from Experimental Data K. Judd, A. Mees Chaos in Symplectic Discretization of the Pendulum and Sine-Gordon Equations B.M. Herbst, C.M. Schober Collapsing Effects in Computation of Dynamical Systems P. Diamond, P. Kloeden, A. Pokrovskii Bifurications in the Falkner-Skan equation C. Sparrow Some Characterizations of Low-dimensional Dynamical Systems with Time-reversal Symmetry J.A.G. Roberts Controlling Complex Systems Control of Chaos by Means of Embedded Unstable Periodic Orbits E. Ott, B.R. Hunt Notch Filter Feedback Control for k-Period Motion in a Chaotic System W.J. Grantham, A.M. Athalye Targeting and Control of Chaos E.J. Kostelich, E. Barreto Adaptive Nonlinear Control: A Lyapunov Approach P.V. Kokotovic, M. Krstic Creating and Targeting Periodic Orbits K. Glass, M. Renton, K. Judd, A. Mees Dynamical Systems, Optimization, and Chaos J.B. Moore Combined Controls for Noisy Chaotic Systems M. Paskota, K.L. Teo, A. Mees Complex Dynamics in Adaptive Systems I.M.Y. Mareels Hitting Times to a Target for the Baker's Map A. Mazer Applications Controllable Targets Near a Chaotic Attractor T.L. Vincent The Dynamics of Evolutionary Stable Strategies Y. Cohen, T.L. Vincent Nitrogen Cycling and the Control of Chaos in a Boreal Forest Model J. Pastor, Y. Cohen Self-organization Dynamics in Chaotic Neural Networks M. Watanabe, K. Aihara, S. Kondo Series: Mathematical Modeling, Volume 8

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Chaos and Nonlinear Dynamics

Chaos and Nonlinear Dynamics introduces students, scientists, and engineers to the full range of activity in the rapidly growing field on nonlinear dynamics. Using a step-by-step introduction to dynamics and geometry in state space as the central focus of understanding nonlinear dynamics, thisbook includes a thorough treatment of both differential equation models and iterated map models (including a derivation of the famous Feigenbaum numbers). It is the only book at this level to include the increasingly important field of pattern formation and a survey of the controversial questions ofquantum chaos. Important tools such as Lyapunov exponents and fractal dimensions are treated in detail. With over 200 figures and diagrams, and analytic and computer exercises for every chapter, the book can be used as a course-text or for self-instruction. This second edition has been restructuredto make the book even more useful as a course text:many of the more complex examples and derivations have been moved to appendices. The extensive collection of annotated references has been updated through January 2000 and now includes listings of World Wide Web sites at many of the major nonlineardynamics research centers. From reviews on the 1/e: 'What has been lacking is a single book that takes the reader with nothing but a knowledge of elementary calculus and physics all the way to the frontiers of research in chaos and nonlinear dynamics in all its facets. [...] a serious student,teacher, or researcher would be delighted to have this book on the shelf as a reference and as a window to the literature in this exciting and rapidly growing new field of chaos.' J.C. Sprott, American Journal of Physics, September 19944 'I congratulate the author on having managed to write anextremely thorough, comprehensive, and entertaining introduction to the fascinating field of nonlinear dynamics. His book is highly self- explanatory and ideally suited for self-instruction. There is hardly any question that the author does not address in an exceptionally readable manner. [...] Istrongly recommend it to those looking for a comprehensive, practical, and not highly mathematical approach to the subject.' E.A. Hunt, IEEE Spectrum, December 1994

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Chaos Control

Chaos control refers to purposefully manipulating chaotic dynamical behaviors of some complex nonlinear systems. There exists no similar control theory-oriented book available in the market that is devoted to the subject of chaos control, written by control engineers for control engineers. World-renowned leading experts in the field provide their state-of-the-art survey about the extensive research that has been done over the last few years in this subject. The new technology of chaos control has major impact on novel engineering applications such as telecommunications, power systems, liquid mixing, internet technology, high-performance circuits and devices, biological systems modeling like the brain and the heart, and decision making. The book is not only aimed at active researchers in the field of chaos control involving control and systems engineers, theoretical and experimental physicists, and applied mathematicians, but also at a general audience in related fields.

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Chaos and Complexity Theory

Do decisions and ever-changing strategies make you believe that your organization operates in a state of chaos? Maybe it does - and for good reason. This issue describes the characteristics of chaos and complexity theory found in most organization and how it affects decisions and business management. A beginners guide shows you how to apply these complex theories to understand your organization and the direct consequences for trainers. A glossary of terms is provided as a guide to your baseline understanding of the field.

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Intelligent Computing Based on Chaos

Chaos is a fascinating phenomenon that has been observed in nature, laboratory, and has been applied in various real-world applications. Chaotic systems are deterministic with no random elements involved yet their behavior appears to be random. Obser- tions of chaotic behavior in nature include weather and climate, the dynamics of sat- lites in the solar system, the time evolution of the magnetic field of celestial bodies, population growth in ecology, to mention only a few examples. Chaos has been observed in the laboratory in a number of systems such as electrical circuits, lasers, chemical reactions, fluid dynamics, mechanical systems, and magneto-mechanical devices. Chaotic behavior has also found numerous applications in electrical and communication engineering, information and communication technologies, biology and medicine. To the best of our knowledge, this is the first book edited on chaos applications in intelligent computing. To access the latest research related to chaos applications in intelligent computing, we launched the book project where researchers from all over the world provide the necessary coverage of the mentioned field. The primary obj- tive of this project was to assemble as much research coverage as possible related to the field by defining the latest innovative technologies and providing the most c- prehensive list of research references.

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On the Order of Chaos

The essays in this volume collectively transform perspectives previously experienced as divergent, conflicting, and inconsistent into a common and complex orientation to problems central to the natural and social sciences involving transitions between order and disorder."--Jacket.

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Clinical Chaos

First published in 1999. Routledge is an imprint of Taylor & Francis, an informa company.

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Out of Chaos

Stresses the fact that refounding persons are essential for the revitalization of religious life.

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Chaos in Circuits and Systems

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 physicists in electrical, electronic, mechanical, physical, chemical and biomedical engineering and science.

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Chaos Based Digital Communication Systems

One of the first books in this area, this text focuses on important aspects of the system operation, analysis and performance evaluation of selected chaos-based digital communications systems – a hot topic in communications and signal processing.

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Nonlinear Phenomena and Chaos in Magnetic Materials

In this book, some of the principal investigators of the phenomena have reviewed their successes. The contributions include an overview of the field by H Suhl, followed by a detailed review of the high-power response of magnetic materials. Following that chapter, a number of authors review the phenomena for a variety of magnetic materials and pumping configurations.In the final chapter, evidence of another nonlinear effect is reviewed. Using a pulsed driving field, it is possible to excite a travelling spin wave. The nonlinear contributions will give rise to a ?bunching? effect which compensates for the dispersive effects to produce a shape-preserving traveling wave pulse known as solitons.Ordered magnetic materials have provided a rich source for the investigation of nonlinear phenomena. These investigations have contributed much to our knowledge of the behavior of chaotic systems, as well as to a better understanding of the high-power response of the magnetic materials themselves.

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Chaos and Order

The scientific discovery that chaotic systems embody deep structures of order is one of such wide-ranging implications that it has attracted attention across a spectrum of disciplines, including the humanities. In this volume, fourteen theorists explore the significance for literary and cultural studies of the new paradigm of chaotics, forging connections between contemporary literature and the science of chaos. They examine how changing ideas of order and disorder enable new readings of scientific and literary texts, from Newton's Principia to Ruskin's autobiography, from Victorian serial fiction to Borges's short stories. N. Katherine Hayles traces shifts in meaning that chaos has undergone within the Western tradition, suggesting that the science of chaos articulates categories that cannot be assimilated into the traditional dichotomy of order and disorder. She and her contributors take the relation between order and disorder as a theme and develop its implications for understanding texts, metaphors, metafiction, audience response, and the process of interpretation itself. Their innovative and diverse work opens the interdisciplinary field of chaotics to literary inquiry.

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The Transition to Chaos

Based on courses given at the University of Texas and the University of California, this book deals with the basic mechanisms that determine the dynamic evolution of classical and quantum systems. The book begins with a discussion of: Noether theorem, integrability, KAM theory, and a definition of chaotic behavior, then continues with a thorough look at: area-preserving maps, integrable quantum systems, spectral properties, path integrals, and periodically driven systems. It then concludes by showing how to apply the ideas to stochastic systems. This new edition is updated and contains a new chapter on open quantum systems.

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Chaos in Biological Systems

In recent years experimental and numerical studies have shown that chaos is a widespread phenomenon throughout the biological hierarchy ranging from simple enzyme reactions to ecosystems. Although a coherent picture of the fundamental mechanisms responsible for chaotic dynamics has started to appear it is not yet clear what the implications of such dynamics are for biological systems in general. In some systems it appears that chaotic dynamics are associated with a pathological condi tion. In other systems the pathological condition has regular periodic dynamics whilst the normal non-pathological condition has chaotic dyna mics. Since chaotic behaviour is so ubiquitous in nature and since the phenomenon raises some fundamental questions about its implications for biology it seemed timely to organize an interdisciplinary meeting at which leading scientists could meet to exchange ideas, to evaluate the current state of the field and to stipulate the guidelines along which future research should be directed. The present volume contains the contributions to the NATO Advanced Research Workshop on "Chaos in Biological Systems" held at Dyffryn House, St. Nicholas, Cardiff, U. K. , December 8-12, 1986. At this meeting 38 researchers with highly different backgrounds met to present their latest results through lectures and posters and to discuss the applica tions of non-linear techniques to problems of common interest. . In spite of their involvement in the study of chaotic dynamics for several years many of the participants met here for the first time.

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Chaos and Society

This publication reflects on the discussion on using chaos theory for the study of society. It explores the interface between chaos theory and the social sciences. A broad variety of fields (including Sociology, Anthropology, Economics, Political Science, Management, Philosophy and Cognitive Sciences) is represented in the book. The leading themes are: Conceptual and Methodological Issues, Social Connectionism and the Connectionist Mind, Social Institutions and Public Policy, and Social Simulations. The book includes the following topics: the relevance of the complexity-chaos paradigm for analyzing social systems, the usefulness of nonlinear dynamics for studying the formation and sustainability of social groups, the comparison between spontaneous social orders and spontaneous biological/natural orders, the building of Artificial Societies, and the contribution of the chaos paradigm to a better understanding and formulation of public policies.

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Directions in Chaos

Volume 2 of Directions in Chaos consists of the contributions made to the Beijing Summer School on Chaotic Phenomena in Nonlinear Systems held in August 1987.

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From Clocks to Chaos

In an important new contribution to the literature of chaos, two distinguished researchers in the field of physiology probe central theoretical questions about physiological rhythms. Topics discussed include: How are rhythms generated? How do they start and stop? What are the effects of perturbation of the rhythms? How are oscillations organized in space? Leon Glass and Michael Mackey address an audience of biological scientists, physicians, physical scientists, and mathematicians, but the work assumes no knowledge of advanced mathematics. Variation of rhythms outside normal limits, or appearance of new rhythms where none existed previously, are associated with disease. One of the most interesting features of the book is that it makes a start at explaining "dynamical diseases" that are not the result of infection by pathogens but that stem from abnormalities in the timing of essential functions. From Clocks to Chaos provides a firm foundation for understanding dynamic processes in physiology.

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Chaos Nonlinearity Complexity

This book explores non-extensive statistical mechanics in non-equilibrium thermodynamics, and presents an overview of the strong nonlinearity of chaos and complexity in natural systems, drawing on relevant mathematics from topology, measure-theory, inverse and ill-posed problems, set-valued analysis, and nonlinear functional analysis. It offers a self-contained theory of complexity and complex systems as the steady state of non-equilibrium systems, denoting a homeostatic dynamic equilibrium between stabilizing order and destabilizing disorder.

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Joyce Chaos and Complexity

Joyce, Chaos, and Complexity studies the manifold relations among twentieth-century mathematics and Science, James Joyce's fiction, and the critical reception of Joyce's work. Calling for profound reassessments, Thomas Jackson Rice compellingly argues that Joyce's work resists postmodernist approaches of ambiguity: Joyce never abandoned his conviction that reality exists, regardless of the human ability to represent it. Placing Joyce in his cultural context, Rice first provocatively traces the previously unacknowledged formative influence of Euclidean and non-Euclidean geometries on Dubliners and A Portrait of the Artist as a Young Man. He then demonstrates that, when later innovations in science transformed entire worldviews, Joyce recognized conventional literary modes of representation as offering merely arbitrary constructions of this new reality. Joyce responded to these developmeats in Ulysses by experimenting with perspective, embedding design, and affirming the existence of reality. Rice contends that Ulysses is a precursor to the multiple tensions of chaos theory; likewise, chaos theory can serve as a model for understanding Ulysses. In Finnegans Wake Joyce consummates his vision and anticipates the theories of complexity science through a dynamic approximation of reality.

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Chaos Complexity and Sociology

The authors of this volume provide a timely collection of articles which examine the emerging myths and theories surrounding the study of chaos and complexity. In the second part methodological matters are considered. Finally, conceptual models and applications are presented. This perceptive and thorough volume will be useful to sociologists and others interested in chaos and complexity theory.

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