Control and Chaos

This is made possible by the unique properties of chaos. In particular, chaotic
attractors typically have an infinite dense set of unstable periodic orbi ts
embedded within them. In this paper we review aspects of controlling chaos by
means of ...

Author: Kevin Judd

Publisher: Springer Science & Business Media

ISBN: 9780817638672

Category: Language Arts & Disciplines

Page: 333

View: 969

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

Chaos and Nonlinear Dynamics

When we consider the case of chaos , there does not seem to be a common
physical explanation . What we do find in common is the behavior of the models
in an abstract state space , the details of which we shall introduce in Chapters 3
and 4 ...

Author: Robert C. Hilborn

Publisher: Oxford University Press on Demand

ISBN: 9780198507239

Category: Mathematics

Page: 650

View: 901

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

Chaos Control

This chapter provides an overview of the state of the art of current chaos
communication schemes and introduces the use of signal processing to improve
the communication performances . Popular communication schemes in the
literature ...

Author: Guanrong Chen

Publisher: Springer Science & Business Media

ISBN: 9783540404057

Category: Technology & Engineering

Page: 374

View: 693

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.

Chaos and Complexity Theory

For this reason , chaos and complexity theory is applicable to organizations . This
Info - line will define chaos and complexity theory and apply this theory to
business management . By describing the characteristics of chaos and
complexity ...

Author: T. J. Titcomb

Publisher: American Society for Training and Development

ISBN: 9781562862299

Category: Business & Economics

Page: 16

View: 333

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.

Intelligent Computing Based on Chaos

Chaos-Based. Cryptography. Jose Maria Amigo Centro de Investigacion
Operativa, Universidad Miguel Hernandez Avda. ... To begin with, it appeared
outside conventional cryptography, first as an application of chaos theory [56].
and a short ...

Author: Ljupco Kocarev

Publisher: Springer Science & Business Media

ISBN: 3540959718

Category: Mathematics

Page: 380

View: 706

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.

On the Order of Chaos

Social Anthropology and the Science of Chaos Mark S. Mosko, Frederick H.
Damon. 8 Afterword Order is What Happens When Chaos Loses Its Temper Roy
Wagner Heuristic Modeling and the Self - Validation of Deception The so - called
 ...

Author: Mark S. Mosko

Publisher: Berghahn Books

ISBN: 9781845450243

Category: Social Science

Page: 276

View: 549

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.

Clinical Chaos

Intermittent chaos, self-organization, and learning from synchronous synaptic
activity in model neuron networks. Proceedings of the National Academy of
Science, USA, 86(9), 2991-2995. Kaplan, D. T., & Cohen, R.J. (1990). Is
fibrillation chaos ...

Author: Linda Chamberlain

Publisher: Routledge

ISBN: 1317714776

Category: Psychology

Page: 242

View: 361

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

Out of Chaos

The Biblical Notion of "Chaos" The word "chaos" was used by the ancient Greeks
to describe the amorphous state of primeval matter prior to creation. This concept
of a murky and watery primitive world-mass, found also in Egypt and ...

Author: Gerald A. Arbuckle

Publisher: Paulist Press

ISBN: 9780809130047

Category: Religion

Page: 201

View: 406

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

Chaos in Circuits and Systems

Some New Circuit Design for Chaos Generation K . S . Tang , K . F . Man , G . Q .
Zhong and G . Chen Centre for Chaos Control and Synchronization Department
of Electronic Engineering City University of Hong Kong , Hong Kong , China ...

Author: Guanrong Chen

Publisher: World Scientific

ISBN: 9789812705303

Category: Mathematics

Page: 656

View: 659

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.

Chaos Based Digital Communication Systems

Chaos generator + s ( t ) Delay of Тр Х +1 or -1 depending on the symbol being
sent ( a ) 1 Correlator | y ( IT ) r ( t ) Х ST , ( . ) dt Recovered symbol Chaos
generator fi ( t ) Х s ( t. Threshold detector Delay of Тр ( b ) Fig . 2.14 . Correlation
- delay ...

Author: Francis C.M. Lau

Publisher: Springer Science & Business Media

ISBN: 9783540006022

Category: Computers

Page: 228

View: 170

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.

Nonlinear Phenomena and Chaos in Magnetic Materials

CHAPTER 6 STRONG CHAOS IN MAGNETIC RESONANCE M. Warden Physics
Institute , University of Zürich , Zürich , Switzerland 1. Introduction In 1974
Zakharov , L'vov , and Starobinets ( 1 ) published an article with the title : " Spin -
wave ...

Author: Philip E. Wigen

Publisher: World Scientific

ISBN: 9789810210052

Category: Science

Page: 248

View: 930

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.

Chaos and Order

Chaos. of. Metafiction. Peter Stoicheff It seems, at first, curious that metafictional
texts possess characteristics of chaotic systems in the phenomenal world, but
they do. I want to present four main characteristics shared by them: nonlinearity,
self- ...

Author: N. Katherine Hayles

Publisher: University of Chicago Press

ISBN: 9780226321448

Category: Literary Criticism

Page: 308

View: 943

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.

The Transition to Chaos

Probably the most widely studied systems , as regards the transition to chaos ,
are systems driven by time - periodic external fields . With a timeperiodic force ,
one can cause a nonlinear system , with only one degree of freedom , to undergo
a ...

Author: Linda Reichl

Publisher: Springer Science & Business Media

ISBN: 9780387987880

Category: Science

Page: 675

View: 461

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.

Chaos in Biological Systems

Author: Hans Degn

Publisher: Springer Science & Business Media

ISBN: 9780306426858

Category: Science

Page: 326

View: 945

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.

Chaos and Society

If social chaoticians want to be taken seriously they must avoid using complexity
and chaos theory as a metaphor to support existing theories rather than a
rigorous methodological process . 1 . The Development of Complexity For
generations ...

Author: A. Albert

Publisher: IOS Press

ISBN: 9789051992144

Category: Computers

Page: 386

View: 679

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.

Directions in Chaos

THE PasT Because quantum mechanics is presumed to contain classical
mechanics as a special case and because classical systems are known to exhibit
chaos, many investigators regard the existence of quantum chaos as an
indisputable ...

Author: Bai-lin Hao

Publisher: World Scientific

ISBN: 9789971503628

Category: Science

Page: 400

View: 394

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.

From Clocks to Chaos

Chapter 3 Noise and Chaos Experimental observation of physiological systems
often reveals data that are not constant in time and do not show regular
periodicities . Such irregularity is often associated with noise , or random
stochastic ...

Author: Leon Glass

Publisher: Princeton University Press

ISBN: 9780691084961

Category: Science

Page: 248

View: 488

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.

Chaos Nonlinearity Complexity

6 The Role of Chaos and Resonances in Brownian Motion John Realpe1 and
Gonzalo Ordonez2 1 Departamento de Física, Universidad del Valle, A.A. 25360,
Cali, COLOMBIA, 2The University of Texas at Austin, University Station, Austin, ...

Author: Ashok Sengupta

Publisher: Springer Science & Business Media

ISBN: 3540317562

Category: Computers

Page: 358

View: 401

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.

Joyce Chaos and Complexity

ULYSSES, CHAOS, AND COMPLEXITY Pause. J. J. O'Molloy took out his
cigarettecase. False lull. Something quite ordinary. Messenger took out his
matchbox thoughtfully and lit his cigar. I have often thought since on looking back
over that ...

Author: Thomas Jackson Rice

Publisher: University of Illinois Press

ISBN: 9780252065835

Category: Literary Criticism

Page: 204

View: 706

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.

Chaos Complexity and Sociology

11 - Chaos and Social Reality An Emergent Perspective R. J. Bird One etymology
of the word " chaos " is " gap " —that which lies in the gap between heaven and
earth . Between physics and God lie many sciences . Can the nature of these ...

Author: Raymond A. Eve

Publisher: SAGE

ISBN: 9780761908906

Category: Social Science

Page: 328

View: 640

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.