Applied Symbolic Dynamics And Chaos

Author : Hao Bailin,Zheng Wei-mou
Publisher : World Scientific
Page : 520 pages
File Size : 41,5 Mb
Release : 2018-05-11
Category : Science
ISBN : 9789813236448

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Applied Symbolic Dynamics And Chaos (Second Edition) by Hao Bailin,Zheng Wei-mou Pdf

Symbolic dynamics is a coarse-grained description of dynamics. It has been a long-studied chapter of the mathematical theory of dynamical systems, but its abstract formulation has kept many practitioners of physical sciences and engineering from appreciating its simplicity, beauty, and power. At the same time, symbolic dynamics provides almost the only rigorous way to understand global systematics of periodic and, especially, chaotic motion in dynamical systems. In a sense, everyone who enters the field of chaotic dynamics should begin with the study of symbolic dynamics. However, this has not been an easy task for non-mathematicians. On one hand, the method of symbolic dynamics has been developed to such an extent that it may well become a practical tool in studying chaotic dynamics, both on computers and in laboratories. On the other hand, most of the existing literature on symbolic dynamics is mathematics-oriented. This book is an attempt at partially filling up this apparent gap by emphasizing the applied aspects of symbolic dynamics without mathematical rigor. Contents: Preface to the Second Edition Preface to the First Edition Introduction Symbolic Dynamics of Unimodal Maps Maps with Multiple Critical Points Symbolic Dynamics of Circle Maps Symbolic Dynamics of Two-Dimensional Maps Application to Ordinary Differential Equations Counting the Number of Periodic Orbits Symbolic Dynamics and Grammatical Complexity Symbolic Dynamics and Knot Theory Appendix References Index Readership: Researchers and students interested in chaotic dynamics. Keywords: Symbolic Dynamics;ChaosReview: Key Features: No previous knowledge of dynamical systems theory is required in order to read this book The revisions concern mainly the application to ordinary differential equations via constructing two-dimensional symbolic dynamics of the corresponding Poincare maps

Author : Bailin Hao,Wei-mou Zheng
Publisher : World Scientific
Page : 460 pages
File Size : 50,5 Mb
Release : 1998-07-04
Category : Science
ISBN : 9789814495974

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Applied Symbolic Dynamics And Chaos by Bailin Hao,Wei-mou Zheng Pdf

Latest Edition: Applied Symbolic Dynamics and Chaos (2nd Edition)Symbolic dynamics is a coarse-grained description of dynamics. It provides a rigorous way to understand the global systematics of periodic and chaotic motion in a system. In the last decade it has been applied to nonlinear systems described by one- and two-dimensional maps as well as by ordinary differential equations. This book will help practitioners in nonlinear science and engineering to master that powerful tool.

Author : Bai-lin Hao,Wei-Mou Zheng
Publisher : World Scientific
Page : 468 pages
File Size : 47,6 Mb
Release : 1998
Category : Science
ISBN : 9810235127

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Applied Symbolic Dynamics and Chaos by Bai-lin Hao,Wei-Mou Zheng Pdf

Symbolic dynamics is a coarse-grained description of dynamics. It provides a rigorous way to understand the global systematics of periodic and chaotic motion in a system. In the last decade it has been applied to nonlinear systems described by one- and two-dimensional maps as well as by ordinary differential equations. This book will help practitioners in nonlinear science and engineering to master that powerful tool.

Author : Hao Bailin
Publisher : World Scientific
Page : 476 pages
File Size : 42,7 Mb
Release : 1989-09-01
Category : Science
ISBN : 9789814520010

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Elementary Symbolic Dynamics and Chaos in Dissipative Systems by Hao Bailin Pdf

This book is a monograph on chaos in dissipative systems written for those working in the physical sciences. Emphasis is on symbolic description of the dynamics and various characteristics of the attractors, and written from the view-point of practical applications without going into formal mathematical rigour. The author used elementary mathematics and calculus, and relied on physical intuition whenever possible. Substantial attention is paid to numerical techniques in the study of chaos. Part of the book is based on the publications of Chinese researchers, including those of the author's collaborators. Contents:Mathematical Models Exhibiting ChaosOne Dimensional MappingsElementary Symbolic DynamicsCircle Mappings and Two-Dimensional MapsChaos in Ordinary Differential EquationsCharacterization of Chaotic AttractorsTransient Behaviour Readership: Condensed matter physicists, applied mathematicians and computer scientists. Keywords:Symbolic Dynamics;One Dimensional Mappings;Circle Mapping;Two-Dimensional Maps;Chaotic Attractors;Transient Behaviour

Author : Bai-lin Hao
Publisher : World Scientific
Page : 472 pages
File Size : 43,5 Mb
Release : 1990
Category : Mathematics
ISBN : 9810200943

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Experimental Study and Characterization of Chaos by Bai-lin Hao Pdf

This is a continuation of the previous two volumes of review papers on chaotic dynamics and related topics, published in 1987 and 1988 respectively. In addition to a few reviews written by active researchers specially for the volume, it also contains several reviews based on lectures delivered at the Spring School on Experimental Study of Chaotic Phenomena, held in Tianjing, China, in May 1989, and at the session on Nonlinear Dynamics during the Workshop on Condensed Matter, Molecular and Atomic Physics, held in June - August, 1989, at the International Centre for Theoretical Physics at Trieste, Italy. The emphasis has been made on multifractals, applied symbolic dynamics, the role of unstable orbits and transient chaos. This volume would be useful to graduate students and researchers in physical sciences and engineering.

Author : Bailin Hao
Publisher : World Scientific
Page : 476 pages
File Size : 52,7 Mb
Release : 1990-05-01
Category : Science
ISBN : 9789814507110

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Experimental Study And Characterization Of Chaos: A Collection Of Reviews And Lecture Notes by Bailin Hao Pdf

This is a continuation of the previous two volumes of review papers on chaotic dynamics and related topics, published in 1987 and 1988 respectively. In addition to a few reviews written by active researchers specially for the volume, it also contains several reviews based on lectures delivered at the Spring School on Experimental Study of Chaotic Phenomena, held in Tianjing, China, in May 1989, and at the session on Nonlinear Dynamics during the Workshop on Condensed Matter, Molecular and Atomic Physics, held in June - August, 1989, at the International Centre for Theoretical Physics at Trieste, Italy. The emphasis has been made on multifractals, applied symbolic dynamics, the role of unstable orbits and transient chaos. This volume would be useful to graduate students and researchers in physical sciences and engineering.

Author : John H. Lowenstein
Publisher : Springer Science & Business Media
Page : 215 pages
File Size : 51,5 Mb
Release : 2013-07-30
Category : Science
ISBN : 9783642281549

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Pseudochaotic Kicked Oscillators by John H. Lowenstein Pdf

"Pseudochaotic Kicked Oscillators: Renormalization, Symbolic Dynamics, and Transport" presents recent developments in pseudochaos, which is concerned with complex branching behaviors of dynamical systems at the interface between orderly and chaotic motion. Pseudochaos is characterized by the trapping of orbits in the vicinity of self-similar hierarchies of islands of stability, producing phase-space displacements which increase asymptotically as a power of time. This monograph is a thorough, self-contained investigation of a simple one-dimensional model (a kicked harmonic oscillator) which exhibits pseudochaos in its purest form. It is intended for graduate students and researchers in physics and applied mathematics, as well as specialists in nonlinear dynamics. Dr. John H. Lowenstein is a Professor Emeritus in the Department of Physics at New York University, USA.

Author : Santo Banerjee,Lamberto Rondoni
Publisher : Springer
Page : 296 pages
File Size : 46,7 Mb
Release : 2013-06-12
Category : Science
ISBN : 9783642340178

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Applications of Chaos and Nonlinear Dynamics in Science and Engineering - Vol. 3 by Santo Banerjee,Lamberto Rondoni Pdf

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 quantitative modeling and analysis of complex, nonlinear phenomena is required, chaos theory and its methods can play a key role. This third 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 fluctuation relations and chaotic dynamics in physics, fractals and their applications in epileptic seizures, as well as chaos synchronization. Featuring contributions from active and leading research groups, this collection is ideal both as a reference and as a ‘recipe book’ full of tried and tested, successful engineering applications.

Author : Alwyn Scott
Publisher : Routledge
Page : 1107 pages
File Size : 50,5 Mb
Release : 2006-05-17
Category : Reference
ISBN : 9781135455583

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Encyclopedia of Nonlinear Science by Alwyn Scott Pdf

In 438 alphabetically-arranged essays, this work provides a useful overview of the core mathematical background for nonlinear science, as well as its applications to key problems in ecology and biological systems, chemical reaction-diffusion problems, geophysics, economics, electrical and mechanical oscillations in engineering systems, lasers and nonlinear optics, fluid mechanics and turbulence, and condensed matter physics, among others.

Author : Sabu M. Thampi,Erol Gelenbe,Mohammed Atiquzzaman,Vipin Chaudhary,Kuan-Ching Li
Publisher : Springer Nature
Page : 705 pages
File Size : 42,6 Mb
Release : 2021-04-20
Category : Technology & Engineering
ISBN : 9789813369771

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Advances in Computing and Network Communications by Sabu M. Thampi,Erol Gelenbe,Mohammed Atiquzzaman,Vipin Chaudhary,Kuan-Ching Li Pdf

This book constitutes the thoroughly refereed post-conference proceedings of the 4th International Conference on Computing and Network Communications (CoCoNet'20), October 14–17, 2020, Chennai, India. The papers presented were carefully reviewed and selected from several initial submissions. The papers are organized in topical sections on Signal, Image and Speech Processing, Wireless and Mobile Communication, Internet of Things, Cloud and Edge Computing, Distributed Systems, Machine Intelligence, Data Analytics, Cybersecurity, Artificial Intelligence and Cognitive Computing and Circuits and Systems. The book is directed to the researchers and scientists engaged in various fields of computing and network communication domains.

Author : Susan G. Williams,American Mathematical Society. Short Course,Short Course on Symbolic Dynamics and Its Applications,American Mathematical Society
Publisher : American Mathematical Soc.
Page : 168 pages
File Size : 46,6 Mb
Release : 2004
Category : Symbolic dynamics
ISBN : 9780821831571

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Symbolic Dynamics and its Applications by Susan G. Williams,American Mathematical Society. Short Course,Short Course on Symbolic Dynamics and Its Applications,American Mathematical Society Pdf

Symbolic dynamics originated as a tool for analyzing dynamical systems and flows by discretizing space as well as time. The development of information theory gave impetus to the study of symbol sequences as objects in their own right. Today, symbolic dynamics has expanded to encompass multi-dimensional arrays of symbols and has found diverse applications both within and beyond mathematics. This volume is based on the AMS Short Course on Symbolic Dynamics and its Applications. It contains introductory articles on the fundamental ideas of the field and on some of its applications. Topics include the use of symbolic dynamics techniques in coding theory and in complex dynamics, the relation between the theory of multi-dimensional systems and the dynamics of tilings, and strong shift equivalence theory. Contributors to the volume are experts in the field and are clear expositors. The book is suitable for graduate students and research mathematicians interested in symbolic dynamics and its applications.

Author : Neal B. Abraham,Alfonso M. Albano,Anthony Passamante,Paul E. Rapp
Publisher : Springer Science & Business Media
Page : 466 pages
File Size : 47,8 Mb
Release : 2013-03-09
Category : Technology & Engineering
ISBN : 9781475706239

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Measures of Complexity and Chaos by Neal B. Abraham,Alfonso M. Albano,Anthony Passamante,Paul E. Rapp Pdf

This volume serves as a general introduction to the state of the art of quantitatively characterizing chaotic and turbulent behavior. It is the outgrowth of an international workshop on "Quantitative Measures of Dynamical Complexity and Chaos" held at Bryn Mawr College, June 22-24, 1989. The workshop was co-sponsored by the Naval Air Development Center in Warminster, PA and by the NATO Scientific Affairs Programme through its special program on Chaos and Complexity. Meetings on this subject have occurred regularly since the NATO workshop held in June 1983 at Haverford College only two kilometers distant from the site of this latest in the series. At that first meeting, organized by J. Gollub and H. Swinney, quantitative tests for nonlinear dynamics and chaotic behavior were debated and promoted [1). In the six years since, the methods for dimension, entropy and Lyapunov exponent calculations have been applied in many disciplines and the procedures have been refined. Since then it has been necessary to demonstrate quantitatively that a signal is chaotic rather than it being acceptable to observe that "it looks chaotic". Other related meetings have included the Pecos River Ranch meeting in September 1985 of G. Mayer Kress [2) and the reflective and forward looking gathering near Jerusalem organized by M. Shapiro and I. Procaccia in December 1986 [3). This meeting was proof that interest in measuring chaotic and turbulent signals is widespread.

Author : Cheuk-yin Wong,Pisin Chen
Publisher : World Scientific
Page : 474 pages
File Size : 51,9 Mb
Release : 2000-04-05
Category : Electronic
ISBN : 9789814543002

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Recent Advances And Cross-century Outlooks In Physics: Interplay Between Theory And Experiment by Cheuk-yin Wong,Pisin Chen Pdf

Author : American Mathematical Society
Publisher : American Mathematical Society(RI)
Page : 166 pages
File Size : 50,5 Mb
Release : 2014-05-10
Category : MATHEMATICS
ISBN : 0821892754

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Symbolic Dynamics and Its Applications by American Mathematical Society Pdf

Symbolic dynamics originated as a tool for analyzing dynamical systems and flows by discretizing space as well as time. The development of information theory gave impetus to the study of symbol sequences as objects in their own right. Today, symbolic dynamics has expanded to encompass multi-dimensional arrays of symbols and has found diverse applications both within and beyond mathematics. This volume is based on the AMS Short Course on Symbolic Dynamics and its Applications. It some of its applications. Topics include the use of symbolic dynamics techniques in coding theory and in complex dynamics, the relation between the theory of multi-dimensional systems and the dynamics of tilings, and strong and are clear expositors. The book is suitable for graduate students and research mathematicians interested in symbolic dynamics and its applications.

Author : Daniel Kaplan,Leon Glass
Publisher : Springer Science & Business Media
Page : 438 pages
File Size : 53,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461208235

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Understanding Nonlinear Dynamics by Daniel Kaplan,Leon Glass Pdf

Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics ( TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mathematical Sciences (AMS) series, which will focus on advanced textbooks and research level monographs. About the Authors Daniel Kaplan specializes in the analysis of data using techniques motivated by nonlinear dynamics. His primary interest is in the interpretation of irregular physiological rhythms, but the methods he has developed have been used in geo physics, economics, marine ecology, and other fields. He joined McGill in 1991, after receiving his Ph.D from Harvard University and working at MIT. His un dergraduate studies were completed at Swarthmore College. He has worked with several instrumentation companies to develop novel types of medical monitors.