Chaotic Dynamics: An Introduction

Book Description

The previous edition of this text was the first to provide a quantitative introduction to chaos and nonlinear dynamics at the undergraduate level. It was widely praised for the clarity of writing and for the unique and effective way in which the authors presented the basic ideas. These same qualities characterize this revised and expanded second edition. Interest in chaotic dynamics has grown explosively in recent years. Applications to practically every scientific field have had a far-reaching impact. As in the first edition, the authors present all the main features of chaotic dynamics using the damped, driven pendulum as the primary model. This second edition includes additional material on the analysis and characterization of chaotic data, and applications of chaos. This new edition of Chaotic Dynamics can be used as a text for courses on chaos for physics and engineering students at the second- and third-year level.

Customer Reviews:

From the pendulum to chaos in straightforward steps.......1998-05-06

Books that take you from undergraduate physics to a nontrivial understanding of nonlinear dynamics, chaos and fractals are rare. Chaotic Dynamics does the job ellegantly. The familiar pendulum is used to illustrate the basic techniques and concepts in nonlinear dynamics. The reader is gently introduced to phase diagrams, Poincare sections, basins of attraction and bifurcation diagrams. Computer code is included in the Appendix. The interested reader can use this code to further illustrate the lessons of the text or to embark on his/her own exploration of the pendulum and other dynamical systems. Having used the pendulum to establish a firm conceptual platform, Baker and Gollub progress gracefully into the logistic map to illustrate concepts such as period doubling, Lyapunov exponent, entropy, stretching and folding, and various measures of fractal dimension. The presentation is nicely rounded off with studies of other maps and nonlinear dynamical systems from a range of fields in physics, chemistry and fluid dynamics.

Chaos and True Basic Code.......1998-03-20

The gateway to experimental chaos research comes through here! The mathematics, the examples and code that illustrates the book is here. It is somewhat narrow in it's beginning approach, but delivers after careful study a beginning of understanding with some real industry. Not for the mathemaically shy or Professors like Ruelle, but for real people wanting real answers! Your unique Associates ID is: thefractaltransl.

Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers

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A good book for introduction
An excellent introduction
A excellent introduction to chaos
fundamental, systematic
Good book!

Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers
Robert Hilborn
Manufacturer: Oxford University Press, USA
ProductGroup: Book
Binding: Paperback

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ASIN: 0198507232

Book Description

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, this book 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 of quantum 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 restructured to 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 nonlinear dynamics 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 an extremely 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. [...] I strongly recommend it to those looking for a comprehensive, practical, and not highly mathematical approach to the subject.' E.A. Hunt, IEEE Spectrum, December 1994

Customer Reviews:

A good book for introduction.......2007-05-22

I have recently bought this book. I have been studying on evolution of the test particles in a particular planewave spacetimes, and I have realized that the system admits a non-integrable structure. I should investigate whether the particle motion emerges chaos or not. But, my knowledge on chaos was almost zero, before buying this book. Now, I am going to complete the full analysis of the book, and I am much more familiar to the concept of chaos. However, this book can be used for just begining. To proceed to the advanced problems you should look for other materials, especially to the articles about chaos. I advise this book as a first book to start chaos.
Dr. Izzet Sakalli

An excellent introduction.......2007-03-09

Covers the basics in an in-depth manner, and exposes the reader to a wide range of exciting problems in dynamical systems theory. THE book to start with if one is interested in chaos.

A excellent introduction to chaos.......2003-11-25

This is an accessible and readable introductory textbook on chaos and nonlinear dynamics. It focuses on the ideas behind the theory of chaos, rather than on the details of the mathematics which can sometimes hinder rather than help the reader gain real insight into the mechanisms of nonlinear systems.

By this I do not mean that the author skips over the required mathematics. The text is intended for people with a solid background in differential equations, and some familiarity with classical dynamical systems is also helpful if not completely necessary. I would say it is targeted for advanced undergraduate or beginning graduate students in the mathematical sciences, as well as scientists/engineers with no background in chaos theory. However he does not get bogged down in mathematics at the expense of physical insight. I have been studying the book on my own and have run into few problems in understanding the explanations.

The first chapter goes over 3 chaotic systems as a practical way of introducing the reader to various features of such systems. This provides a basis of practical experience to draw upon for the rest of the book, where the principles of chaos are examined in greater detail. The extensive references given in the book are a valuable addition that can be used to further explore the scientific literature. The references include journal papers as well as books, articles, and software for dynamical systems.

If you have the requisite mathematical background and want to learn the basics of chaos and nonlinear dynamics, I highly recommend this book.

fundamental, systematic.......2001-11-07

If you are looking for a textbook or reference on chaos theory, I recommend you to buy this book.

If you read other books, you will eventually comment,'chaos is something related to mathematics, very abstract, has nothing to do with my messy bedroom...'

But if you read this book, you will scream,'Great! I have figured out the richness of the nonlinear world. I understand the different dynamical routes to chaos. I know different quantifying methods with their pros and cons. Most fascinating is that chaos is related to pattern formation and self organization, which I consider them as another field of knowledge before. Also chaos may provide a new approach to quantum mechanics, a good news for those including me who do not believe in the parallel universe interpretation. By the way, I learnt a lot from this book!'

Good book!.......2000-08-05

If you want to get on into chaos, just read this book. I especially like the very wide scope of the subjects considered and the insight provided by the author in pattern formation or quantum chaos.

Introduction to Control of Oscillations and Chaos (World Scientific Series on Nonlinear Science. Series a, Monographs and Treatises, V. 35)

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Introduction to Control of Oscillations and Chaos (World Scientific Series on Nonlinear Science. Series a, Monographs and Treatises, V. 35)
A. L. Fradkov , and Alexander L. Fradkov
Manufacturer: World Scientific Publishing Company
ProductGroup: Book
Binding: Hardcover

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ASIN: 9810230699

Book Description

This book gives an exposition of the exciting field of control of oscillatory and chaotic systems, which has numerous potential applications in mechanics, laser and chemical technologies, communications, biology and medicine, economics, ecology, etc.

A novelty of the book is its systematic application of modern nonlinear and adaptive control theory to the new class of problems. The proposed control design methods are based on the concepts of Lyapunov functions, Poincare maps, speed-gradient and gradient algorithms. The conditions which ensure such control goals as an excitation or suppression of oscillations, synchronization and transformation from chaotic mode to the periodic one or vice versa, are established. The performance and robustness of control systems under disturbances and uncertainties are evaluated.

The described methods and algorithms are illustrated by a number of examples, including classical models of oscillatory and chaotic systems: coupled pendula, brusselator, Lorenz, Van der Pol, Duffing, Henon and Chua systems. Practical examples from different fields of science and technology such as communications, growth of thin films, synchronization of chaotic generators based on tunnel diods, stabilization of swings in power systems, increasing predictability of business-cycles are also presented.

The book includes many results on nonlinear and adaptive control published previously in Russian and therefore were not known to the West.

Book Description

What is calculus really for? This book is a highly readable introduction to applications of calculus, from Newton's time to the present day. These often involve questions of dynamics, i.e. of how - and why - things change with time. Problems of this kind lie at the heart of much of applied mathematics, physics, and engineering. From Calculus to Chaos takes a fresh approach to the subject as a whole, by moving from first steps to the frontiers, and by highlighting only the most important and interesting ideas, which can get lost amid a snowstorm of detail in conventional texts. The book is aimed at a wide readership, and assumes only some knowledge of elementary calculus. There are exercises (with full solutions) and simple but powerful computer programs which are suitable even for readers with no previous computing experience. David Acheson's book will inspire new students by providing a foretaste of more advanced mathematics and showing just how interesting the subject can be.

Customer Reviews:

Recommended.......1999-10-30

The author manages to express in an easily understandable form many of the more interesting applications of calculus, from planetary motion to the Indian Rope Trick (almost). This book is ideally suited for first year undergraduates and sixth-formers with a strong interest in Mechanics. All those doing maths at Oxford University MUST buy this book (the author spends most of the lectures making references to it and to not buy the book would be to not understand the mechanics course).

Introduction to Applied Nonlinear Dynamical Systems and Chaos (Texts in Applied Mathematics)

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Great reference or grad school level course text on general nonlinear dynamics
Effective overview of a useful subject

Introduction to Applied Nonlinear Dynamical Systems and Chaos (Texts in Applied Mathematics)
Stephen Wiggins
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 0387001778

Book Description

This volume is intended for advanced undergraduate or first-year graduate students as an introduction to applied nonlinear dynamics and chaos. The author has placed emphasis on teaching the techniques and ideas that will enable students to take specific dynamical systems and obtain some quantitative information about the behavior of these systems. He has included the basic core material that is necessary for higher levels of study and research. Thus, people who do not necessarily have an extensive mathematical background, such as students in engineering, physics, chemistry, and biology, will find this text as useful as students of mathematics.

This new edition contains extensive new material on invariant manifold theory and normal forms (in particular, Hamiltonian normal forms and the role of symmetry). Lagrangian, Hamiltonian, gradient, and reversible dynamical systems are also discussed. Elementary Hamiltonian bifurcations are covered, as well as the basic properties of circle maps. The book contains an extensive bibliography as well as a detailed glossary of terms, making it a comprehensive book on applied nonlinear dynamical systems from a geometrical and analytical point of view.

Customer Reviews:

Great reference or grad school level course text on general nonlinear dynamics.......2007-04-15

This book served as the "hidden basis" for a course in nonlinear dynamics by the late John David Crawford back at the University of Pittsburgh (the overt basis was Glendinning's book, which has proved less appealing as a reference). It's subsequently been useful to me in its treatment of Melnikov's method, and to review ideas in bifurcation theory.

As the other reviewer pointed out, it is weak in the section on symbolic dynamics. In its defense, I only know of one book which treats symbolic dynamics in a way that isn't utterly confusing, so perhaps leaving a lot of it out helps keep the student on track towards what the author is trying to present. Certainly, if he stuck to his theorem heavy style, one could get very lost in symbolic dynamics land. I'll also complain he never mention's Painleve's property. There are probably deep "theorist" reasons I'll never understand for his not mentioning this weird little thing. I hear the full treatment of Painleve's property is pretty complex, but I have always found it very helpful in understanding what integrability really is, in my "seat of the pants" way. I also would have liked more detail on Peixoto's theorem. Sure it's only useful in R2; if you're on the 'applied' side of things (or a student, learning by examining practical examples) -how often will you leave R2-land?

These complaints are minor, and they're probably effectively complaints that the book's author has a different purpose in mind than I would for writing such an introductory text, were I actually qualified to do such a thing. Wiggins writes very clearly, and he writes for physicists rather than mathematicians, and brings an amateur in the subject to a fairly high level of sophistication by the end of the text. The problem sets are also excellent.

Effective overview of a useful subject.......2001-06-10

The subject of dynamical systems has been around for over a century now, having been defined by Henri Poincare in the early 1900s, but having its roots in Hamiltonian and Lagrangian mechanics in the 19th century. In this book ths author has done a fine job of overviewing the subject of dynamical systems, particularly with regards to systems that exhibit chaotic behavior. There are 292 illustrations given in the book, and they effectively assist in the understanding of a sometimes abstract subject.

After a brief introduction to the terminology of dynamical systems in Section 1.1, the author moves on to as study of the Poincare map in the next section. Recognizing that the construction of the Poincare map is really an art rather than a science, the author gives several examples of the Poincare map and discusses in detail the properties of each. Structural stability, genericity, transversality are defined, and, as preparation for the material later on, the Poincare map of the damped, forced Duffing oscillator is constructed. The later system serves as the standard example for dynamical systems exhibiting chaotic behavior.

The simplification of dynamical systems by means of normal forms is the subject of the next part, which gives a thorough discussion of center manifolds. Unfortunately, the center manifold theorem is not proved, but references to the proof are given.

Local bifurcation theory is studied in the next part, with bifurcations of fixed points of vector fields and maps given equal emphasis. The author defines rigorously what it means to bifurcate from a fixed point, and gives a classification scheme in terms of eigenvalues of the linearized map about the fixed point. Most importantly, the author cautions the reader in that dynamical systems having time-dependent parameters and passing through bifurcation values can exhibit behavior that is dramatically different from systems with constant parameters. He does give an interesting example that illustrates this, but does not go into the singular perturbation theory needed for an effective analysis of such systems.

An introduction to global bifurcations and chaos is given in the next part, which starts off with a detailed construction of the Smale horseshoe map. Symbolic dynamics, so important in the construction of the actual proof of chaotic behavior is only outlined though, with proofs of the important results delegated to the references. The Conley-Moser conditions are discussed also, with the treatment of sector bundles being the best one I have seen in the literature. The theory is illustrated nicely for the case of two-dimensional maps with homoclinic points. The all-important Melnikov method for proving the existence of transverse homoclinic orbits to hyperbolic periodic orbits is discussed and is by far one of the most detailed I have seen in the literature. The author employs many useful diagrams to give the reader a better intuition behind what is going on. He employs also the pips and lobes terminology of Easton to study the geometry of the homoclinic tangles. Homoclinic bifurcation theory is also treated in great detail. This is followed by an overview of the properties of orbits homoclinic to hyperbolic fixed points. A brief introduction to Lyapunov exponents and strange attractors is also given.

Book Description

Presents the newer field of chaos in nonlinear dynamics as a natural extension of classical mechanics as treated by differential equations. Employs Hamiltonian systems as the link between classical and nonlinear dynamics, emphasizing the concept of integrability. Also discusses nonintegrable dynamics, the fundamental KAM theorem, integrable partial differential equations, and soliton dynamics.

Customer Reviews:

Great book !.......2004-08-05

This is a very good book. Has a lot of relevant stuffs covered and it's at least light years ahead of similar books in terms of digestibility. Tightly-written yet not patronisingly simple. Check it out.

Thermodynamics of Chaotic Systems: An Introduction (Cambridge Nonlinear Science Series)

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Thermodynamics of Chaotic Systems: An Introduction (Cambridge Nonlinear Science Series)
Christian Beck , and Friedrich Schögl
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Paperback

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ASIN: 0521484510

Book Description

This book deals with the various thermodynamic concepts used for the analysis of nonlinear dynamical systems. The most important invariants used to characterize chaotic systems are introduced in a way that stresses the interconnections with thermodynamics and statistical mechanics. Among the subjects treated are probabilistic aspects of chaotic dynamics, the symbolic dynamics technique, information measures, the maximum entropy principle, general thermodynamic relations, spin systems, fractals and multifractals, expansion rate and information loss, the topological pressure, transfer operator methods, repellers and escape. The more advanced chapters deal with the thermodynamic formalism for expanding maps, thermodynamic analysis of chaotic systems with several intensive parameters, and phase transitions in nonlinear dynamics.

Introduction to Experimental Nonlinear Dynamics: A Case Study in Mechanical Vibration

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Introduction to Experimental Nonlinear Dynamics: A Case Study in Mechanical Vibration
Lawrence N. Virgin
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Paperback

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ASIN: 0521779316

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Nonlinear behavior can be found in such highly disparate areas as population biology and aircraft wing flutter. For this reason, nonlinear dynamics and chaos have become very active fields of research. This work uses an extended case study--an experiment in mechanical vibration--to introduce and explore the subject of nonlinear behavior and chaos from an engineering perspective. After a review of basic principles, the text then describes a cart-on-a-track oscillator and shows what happens when it is gradually subjected to greater excitation, thereby encountering the full spectrum of nonlinear behavior, from simple free decay to chaos. Advanced undergraduate and graduate students, as well as practicing engineers, will find this book a lively, accessible introduction to the subject.

Chaotic Vibrations: An Introduction for Applied Scientists and Engineers

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Chaotic Vibrations: An Introduction for Applied Scientists and Engineers
Francis C. Moon
Manufacturer: Wiley-Interscience
ProductGroup: Book
Binding: Hardcover

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ASIN: 0471856851

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Translates new mathematical ideas in nonlinear dynamics and chaos into a language that engineers and scientists can understand, and gives specific examples and applications of chaotic dynamics in the physical world. Also describes how to perform both computer and physical experiments in chaotic dynamics. Topics cover Poincare maps, fractal dimensions and Lyapunov exponents, illustrating their use in specific physical examples. Includes an extensive guide to the literature, especially that relating to more mathematically oriented works; a glossary of chaotic dynamics terms; a list of computer experiments; and details for a demonstration experiment on chaotic vibrations.

Chaos and Chance: An Introduction to Stochastic Aspects of Dynamics

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Chaos and Chance: An Introduction to Stochastic Aspects of Dynamics
Arno Berger
Manufacturer: Walter de Gruyter
ProductGroup: Book
Binding: Paperback

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With emphasis on stochastic aspects of deterministic systems this short book introduces the reader to the basic facts and some special topics of applied ergodic theory. It addresses advanced undergraduate and graduate students from various disciplines, i.e. mathematicians, physicists, electrical and mechanical engineers. Based upon a sound (but non-technical) mathematical introduction, a number of typical examples from applications (mostly from mechanics) are thoroughly discussed. By studying both probabilistic and deterministic features of dynamical systems the reader will develop what might be considered a unified view on chaos and chance as two sides of the same thing.

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