Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers

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.

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Introduction to Nonlinear Physics

Manufacturer: Springer
ProductGroup: Book
Binding: Paperback

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ASIN: 038740614X

Book Description

This textbook provides an introduction to the new science of nonlinear physics for advanced undergraduates, beginning graduate students, and researchers entering the field. The chapters, by pioneers and experts in the field, share a unified perspective. Nonlinear science developed out of the increasing ability to investigate and analyze systems for which effects are not simply linear functions of their causes; it is associated with such well-known code words as chaos, fractals, pattern formation, solitons, cellular automata, and complex systems. Nonlinear phenomena are important in many fields, including dynamical systems, fluid dynamics, materials science, statistical physics, and paritcel physics. The general principles developed in this text are applicable in a wide variety of fields in the natural and social sciences. The book will thus be of interest not only to physicists, but also to engineers, chemists, geologists, biologists, economists, and others interested in nonlinear phenomena. Examples and exercises complement the text, and extensive references provide a guide to research in the field.

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Introduction to Nonlinear Science
G. Nicolis
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Paperback

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ASIN: 0521467829

Book Description

One of the most unexpected results in science in recent years is that quite ordinary systems obeying simple laws can give rise to complex, nonlinear or chaotic, behavior. In this book, the author presents a unified treatment of the concepts and tools needed to analyze nonlinear phenomena and to outline some representative applications drawn from the physical, engineering, and biological sciences. Some of the interesting topics covered include: dynamical systems with a finite number of degrees of freedom, linear stability analysis of fixed points, nonlinear behavior of fixed points, bifurcation analysis, spatially distributed systems, broken symmetries, pattern formation, and chaotic dynamics. The author makes a special effort to provide a logical connection between ordinary dynamical systems and spatially extended systems, and to balance the emphasis on chaotic behavior and more classical nonlinear behavior. He also develops a statistical approach to complex systems and compares it to traditional deterministic phase space descriptions. This book is suitable for senior undergraduate and graduate students taking nonlinear courses from many different perspectives including physics, chemistry, biology, and engineering.

An Introduction to Nonlinear Chemical Dynamics: Oscillations, Waves, Patterns, and Chaos (Topics in Physical Chemistry)

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An Introduction to Nonlinear Chemical Dynamics: Oscillations, Waves, Patterns, and Chaos (Topics in Physical Chemistry)
Irving R. Epstein , and John A. Pojman
Manufacturer: Oxford University Press, USA
ProductGroup: Book
Binding: Hardcover

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ASIN: 0195096703

Book Description

Just a few decades ago, chemical oscillations were thought to be exotic reactions of only theoretical interest. Now known to govern an array of physical and biological processes, including the regulation of the heart, these oscillations are being studied by a diverse group across the sciences. This book is the first introduction to nonlinear chemical dynamics written specifically for chemists. It covers oscillating reactions, chaos, and chemical pattern formation, and includes numerous practical suggestions on reactor design, data analysis, and computer simulations. Assuming only an undergraduate knowledge of chemistry, the book is an ideal starting point for research in the field. The book begins with a brief history of nonlinear chemical dynamics and a review of the basic mathematics and chemistry. The authors then provide an extensive overview of nonlinear dynamics, starting with the flow reactor and moving on to a detailed discussion of chemical oscillators. Throughout the authors emphasize the chemical mechanistic basis for self-organization. The overview is followed by a series of chapters on more advanced topics, including complex oscillations, biological systems, polymers, interactions between fields and waves, and Turing patterns. Underscoring the hands-on nature of the material, the book concludes with a series of classroom-tested demonstrations and experiments appropriate for an undergraduate laboratory.

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
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Binding: Paperback

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ASIN: 0521484510

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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.

An Introduction to Nonlinear Finite Element Analysis

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classic

An Introduction to Nonlinear Finite Element Analysis
J. N. Reddy
Manufacturer: Oxford University Press, USA
ProductGroup: Book
Binding: Hardcover

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ASIN: 019852529X

Book Description

This book presents the theory and computer implementation of the finite element method as applied to nonlinear problems of heat transfer and similar field problems, fluid mechanics (flows of incompressible fluids), and solid mechanics (elasticity, beams and plates). Both geometric as well as material nonlinearities are considered, and static and transient (i.e. time-dependent) responses are studied. Although there exist a number of books on nonlinear finite elements that serve as good references for engineers who are familiar with the subject and wish to learn advanced topics or the latest developments, there is currently no book which is suitable as a textbook for a first course on nonlinear finite element analysis. This book fills the void in the market, providing a clear understanding of the concepts of nonlinear finite element analyses through detailed theoretical formulations and computer implementation steps, examples and exercises. In addition, the book serves as a prelude to more advanced books on the subject.

Customer Reviews:

classic.......2004-08-01

There is this one thing I know. When you are learning from a superior intelligence you can find that out pretty quick. My greed for calculus and math finds an apt expression here. The way he presents non linear finite elements is unparalled.

There is another thing I have learnt. The people who can explain things clearly, are the ONLY ones who know it. And they are not too many, when it comes to horribly complicated problems, besides. Math cuts out a lot of verbiage, in understanding a problem. A simple math problem when described in words could go on and on and on. If you have a apetite for calculus and a craving for numerical analysis, you would be a poorer man if you didnt have this book. If you dont, well you are not good enough to pick up finite elements anyhow, forget about non linear analysis.

One small note. This is just pertinent to me. I dont write code in fortran so parts of the book were not of much use to me. But the concept is laid out very well. I would have loved it if the code was in C++. But its okay. If I were to just copy code, that would be shabby learning anyhow. So it works out fine.

An Introduction to Linear and Nonlinear Finite Element Analysis: A Computational Approach

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An Introduction to Linear and Nonlinear Finite Element Analysis: A Computational Approach
Prem Kythe , and Dongming Wei
Manufacturer: Birkhäuser Boston
ProductGroup: Book
Binding: Hardcover

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ASIN: 0817643087

Book Description

Although finite element courses have become more popular in the undergraduate and graduate engineering, science, and applied mathematics curricula, there are very few introductory textbooks geared toward students accustomed to using computers for everyday assignments and research. 'An Introduction to Linear and Nonlinear Finite Element Analysis' fills this gap, offering a concise, integrated presentation of methods, applications, computational software tools, and hands-on programming projects. Suitable for junior/senior undergraduate and first-year graduate courses, the book is aimed at students from a variety of disciplines: engineering, physics, geophysics, and applied mathematics.

Unlike existing texts designed with specific applications to a particular field of mechanical, civil, or chemical engineering, the emphasis here is on interdisciplinary applications. One- and two-dimensional linear and nonlinear initial/boundary value problems are solved using finite element, Newton's, and conjugate gradient methods. Mathematical theory is kept to a minimum, making the text accessible to students with varied backgrounds.

Features:

* Software tools using Mathematica, Matlab, Fortran, and commercial finite element codes, such as Ansys, integrated throughout the text

* Numerous examples and exercises with diverse applications to linear and nonlinear heat transfer, fluid flows, mechanical vibrations, electromagnetics, and structures

* Supporting material and selected solutions to problems available at the authors' websites: http://www.math.uno.edu/fac/pkythe.html and http://www.math.uno.edu/fac/dwei.html

* Minimal prerequisites: a course in calculus of several variables, differential equations and linear algebra, as well as some knowledge of computers

Primarily a classroom resource, the book may also be used as a self-study reference for researchers and practitioners who need a quick introduction to finite element methods.

Extreme Nonlinear Optics: An Introduction (Advanced Texts in Physics)

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Extreme Nonlinear Optics: An Introduction (Advanced Texts in Physics)
Martin Wegener
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 354022291X

Book Description

Following the birth of the laser in 1960, the field of "nonlinear optics" rapidly emerged.

Today, laser intensities and pulse durations are readily available, for which the concepts and approximations of traditional nonlinear optics no longer apply. In this regime of "extreme nonlinear optics," a large variety of novel and unusual effects arise, for example frequency doubling in inversion symmetric materials or high-harmonic generation in gases, which can lead to attosecond electromagnetic pulses or pulse trains. Other examples of "extreme nonlinear optics" cover diverse areas such as solid-state physics, atomic physics, relativistic free electrons in a vacuum and even the vacuum itself.

This book starts with an introduction to the field based primarily on extensions of two famous textbook examples, namely the Lorentz oscillator model and the Drude model. Here the level of sophistication should be accessible to any undergraduate physics student. Many graphical illustrations and examples are given. The following chapters gradually guide the student towards the current "state of the art" and provide a comprehensive overview of the field. Every chapter is accompanied by exercises to deepen the reader's understanding of important topics, with detailed solutions at the end of the book.

Nonlinear Ordinary Differential Equations: An Introduction to Dynamical Systems (Oxford Applied and Engineering Mathematics)

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Not an instructive textbook
very non-rigorous approach with a sizeable number of typos
Approachable introduction to nonlinear ODE's

Nonlinear Ordinary Differential Equations: An Introduction to Dynamical Systems (Oxford Applied and Engineering Mathematics)
D. W. Jordan , and Peter Smith
Manufacturer: Oxford University Press, USA
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Binding: Paperback

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ASIN: 0198565623

Book Description

Nonlinear ordinary differential equations was first published in 1977 and has since become a standard text in the teaching of the subject. It takes a qualitative approach, and is designed for advanced undergraduate and graduate students of dynamical systems in mathematics or mathematics-related subjects. The text of this third edition has been completely revised to bring it into line with current teaching, including an expansion of the material on bifurcations and chaos. The book is directed towards practical applications of the theory, with several hundred examples and problems covering a wide variety of applications. Prerequisites are kept to a minimum, with appendices containing the necessary mathematical theory new to this edition. From reviews of the first edition: The book can profitably be used in a senior undergraduate course. It is well written, well motivated and contains some recent developments of interest which have not been readily accessible before at this level. V. Lakshmikantham in Mathematical Reviews From reviews of the second edition: The subject has wide applications in physical, biological, and social sciences which continuously supply new problems of practical and theoretical importance. The book does a good job in motivating the reader in such pursuits, and presents the subject in a simple but elegant style. P. K. Kythe in Applied Mechanics Reviews

Customer Reviews:

Not an instructive textbook.......2006-03-06

I am in an introductory graduate level math course using this textbook. I agree with the other reviewer who criticizes its lack of rigor, numerous typos, and overabundance of examples. The text is not well-written, so the authors wander among seemingly related topics within each chapter without giving much explanation of their background or intuitive insight into the physical phenomena they describe. Moreover, the examples have not been very instructive for me. They often leave out several steps (for example, many assume that you already have an analytic solution for a differential equation, thus I sometimes find myself needing to use Mathematica to derive one). The problems are loosely related to the examples, but there is enough of a disconnect between the two so that I have trouble doing the homework assignments. I find myself referring to other (more elementary) texts on differential equations for better insight into the problems.

I strongly discourage the use of this book and am looking forward to when the class ends.

very non-rigorous approach with a sizeable number of typos.......2006-02-24

(I am referring to the paperpack 3rd edition)

The text serves as an ok introduction to nonlinear ODEs. I would not recommend it for any kind of rigorous course, since the approach is very nonrigorous. There are no theorems, and no attempt at analysis, so you must take everything at the author's word. The book is mainly a large collection of examples. The difficulty of the problems depends on how rigorous you want the answers to be, and there are a lot of answers in the appendix (but without any comments about how they were derived).

Personally, the book irritates me, but I can see its usefulness. One of the main causes of irritation was the unusually high number of typos, at the rate of one per page in some chapters (and in the problems and their solutions too). I find this quite significant. This is the third edition, and there is no excuse for so many errors. I have never encountered a published book with this kind of error rate.

I do not have much experience with similar books, so I can't rate this text in context very well. It is similar to, say, Marion and Thornton's Classical Dynamics, except with less physics (of course) and more on difficult nonlinear ODEs, and with more typos.

Approachable introduction to nonlinear ODE's.......2000-04-07

Certainly worth the price. Very approachable. I haven't reviewed many similar books -- this text is good enough that I haven't felt the need.

Covers: solution, characterization, and stability analysis, including bifurcation and chaos.

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