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.

Nonlinear and Stochastic Dynamics of Compliant Offshore Structures (Solid Mechanics and Its Applications)

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Nonlinear and Stochastic Dynamics of Compliant Offshore Structures (Solid Mechanics and Its Applications)
Seon Mi Han , and H. Benaroya
Manufacturer: Springer
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Binding: Hardcover

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ASIN: 1402005733

Book Description

The purpose of this monograph is to show how to model a compliant offshore structure in an ocean environment. Such structures are of increasing importance because of the desire to access the deep ocean. A brief history and an extensive review of the four existing transverse beam models are presented. The four beam models are Euler-Bernoulli, Rayleigh, shear and Timoshenko models. These are the fundamental models for the preliminary studies of offshore structures. The complete analytical solutions are given for each model. This review is followed by a chapter on the stochastic modelling of environmental forces. The waves are assumed to be random, and the fluid force is modelled using the Morison Equation. In subsequent chapters, the models are expanded to include the axial motion as well as the transverse motion in two and three dimensions.
Numerical results are obtained using both deterministic and random forces. A detailed description of the numerical methods is provided so that the reader can adapt these methods to his or her particular problem. Researchers in the fields of structural mechanics and ocean engineering, especially those with an interest in nonlinear hybrid beam/cable models, will find this a useful book.

Quantized Vortex Dynamics and Superfluid Turbulence

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Quantized Vortex Dynamics and Superfluid Turbulence

Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 3540422269

Book Description

This book is primarily concerned with turbulence in superfluid helium. Quantized vorticity has traditionally generated great interest among physicists, but there are now also important engineering applications such as liquid helium cooling of superconducting magnets. Presently much research is done on the relationship between superfluid turbulence and classical turbulence, as intense turbulence can be generated in liquid helium due to its small kinematic viscosity. There is also a close relationship between superfluid behaviour and quantized vorticity in liquid helium and in atomic Bose--Einstein condensates. Putting special emphasis on the interplay between the different disciplines involved, this readable account of recent research will appeal not only to established researchers but also to newcomers and graduate students wishing to enter the field.

Applied Asymptotic Methods in Nonlinear Oscillations (Solid Mechanics and Its Applications)

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Compact and well structured

Applied Asymptotic Methods in Nonlinear Oscillations (Solid Mechanics and Its Applications)
Yuri A. Mitropolsky , and Nguyen Van Dao
Manufacturer: Springer
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Binding: Hardcover

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ASIN: 079234605X

Book Description

The present volume addresses the application of asymptotic methods in nonlinear oscillations. Such methods see a large variety of applications in physics, mechanics and engineering.
The advantages of using asymptotic methods in solving nonlinear problems are firstly simplicity, especially for computing higher approximations, and secondly their applicability to a large class of quasi-linear systems.
In contrast to the existing literature, this book is concerned with the applied aspects of the methods concerned and also contains problems relevant to the everyday practice of engineers, physicists and mathematicians.
Usually, dynamics systems are classified and examined by their degrees of freedom. This book is constructed from another point of view based upon the originating mechanism of the oscillations: free oscillation, self-excited oscillation, forced oscillation, and parametrically excited oscillation.
The text has been designed to cover material from the elementary to the more advanced, in increasing order of difficulty. It is of considerable interest to both students and researchers in applied mathematics, physical and mechanical sciences, and engineering.

Customer Reviews:

Compact and well structured.......1999-07-23

The book is a more compact version of the 'Asymptotic methods in the theory of nonlinear oscillations' by Mitropolskii and Bogoliobov published years back. Nonlinear equations close to linear ones are solved using the methods suggested by Krylov and Bogoliobov. The presentation is orderly dealing with free oscillations first, then self oscillations leading to forced oscillations. A neat article on the averaging method ends the book in a nice fashion bringing about some of the connections.

Chaotic Mechanics in Systems With Impacts and Friction (World Scientific Series on Nonlinear Science , No a)

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Chaotic Mechanics in Systems With Impacts and Friction (World Scientific Series on Nonlinear Science , No a)
Barbara Blazejczyk-Okolewska , Krzysztof Czolczynski , Tomasz Kapitaniak , and Jerzy Wojewoda
Manufacturer: World Scientific Publishing Company
ProductGroup: Book
Binding: Hardcover

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ASIN: 9810237162

The Frenkel-Kontorova Model: Concepts, Methods, and Applications (Theoretical and Mathematical Physics)

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Excellent overview !
The definitive reference on the subject

The Frenkel-Kontorova Model: Concepts, Methods, and Applications (Theoretical and Mathematical Physics)
O.M. Braun , and Y.S. Kivshar
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 3540407715

Book Description

This book presents an overview of the basic concepts, methods and applications of nonlinear low-dimensional solid-state physics based on the Frenkel--Kontorova model and its generalizations. It allows a nonspecialist to acquire foundations in the interdisciplinary concepts and methods of both solid-state physics and nonlinear science. It covers many important topics such as the nonlinear dynamics of discrete systems, the dynamics of solitons and their interaction, commensurate and incommensurate systems, statistical mechanics of nonlinear systems, ratchets, and nonequilibrium dynamics of interacting many-body systems. Also treated are the principal nonlinear equations along with the properties of their localized solutions and methods for their analysis.

Customer Reviews:

Excellent overview !.......2004-04-20

In sciences, "simple" low-dimensional models are often called into play to understand and clarify fundamental processes involved in complicated physical phenomena. Universal models which can be applied to illustrate a variety of effects of different physical origin are rare and, therefore, they are of CRUCIAL importance.
Recently, with respect to this, Frenkel-Kontorova type models have attracted so much attention for their ability to describe a broad spectrum of phenomena of distinct physical origin as, for example, fundamental aspects in tribology and mass transport, Josephson transmission lines, DNA dynamics, charge-density waves, commensurable-incommensurable phase transitions and so on. It is possible to count almost 200 publications, in the last 5 years only, in the most relevant scientific journals related to Frenkel-Kontorova models.
Braun and Kivshar are undoubtedly internationally famous specialists in Solid State Physics and Nonlinear Physics of discrete dynamical systems, and their book represents certainly a comprehensive and exhaustive treatment (from fundamentals to recent and advanced developments) of the subject. Describing fundamental concepts and theoretical procedures of nonlinear dynamics, related numerical techniques and methods, down to possible experimental and technological applications based on this intriguing model and its generalizations, this book suits both the needs of students and beginners as well as the requests of most experienced researchers wishing to be acquainted with new and complementary aspects in this field. The table of contents, together with an up to date list of references, shows at first glance the comprehensiveness of the treatment.
Personally, as an active researcher in this field, I would highly recommend the book to both graduate students and any much more experienced scientist who is working or just interested in nonlinear dynamics and condensed matter modeling.

The definitive reference on the subject.......2004-04-13

As an active researcher on this field, I find this book will become THE reference. The authors, with over 20 years of experience themselves, take you from the basics to the current hot topics. Their coverage is certainly exhaustive, with an up to date list of 876 references. All aspects of the Frenkel-Kontorova/sine-Gordon model are discussed, from statistical mechanics to the effect of forces through the thermal version. The mathematical details are provided but also commented upon in extent for the reader to grasp their implications. One point I particularly liked is that the connection between Frenkel-Kontorova and sine-Gordon is always kept in mind along the book, a point that had been an obscure one for me when touching upon different aspects of the problem. The chapter on applications helps make the link between the different disguises of the model. Finally, I do believe the book will be useful for a more general audience interested in nonlinear problems beyond those discussed, as most of the techniques and viewpoints apply in general. All in all, a must for researchers in nonlinear science and condensed matter models, and an excellent way to introduce oneself to this subject for anybody beginning to work on it, as no background is assumed.

IUTAM Symposium on Advances in Nonlinear Stochastic Mechanics (Solid Mechanics and Its Applications)

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IUTAM Symposium on Advances in Nonlinear Stochastic Mechanics (Solid Mechanics and Its Applications)

Manufacturer: Springer
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Binding: Hardcover

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Book Description

This volume contains 45 full-length papers presented at the IUTAM Symposium on Advances in Nonlinear Stochastic Mechanics in Trondheim, Norway in July 1995. The contributions span the range from basic theoretical research to engineering applications. Particular areas covered include stochastic stability, nonlinear active control, nonlinear stochastic response, random material and system properties, stochastic finite elements, methods for non-gaussian processes, system identification, and modelling of environmental load processes. Specific applications include material fatigue, wind loading and response, offshore and earthquake engineering, and railway vibrations. The volume gives a representative overview of recent progress in theoretical methods and selected engineering applications and is a valuable reference for researchers in this very active field.

IUTAM Symposium on New Applications of Nonlinear and Chaotic Dynamics in Mechanics (Solid Mechanics and Its Applications)

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IUTAM Symposium on New Applications of Nonlinear and Chaotic Dynamics in Mechanics (Solid Mechanics and Its Applications)

Manufacturer: Springer
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ASIN: 0792352769

Book Description

This book presents the latest research results in the area of applied nonlinear dynamics and chaos theory as presented at the IUTAM Symposium on New Applications of Nonlinear and Chaotic Dynamics in Mechanics. The papers address new applications of nonlinear dynamics to mechanics, including fluid-structure interaction, machining and mechanics of solids, aircraft and vehicle dynamics and many other applications. The authors include three academic generations including the early pioneers, the first generation of students, now quite distinguished themselves, as well as novitiates to the field. The subjects span the following areas: analysis tools, bifurcation theory, elastica, cables and shell dynamics, inelasticity, materials processing, machine system dynamics, impact and non-smooth systems, circuits, control, cardiac modelling, vehicle and ship dynamics, fluid-elastic and fluid systems, spatio-temporal chaos. The papers contain valuable references to the literature which will be useful to both new and senior researchers.
This volume will be of interest to researchers and engineers in the field of applied mathematics, physical and mechanical sciences, and engineering.

IUTAM Symposium on Nonlinear Stochastic Dynamics (Solid Mechanics and Its Applications)

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IUTAM Symposium on Nonlinear Stochastic Dynamics (Solid Mechanics and Its Applications)

Manufacturer: Springer
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Binding: Hardcover

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ASIN: 1402014716

Book Description

Non-linear stochastic systems are at the center of many engineering disciplines and progress in theoretical research had led to a better understanding of non-linear phenomena. This book provides information on new fundamental results and their applications which are beginning to appear across the entire spectrum of mechanics.
The outstanding points of these proceedings are Coherent compendium of the current state of modelling and analysis of non-linear stochastic systems from engineering, applied mathematics and physics point of view. Subject areas include: Multiscale phenomena, stability and bifurcations, control and estimation, computational methods and modelling.
For the Engineering and Physics communities, this book will provide first-hand information on recent mathematical developments. The applied mathematics community will benefit from the modelling and information on various possible applications.

IUTAM Symposium on Nonlinearity and Stochastic Structural Dynamics - held in Madras, Chennai, India, 4--8 January 1999 (Solid Mechanics and its Applications, Volume 85)

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IUTAM Symposium on Nonlinearity and Stochastic Structural Dynamics - held in Madras, Chennai, India, 4--8 January 1999 (Solid Mechanics and its Applications, Volume 85)

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ASIN: 0792367332

Book Description

Nonlinearity and stochastic structural dynamics is of common interest to engineers and applied scientists belonging to many disciplines. Recent research in this area has been concentrated on the response and stability of nonlinear mechanical and structural systems subjected to random escitation. Simultaneously the focus of research has also been directed towards understanding intrinsic nonlinear phenomena like bifurcation and chaos in deterministic systems. These problems demand a high degree of sophistication in the analytical and numerical approaches. At the same time they arise from considerations of nonlinear system response to turbulence, earthquacke, wind, wave and guidancy excitations. The topic thus attracts votaries of both analytical rigour and practical applications.
This books gives important and latest developments in the field presenting in a coherent fashion the research findings of leading international groups working in the area of nonlinear random vibration and chaos.

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