Nonlinear Dynamics and Chaos: Geometrical Methods for Engineers and Scientists

Book Description

Emphasizes the qualitative description of long-term recurrent motions of dissipative systems governed by genuinely nonlinear equations, with no assumptions of near-linearity. General concepts of the geometric theory are illustrated using computer simulations of specific ordinary differential and difference equations. The nonlinear phenomena discussed include the multiple attractors observable in a single system, chaotic long-term behaviour and its underlying order and structure, and discontinuous jump and hysteresis phenomena.

Customer Reviews:

Not that good.......2005-02-07

This book contains some standard topics treated on an elementary way. Unfortunatelly mathemathical formalism is almost left out.
The approach to the subject is pretty popular.
I think one is going to invest her/his own time in a better way by working first on V.I.Arnold's "Classical Mechanics" (symplectic formalism) then going on with E. Ott's "Chaos" (one of the best on the subject, but Lichtenberg-Liebermann is also a good one, in my opinion) and, finally, taking a look into some parts of Arnold's "Geometrical methods of ODE". More stuff is available on the Web (arxiv.org --> recent abstracts and new approaches on dynamical systems in Physics). This is a good way to gain a technical basis instead of a popular one.

Good Introduction To Chaos.......2004-03-27

The book is complex enough to provide good information on NLD, chaos, and the associated differential equations, but not so complex you can't get a firm working grasp of the subject. Lots of nice illustrations, clearly and concisely explained. Bifurcations, attractors and all that jazz is in there too if you want to make your own Poincare maps (also explained). I used the information from the book to generate visualizations of an externally excited system moving in and out of different modes of vibration. Such a techinique is not directly explaned in the text, but a good read of the first few chapters will provide the tools to do so. Recommended.

Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers

Average customer rating:

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.

Nonlinear Dynamics and Chaos: With Applications in Physics, Biology, Chemistry, and Engineering (Studies in Nonlinearity)

Average customer rating:

Superb book.
Great book for beginners
Great for an introduction but not for digging in for details
Shockingly Readable
incredible!

Nonlinear Dynamics and Chaos: With Applications in Physics, Biology, Chemistry, and Engineering (Studies in Nonlinearity)
Steven H. Strogatz
Manufacturer: Addison Wesley Publishing Company
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Binding: Hardcover

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ASIN: 0201543443

Customer Reviews:

Superb book........2007-06-15

This book provides an exceptional introduction to nonlinear dynamics. Math books are often trapped in equating rigor with formalisms and in compromising intuition to generalities. Strogatz book provides an exemplary guideline how both intuition and rigor may be served to transform a difficult topic into fun reading and highly applicable set of ideas. Here are the key elements of what you will find in this book.

A. The book builds up intuitive understanding of the key ideas of the field
from simple one dimensional dynamics to complex multi-dimensional behaviors.
B. Each chapter contains fascinating applications -- from fireflies synchronization and josephson junction to population dynamics and chaotic laser behaviors-- which are
fun to read and useful if you need to apply dynamics to solve research problems.
C. There are ample exercises and solutions to render this ideal book for self-learners. It provides a relatively broad coverage of the key ideas of the field, without taxing the reader with far corners of little interest.

Great book for beginners.......2007-05-14

Nonlinear dynamics and chaos is an excellent introductory book. It explains this complex looking subject in very simple and intuitive fashion. I recommend this book anyone who are interested in chaos/nonlinear dynamics. It even doubles as a fun book!

Great for an introduction but not for digging in for details.......2007-01-05

I think this is one of the best books for understanding the Phase Spaces and Bifurcations. It is really easy to follow and understand, even for people without background on nonlinear subjects. Yet, it is not the right book for engineers to read and start to solve their own detailed problems. People who seeks for a book to get into the subject or who wants to have a nice reference; BUY THIS BOOK. By the way, its price is reasonable.

Shockingly Readable.......2007-01-04

I bought this book as a textbook for a class, and I have to say that it is a surprisingly readable math book. The class only used the first few chapters, but I find myself flipping through the rest of the book and trying to understand more advanced material. This is a good book for a scientist who needs to learn linear and nonlinear dynamics but is a little intimidated.

Keep in mind, this is a math book, and no writer can turn math into something it isn't. Still, the writer gives lots of relevant examples (especially in the problems--the only complaint I have is that the solutions in the back don't give any explanation, and these solutions are a bit sparse), and milks as much storytelling out of the subject matter as is possible. I thoroughly recommend it--it brings out the closet math geek in everyone!

incredible!.......2006-06-13

This is probably the best math book I've ever read. Unlike other stuffy books, this one is very personable and informal. It is extremely readable, the explanations are crystal-clear and very intuitive and well-motivated, plus the author inserts a lot of humor (it's so nice to be reminded that mathematicians are humans). There are fascinating examples culled from applications.
I should note two things. First, it is not a proof-based book. It discuesses the cool theorems and gives intuitive justifications, but the author is clear that his goal is to build intuition and give experience with the techniques, rather than mathematical rigor (thankfully, he is honest about this and points to areas where more rigor could be introduced, rather than giving the unnatural and awkward hybrid of rigor and intuition attempted by many calculus books). Second, a lot of the problems (though certainly not all) deal with pathological and/or special cases, so it's possible for teachers to give fairly onerous homeworks.

Nonlinear Dynamics in Physiology: A State-space Approach

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Nonlinear Dynamics in Physiology: A State-space Approach
Mark Shelhamer
Manufacturer: World Scientific Publishing Company
ProductGroup: Book
Binding: Hardcover

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ASIN: 9812700293

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
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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

This book treats nonlinear dynamics in both Hamiltonian and dissipative systems. The emphasis is on the mechanics for generating chaotic motion, methods of calculating the transitions from regular to chaotic motion, and the dynamical and statistical properties of the dynamics when it is chaotic. The book is intended as a self consistent treatment of the subject at the graduate level and as a reference for scientists already working in the field. It emphasizes both methods of calculation and results. It is accessible to physicists and engineers without training in modern mathematics. The new edition brings the subject matter in a rapidly expanding field up to date, and has greatly expanded the treatment of dissipative dynamics to include most important subjects. It can be used as a graduate text for a two semester course covering both Hamiltonian and dissipative dynamics.

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

Average customer rating:

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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Accessories:

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

Explore the remarkable variety of nature's dynamics
The development of the computer over the latter half of the twentieth century has greatly advanced our ability to explore the complex dynamics that occur in nature. With the aid of the computer, we can now study nonlinear types of dynamics that cannot generally be studied by mathematics. Realistic computer models of natural dynamics can now be developed, and even the simplest have uncovered remarkable and unexpected types of natural dynamics.
Researchers have found that simple dynamic actions over short periods of time can produce long-term dynamics that were never dreamt of in the past. Even the smallest changes in a system's short-time behavior can have enormous effects on the future of the system. Slightly different initial configurations can also produce very different future dynamics, which is now recognized as the important "sensitivity" feature of many dynamic systems.
Exploring Nature's Dynamics offers an introductory opportunity to learn about-and explore for yourself-some of the diverse forms of dynamics that occur in nature's reproduction processes. These forms include the competitive and cooperative interactions between species, neurological behaviors, dynamic spatial organizations, and the amazing constructive contributions of chaotic dynamics to our minds and hearts, the evolution of our solar system, and the human species itself. All you need to explore these ideas is a healthy curiosity and your own imagination. The accompanying disk includes simple Qbasic computer programs that allow you to witness dynamic systems at work. The methods for using these programs-and for making modifications based on your own creativity-are fully explained for people who have never used computer programs before. So come explore!

Chaos and Integrability in Nonlinear Dynamics: An Introduction

Average customer rating:

Great book !

Chaos and Integrability in Nonlinear Dynamics: An Introduction
Michael Tabor
Manufacturer: Wiley-Interscience
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Binding: Hardcover

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Principles of Applied Mathematics: Transformation and Approximation (Advanced Book Program)

ASIN: 0471827282

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.

Chaos, Catastrophe, and Human Affairs: Applications of Nonlinear Dynamics To Work, Organizations, and Social Evolution

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A highly sophisticated discussion.

Chaos, Catastrophe, and Human Affairs: Applications of Nonlinear Dynamics To Work, Organizations, and Social Evolution
Stephen J. Guastello
Manufacturer: Lawrence Erlbaum
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Binding: Hardcover

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ASIN: 0805816348

Book Description

Whether talking about steering a wheelbarrow over rugged terrain or plotting the course of international relations, human performance systems involve change. Sometimes changes are subtle or evolutionary, sometimes they are catastrophic or revolutionary, and sometimes the changes are from periods of relative calm to periods of vibrant oscillations to periods of chaos. As a general rule, more complex systems are likely to produce more complex forms of change. br br Although social scientists have long acknowledged that change occurs and have considered ways to effect desirable change, the dynamical processes of change have been poorly understood in the past. This volume combines recent advances in mathematics and experimental design with the best available social science theories to produce a new, integrated, and compact theory of work, organizations, and social evolution. The domains of application extend from human decision-making processes to personnel selection and work motivation, work performance under conditions of stress, accident and health risk analysis, the development of social institutions and economic systems, creativity and innovation, organizational development and group dynamics, and political revolutions and war. br br Relative to other literature on nonlinear dynamical systems theory (NDS), this book is unique in that it integrates new developments in NDS with substantive psychological theory. It builds on many recent developments in organizational theory to show that nonlinear dynamics were often implicit in those works all along. The result is an entirely new way of viewing social events, understanding change processes, and asking questions about social systems. This book also contains much new empirical work and explains the newly developed methods for testing these new hypotheses. br

Customer Reviews:

A highly sophisticated discussion........1999-03-02

Topics covered in this work, apart from the core mathematical theories, are centered around catastrophe and chaos theory applications to human problems in industry since 1980. The author provides a highly sophisticated discussion of such subjects as decision making, the dynamics of motivation and conflict, stress and performance, and the evolution of human systems. Excellent references. Highly recommended.

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