Product Description
The first truly up-to-date look at the theory and capabilities of nonlinear dynamical systems that take the form of feedforward neural network structures
Considered one of the most important types of structures in the study of neural networks and neural-like networks, feedforward networks incorporating dynamical elements have important properties and are of use in many applications. Specializing in experiential knowledge, a neural network stores and expands its knowledge base via strikingly human routes-through a learning process and information storage involving interconnection strengths known as synaptic weights.
In Nonlinear Dynamical Systems: Feedforward Neural Network Perspectives, six leading authorities describe recent contributions to the development of an analytical basis for the understanding and use of nonlinear dynamical systems of the feedforward type, especially in the areas of control, signal processing, and time series analysis. Moving from an introductory discussion of the different aspects of feedforward neural networks, the book then addresses:
* Classification problems and the related problem of approximating dynamic nonlinear input-output maps
* The development of robust controllers and filters
* The capability of neural networks to approximate functions and dynamic systems with respect to risk-sensitive error
* Segmenting a time series
It then sheds light on the application of feedforward neural networks to speech processing, summarizing speech-related techniques, and reviewing feedforward neural networks from the viewpoint of fundamental design issues. An up-to-date and authoritative look at the ever-widening technical boundaries and influence of neural networks in dynamical systems, this volume is an indispensable resource for researchers in neural networks and a reference staple for libraries. ... Read more

Product Description
This book gives an in-depth introduction to the areas of modeling, identification, simulation, and optimization. These scientific topics play an increasingly dominant part in many engineering areas such as electrotechnology, mechanical engineering, aerospace, and physics. This book represents a unique and concise treatment of the mutual interactions among these topics.Techniques for solving general nonlinear optimization problems as they arise in identification and many synthesis and design methods are detailed. The main points in deriving mathematical models via prior knowledge concerning the physics describing a system are emphasized. Several chapters discuss the identification of black-box models. Simulation is introduced as a numerical tool for calculating time responses of almost any mathematical model. The last chapter covers optimization, a generally applicable tool for formulating and solving many engineering problems. ... Read more

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This introduction to applied nonlinear dynamics and chaos places emphasis on teaching the techniques and ideas that will enable students to take specific dynamical systems and obtain some quantitative information about their behavior. The new edition has been updated and extended throughout, and contains a detailed glossary of terms.

From the reviews:

"Will serve as one of the most eminent introductions to the geometric theory of dynamical systems." --Monatshefte für Mathematik

Customer Reviews (2)

Great reference or grad school level course text on general nonlinear dynamics
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
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.

This book has served well as a reference book and should be useful to students and other individuals who are interested in going into this area. It is a subject that has found innumerable applications, and it will continue to grow as more tools and better computational facilities are developed to study the properties of dynamical systems. ... Read more

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While many books have discussed methodological advances in nonlinear dynamical systems theory (NDS), this volume is unique in its focus on NDS's role in the development of psychological theory. After an introductory chapter covering the fundamentals of chaos, complexity, and other nonlinear dynamics, subsequent chapters provide in-depth coverage of each of the specific topic areas in psychology. A concluding chapter takes stock of the field as a whole, evaluating important challenges for the immediate future. The chapters are written by experts in the use of NDS in each of their respective areas, including biological, cognitive, developmental, social, organizational, and clinical psychology. Each chapter provides an in-depth examination of theoretical foundations and specific applications and a review of relevant methods. This edited collection represents the state of the art in NDS science across the disciplines of psychology. ... Read more

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The study of nonlinear dynamical systems has exploded in the past 25 years, and Robert L. Devaney has made these advanced research developments accessible to undergraduate and graduate mathematics students as well as researchers in other disciplines with the introduction of this widely praised book. In this second edition of his best-selling text, Devaney includes new material on the orbit diagram fro maps of the interval and the Mandelbrot set, as well as striking color photos illustrating both Julia and Mandelbrot sets. This book assumes no prior acquaintance with advanced mathematical topics such as measure theory, topology, and differential geometry, Assuming only a knowledge of calculus, Devaney introduces many of the basic concepts of modern dynamical systems theory and leads the reader to the point of current research in several areas. ... Read more

Customer Reviews (5)

Great Introduction to the topic
This is a very good book.Actually, Devaney's "First Course in Chaotic Dynamical Systems," is a good accompanying text.Fascinating subject...

Excellent book; unique in its accessibility and coverage of deep results
This book is an introduction to dynamical systems defined by iterative maps of continuous functions.It doesn't require much advanced knowledge, but it does require a familiarity and certain level of comfort with proofs.The basic idea of this book is to explore (in the context of iterative maps) the major themes of dynamical systems, which can later be explored in the messier setting of differential equations and continuous-time systems.While this book doesn't discuss differential equations directly, the techniques used here can be transferred (with considerable work and thought) to that setting.Someone wanting an elementary book covering differential equations as dynamical systems might want to check out the excellent multi-volume work by J. Hubbard; the combination of that work with this book would provide the background to tackle the tougher and less-accessible texts dealing with chaotic systems of differential equations.

Although this is a pure math book, the book does mention key applications and motivation behind the material; applied mathematicians will find this book quite useful, not necessarily because of the choice of topics but just because it greatly helps develop ones' intuition.The material is presented in a way that gives the student a sense of the big picture--what the theorems mean, how they fit together.Proofs are rigorous but as easy to follow as I have seen them in this subject.

The choice and order of subjects is also both practical and fun.The book begins with 1-dimensional systems and explores just about everything interesting that happens with them (including Sarkovski's Theorem, one of the most bizarre and surprising mathematical results), before moving into two-dimensions and then dynamics in the complex plane.

The bottom line?This book would be excellent both as a textbook and for self-study.If you're interested in this subject at all, this is a book you will want on your shelf.I know of no other book on the subject that covers such deep material while remaining as accessible.

Good introduction to the beginning student
This book gives a quick and elementary introduction to the field of chaotic dynamical systems that could be read by anyone with a background in calculus and linear algebra. The approach taken by the author is very intuitive, lots of diagrams are used to illustrate the major points, and there are many useful exercises throughout the book. It could serve well in an undergraduate mathematics course in dynamical systems, and in a physics undergraduate course in advanced mechanics. The author emphasizes the mathematical aspects of dynamical systems, and readers will be well prepared after finishing it to read more advanced books on dynamical systems.

Chapter 1 introduces one-dimensional dynamics, with the analysis of the quadratic map given particular attention. Called the logistic map in some circles, this very important dynamical system has been the subject of much study, and exhibits generically the properties of chaotic dynamical systems. The author also gives a brief review of some elementary notions in calculus needed for the chapter, making the book even more accessible to a wider readership. The important concept of hyperbolicity is discussed in the context of one-dimensional maps and a good discussion is given on symbolic dynamics. Structural stability, which is really useful only in dynamical systems in higher dimensions, is treated here. The intuition gained in one-dimension is invaluable though before moving on to higher-dimensional examples. Sarkovskii's theorem, which states that a one-dimensional dynamical system with a period three periodic orbit has periodic orbits for all other periods, is proved in detail. In addition, the Schwarzian derivative, so important in complex dynamics, is defined here. The author also gives an introduction to bifurcation theory, which again, is most interesting in high dimensions, and introduces the concept of homoclinicity in this discussion. Maps of the circle and the all-important Morse-Smale diffeomorphisms, are treated in this chapter also. The author introduces the reader briefly to the idea of genericity when discussing Morse-Smale diffeomorphisms. Kneading theory, so important in the mathematical theory of dynamical systems, is introduced here also.

In chapter 2, the author generalizes the results to higher dimensions, and begins with a review of linear algebra and some results from multivariable calculus, such as the implicit function theorem and the contraction mapping theorem. This is followed by a treatment of the dynamics of linear maps in two and three dimensions. Whereas the canonical example of one-dimensional dynamics is represented by the logistic map, in higher-dimensional dynamics this is represented by the Smale horseshoe map. The author carefully constructs this map and details its properties. Then he takes up the hyperbolic toral automorphisms (or Anosov systems as they are called in some books). Both the Smale horseshoe map and the toral automorphisms are excellent, easily understandable examples of higher dimensional dynamics and the associated symbolic dynamics.

The concept of an attractor is also treated in chapter 2 in the context of the solenoid and the Plykin attractor. Both of these are of purely mathematical interest, but by studying them the physicist reader can get a better understanding of what to look for in actual physical examples of attractors (or the more exotic concept of a strange attractor). The author also gives a proof of the stable manifold theorem in dimension two. This is the best part of the book, for this theorem is rarely proved in textbooks on chaotic dynamics, the proof being delegated to the original papers. However, the proof in these papers is extremely difficult to get through, and so the author has given the reader a nice introduction to this important result, even though it is done only in two dimensions. This is followed by a very understandable discussion of Morse-Smale diffeomorphisms. In addition, the author introduces the Hopf bifurcation, of upmost importance in applications, and introduces the Henon map as an application of the results obtained so far.

The last chapter of the book is a brief overview of complex analytic dynamics. Complex dynamical systems are very important from a mathematical point of view, and they have fascinating connections with number theory, cryptography, algebraic geometry, and coding theory. The author reviews some elementary complex analysis and then reintroduces the quadratic maps but this time over the complex plane instead of the real line. The Julia set is introduced, and the reader who has not seen the computer graphical images of this set should peruse the Web for these images, due to their beauty. The geometry of the Julia set and the associated complex polynomial maps are given a fairly detailed treatment by the author in the space provided.

The best starting point.
This book covers almost every aspect of theory of discrete dynamical systems and by far the easiest explains and proofs with useful exercises, anyone with solid calculus and linear algebra background shouldn't have anyproblem absorbing this material and is highly recommended to whom wants toknow about the theory of chaos from the scratch.

The best starting point.
This book covers almost every aspect of theory of discrete dynamical systems and by far the easiest explains and proofs with useful exercises, anyone with solid calculus and linear algebra background shouldn't have anyproblem absorbing this material and is highly recommended to whom wants toknow about the theory of chaos from the scratch. ... Read more

Product Description
Technical problems often lead to differential equations with piecewise-smooth right-hand sides. Problems in mechanical engineering, for instance, violate the requirements of smoothness if they involve collisions, finite clearances, or stick–slip phenomena. Systems of this type can display a large variety of complicated bifurcation scenarios that still lack a detailed description. This book presents some of the fascinating new phenomena that one can observe in piecewise-smooth dynamical systems. The practical significance of these phenomena is demonstrated through a series of well-documented and realistic applications to switching power converters, relay systems, and different types of pulse-width modulated control systems. Other examples are derived from mechanical engineering, digital electronics, and economic business-cycle theory.

The topics considered in the book include abrupt transitions associated with modified period-doubling, saddle-node and Hopf bifurcations, the interplay between classical bifurcations and border-collision bifurcations, truncated bifurcation scenarios, period-tripling and -quadrupling bifurcations, multiple-choice bifurcations, new types of direct transitions to chaos, and torus destruction in nonsmooth systems.

In spite of its orientation towards engineering problems, the book addresses theoretical and numerical problems in sufficient detail to be of interest to nonlinear scientists in general. ... Read more

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"The text treats a remarkable spectrum of topics and has a little for everyone. It can serve as an introduction to many of the topics of dynamical systems, and will help even the most jaded reader, such as this reviewer, enjoy some of the interactive aspects of studying dynamics using Maple."

—UK Nonlinear News (Review of First Edition)

"The book will be useful for all kinds of dynamical systems courses…. [It] shows the power of using a computer algebra program to study dynamical systems, and, by giving so many worked examples, provides ample opportunity for experiments. … [It] is well written and a pleasure to read, which is helped by its attention to historical background."

—Mathematical Reviews (Review of First Edition)

Since the first edition of this book was published in 2001, Maple™ has evolved from Maple V into Maple 13. Accordingly, this new edition has been thoroughly updated and expanded to include more applications, examples, and exercises, all with solutions; two new chapters on neural networks and simulation have also been added. There are also new sections on perturbation methods, normal forms, Gröbner bases, and chaos synchronization.

The work provides an introduction to the theory of dynamical systems with the aid of Maple. The author has emphasized breadth of coverage rather than fine detail, and theorems with proof are kept to a minimum. Some of the topics treated are scarcely covered elsewhere. Common themes such as bifurcation, bistability, chaos, instability, multistability, and periodicity run through several chapters.

The book has a hands-on approach, using Maple as a pedagogical tool throughout. Maple worksheet files are listed at the end of each chapter, and along with commands, programs, and output may be viewed in color at the author’s website. Additional applications and further links of interest may be found at Maplesoft’s Application Center.

Dynamical Systems with Applications using Maple is aimed at senior undergraduates, graduate students, and working scientists in various branches of applied mathematics, the natural sciences, and engineering.

ISBN 978-0-8176-4389-8

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Also by the author:

Dynamical Systems with Applications using MATLAB^®, ISBN 978-0-8176-4321-8

Dynamical Systems with Applications using Mathematica^®, ISBN 978-0-8176-4482-6

Customer Reviews (8)

Maple a powerfull tool
This is an excellent book. It helps the beginners of "Dynamical Systems" to understand this branch of Mathematical Physics using Maple. It is very usefulfor undergraduate students as well as for teachers.

More information
Thought I'd give a more in depth review than the others here.

Most advanced math textbooks contain one or two chapters that turn me off. I must say that every chapter in this book had useful information or very good applications.

The opening chapter is a brief introduction to Maple V (some Maple 8 commands are posted on the books website). Note that Maple 9 is now out and no doubt Maple X will soon follow.

Chapters 1-7 cover planar systems in some detail, vectorfield in DEplot is a real winner here. Chapters 8 and 9 cover 3D and nonautonomous systems - the poincare command in Maple is a real time saver.

Chapters 10-12 cover a lot of research results on limit cycles - the most lucid I have seen in any textbook.

The remaining half of the book concentrates on both real and complex discrete systems. There are the usual cobweb diagrams, bifurcation diagrams and Mandelbrot set. Where this book comes into its own, however, is in Chapters 16-20.

Lasers and nonlinear optics are investigated using complex iterative maps. Fractals and even multifractals are discussed in some detail. The book ends with a chapter dedicated to chaos control.

Overall, the book is concise with pertinent examples and applications. It is not dogged down with math notation, theorems and proofs.

Strogatz, Perko and Allgood are good books to practice more Maple programing techniques.

This is great book
This is only book I find with program files that work right away. Graphics in Maple is excelent for chaotic system and algebra very powerful. I like to rotate figures in 3D and use animation. I learn more about optics, it nice to see complex numbers used in applications. Lots of other applications also.

Book is best for students who want to get programs working quickly. There is a website with working programs. You should also look at Maple Application website for many many examples.

I recomend book to everyone.

very nice introduction to dynamical systems
This book is a very nice introduction to the theory of dynamical
systems. It covers all aspects and even more than usually thaught
in a class on dynamical systems. Especially, I like to see
many examples for various applications. These examples and the
Maple programs make it well suitable for students to learn
on dynamical systems by themself.

The MAPLE programs and web pages make this book unique.
A great book. Great web pages and short, easy to copy and edit
Maple programs. Lots of material not covered in other books on this topic. Maple is my favorite package. The others are not
as user friendly. I felt I must write again since amazon have been showing excerpts from book. What a geat idea. Chapters in this book that interested me were fractals, multifractals and
optics. Authors web-site is given on back cover of book. Enjoy! ... Read more

Product Description

This volume deals with controllability and observability properties of nonlinear systems, as well as various ways to obtain input-output representations. The emphasis is on fundamental notions as (controlled) invariant distributions and submanifolds, together with algorithms to compute the required feedbacks.

Customer Reviews (2)

Very good
It has arrived in the time due, and the conditions are very good. Nothing more to say.

Nonlinear Dynamical Systems from Nijmeier and van der Schaft
This is an excelent, book where students of nonlinear control theory can be oriented into the heart of the theory, and also expertises in this topic can find a great amount of results written in a very readable and conscious style. ... Read more

Product Description
Several distinctive aspects make Dynamical Systems unique, including:otreating the subject from a mathematical perspective with the proofs of most of the results includedoproviding a careful review of background materialsointroducing ideas through examples and at a level accessible to a beginning graduate studentofocusing on multidimensional systems of real variablesThe book treats the dynamics of both iteration of functions and solutions of ordinary differential equations. Many concepts are first introduced for iteration of functions where the geometry is simpler, but results are interpreted for differential equations. The dynamical systems approach of the book concentrates on properties of the whole system or subsets of the system rather than individual solutions. The more local theory discussed deals with characterizing types of solutions under various hypothesis, and later chapters address more global aspects. ... Read more

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This book explores the process of modeling complex systems in the widest sense of that term, drawing on examples from such diverse fields as ecology, epidemiology, sociology, seismology, as well as economics. It also provides the mathematical tools for studying the dynamics of these systems. Boccara takes a carefully inductive approach in defining what it means for a system to be "complex" (and at the same time addresses the equally elusive concept of emergent properties). This is the first text on the subject to draw comprehensive conclusions from such a wide range of analogous phenomena.

Customer Reviews (2)

A very good intructory book
This book encloses a large variety of models in an introductory level and opens the possibility to the students to go deep in specific topics through its references. So, it is adequate for a regular course on complex systems. The mean-field part of book provides a concise, clear and complete presentation of dynamical systems. In my opinion, the agent-based chapters iswell presented, but do not cover satisfactorily the criticality of epidemic spreading, a central point in complex system modeling.

A good comprehensive presentation of the state of the art
This is a fine book to learn the state of the art in 2004 in the field of complex systems modeling. It has the right blend of useful illustrations from many types of applications and of clean mathematics, without overdoing it in terms of abstraction. It is expensive but I don't regret my purchase. ... Read more

Product Description
Discrete dynamics is the study of change.In particular, it shows how to translate real world situations into the language of mathematics.With the increase in computational ability and the recent interest in chaos, discrete dynamics has emerged as an important area of mathematical study.This text is the first to provide an elementary introduction to the world of dynamical systems. The aim of the text is to explain both the wide variety of techniques used to study dynamical systems and their many applications in areas ranging from population growth to problems in genetics.This investigation leads to the fruitful concepts of stability, strange attractors, chaos, and fractals.Very little previous mathematical knowledge is assumed and students with an elementary exposure to calculus and linear algebra will be able to follow the text easily.A large number of worked examples and exercises are provided to assist instruction. Throughout, students are encouraged to experiment with models of dynamical systems on computers and explore this fascinating area of mathematics on their own. ... Read more

Customer Reviews (1)

Excellent textbook on chaos!
Although this text lacks the brightly-colored fractals of many other works, the coverage it gives to the mathematics end of things more than makes up for it.It deals very well with the concepts of statistics and dynamic equations that are necessary for the understanding of chaos, presuming very little in the way of mathematical knowledge on the part of the reader.All definitions are clearly delineated, and the answers to the exercises are provided in the back. ... Read more

Product Description
This book is an introduction to topological dynamics and ergodic theory. It is divided into a number of relatively short chapters with the intention that each may be used as a component of a lecture course tailored to the particular audience. The authors provide a number of applications, principally to number theory and arithmetic progressions (through Van der Waerden's theorem and Szemerdi's theorem). This text is suitable for advanced undergraduate and beginning graduate students. ... Read more

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Customer Reviews (2)

Different view
Among the loads of literature on chaos theory, this one is definitely different and the one to chek up on.

Sanity confronts chaos theory
The author investigates the question: with all the research (and hype) in chaos theory, what has been the actual impact on our understanding of the world? I give the book 5 stars for completing it's stated mission, being readable and enjoyable, and for not pandering to a lcd.

Kellert approaches this question from a philosophical, but down-to-earth, view. From the start, this is certainly not a "gee-whiz" hop-on-the-bandwagon book. In fact, the prologue begins: "Chaos theory is not as interesting as it sounds. How could it be?"

Yet, Kellert is not out to dismiss chaos theory, but rather to make sense of what the implications of chaos theory are. Unpredictability and determinism are two such topics potentially affected by chaos theory. Quantum mechanics is another topic influenced by chaos theory. And later in the book he ponders the historical question: why did it take so long for nonlinear dynamics (chaotic systems) to come under study?

There is very little math. The intended audience seems to be those who have some notion of chaos theory already, and although an introductory chapter is included, it would be helpful to understand conceptually what a Lyapunov exponent is and what bifurcation means.

The book is footnoted sufficiently but not overdone. It is heavily (but not annoyingly) referenced with everyone from Poincare to Prigogine. Despite the years that have passed since initial publication, I do not think this book has become obsolete. Another way to say this is: chaos theory (and it's results) is still not the mind-shattering revolution that some have made it out to be.

If you have some science and math background and have been asking yourself "So, just what the heck does all this talk about chaos theory really mean??", then this book is for you. ... Read more

Customer Reviews (1)

The Seminal Book on Chaos Theory in Psychology
This was the first book to explicitly describe how non-linear dynamics applied to psychology. In writing it, Fred Abraham drew on the 4-volume series on visual mathematical books on Dynamics, by Fred's brother Ralph Abraham (a pioneer in chaos theory) and Christopher Shaw. As such, it not only applied non-linear dynamical concepts like Attractors, State Spaces, and Bifurcations to psychology, it actually showed what such mathematical concepts looked like. Though chaos theory has been most useful for psychology as metaphor, the metaphor is immeasurably enriched by understanding - and visualizing - the actual under-pinnings of dynamic change. A difficult to find book at present, but well worth it for anyone interested in how non-linear dynamics is important for not only psychology but any of the so-called "soft" sciences. ... Read more

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Product Description

In this volume, the authors present a collection of surveys on various aspects of the theory of bifurcations of differentiable dynamical systems and related topics. By selecting these subjects, they focus on those developments from which research will be active in the coming years. The surveys are intended to educate the reader on the recent literature on the following subjects: transversality and generic properties like the various forms of the so-called Kupka-Smale theorem, the Closing Lemma and generic local bifurcations of functions (so-called catastrophe theory) and generic local bifurcations in 1-parameter families of dynamical systems, and notions of structural stability and moduli.

Product Description
This is an introductory textbook on the geometrical theory of dynamical systems, fluid flows and certain integrable systems. The topics are interdisciplinary and extend from mathematics, mechanics and physics to mechanical engineering, and the approach is very fundamental. The main theme of this book is a unified formulation to understand dynamical evolutions of physical systems within mathematical ideas of Riemannian geometry and Lie groups by using well-known examples. Underlying mathematical concepts include transformation invariance, covariant derivative, geodesic equation and curvature tensors on the basis of differential geometry, theory of Lie groups and integrability. These mathematical theories are applied to physical systems such as free rotation of a top, surface wave of shallow water, action principle in mechanics, diffeomorphic flow of fluids, vortex motions and some integrable systems. In the latest edition, a new formulation of fluid flows is also presented in a unified fashion on the basis of the gauge principle of theoretical physics and principle of least action along with new type of Lagrangians. A great deal of effort has been directed toward making the description elementary, clear and concise, to provide beginners easy access to the topics. ... Read more

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Randomness and Recurrence in Dynamical Systems makes accessible, at the undergraduate or beginning graduate level, results and ideas on averaging, randomness and recurrence that traditionally require measure theory. Assuming only a background in elementary calculus and real analysis, new techniques of proof have been developed, and known proofs have been adapted, to make this possible. The book connects the material with recent research, thereby bridging the gap between undergraduate teaching and current mathematical research. The various topics are unified by the concept of an abstract dynamical system, so there are close connections with what may be termed 'Probabilistic Chaos Theory' or 'Randomness'. The work is appropriate for undergraduate courses in real analysis, dynamical systems, random and chaotic phenomena and probability. It will also be suitable for readers who are interested in mathematical ideas of randomness and recurrence, but who have no measure theory background. ... Read more

Product Description
A text devoted to the study of non-smooth dynamical systems. Develops a rigorous theory by working with only simple model problems, in order to produce good results. For mathematicians, researchers, and engineers interested in mathematical techniques for analysis of non-smooth dynamical systems. Softcover. ... Read more