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41. Nonlinear Dynamical Systems: Feedforward Neural Network Perspectives (Adaptive and Learning Systems for Signal Processing, Communications and Control Series) by Irwin W. Sandberg, James T. Lo, Craig L. Fancourt, José C. Principe, Shigeru Katagiri, Simon Haykin | |
Hardcover: 312
Pages
(2001-02-21)
list price: US$147.95 -- used & new: US$44.70 (price subject to change: see help) Asin: 0471349119 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
42. Modeling Identification and Simulation of Dynamical System by P. P. J. van den Bosch, A. C. van der Klauw | |
Hardcover: 208
Pages
(1994-09-30)
list price: US$89.95 -- used & new: US$71.96 (price subject to change: see help) Asin: 0849391814 Canada | United Kingdom | Germany | France | Japan | |
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43. Introduction to Applied Nonlinear Dynamical Systems and Chaos (Texts in Applied Mathematics) by Stephen Wiggins | |
Paperback: 808
Pages
(2010-11-02)
list price: US$109.00 -- used & new: US$87.00 (price subject to change: see help) Asin: 1441918078 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description 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
Effective overview of a useful 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 |
44. Chaos and Complexity in Psychology: The Theory of Nonlinear Dynamical Systems | |
Hardcover: 552
Pages
(2008-11-10)
list price: US$110.00 -- used & new: US$83.99 (price subject to change: see help) Asin: 0521887267 Canada | United Kingdom | Germany | France | Japan | |
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45. Dynamical Systems (Dover Books on Mathematics) by Shlomo Sternberg | |
Paperback: 272
Pages
(2010-07-21)
list price: US$14.95 -- used & new: US$9.46 (price subject to change: see help) Asin: 0486477053 Canada | United Kingdom | Germany | France | Japan | |
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46. An Introduction to Chaotic Dynamical Systems, 2nd Edition by Robert Devaney, Robert L. Devaney | |
Paperback: 360
Pages
(2003-01)
list price: US$49.00 -- used & new: US$45.75 (price subject to change: see help) Asin: 0813340853 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (5)
Great Introduction to the topic
Excellent book; unique in its accessibility and coverage of deep results
Good introduction to the beginning student 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.
The best starting point. |
47. Bifurcations and Chaos in Piecewise-Smooth Dynamical Systems: Applications to Power Converters, Relay and Pulse-Width Modulated Control Systems, and Human ... Series on Nonlinear Science, Series a) by Zhanybai T. Zhusubaliyev, Erik Mosekilde | |
Hardcover: 370
Pages
(2003-08)
list price: US$142.00 -- used & new: US$130.56 (price subject to change: see help) Asin: 9812384200 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description 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. |
48. Dynamical Systems with Applications using Maple by Stephen Lynch | |
Paperback: 500
Pages
(2009-12-01)
list price: US$69.95 -- used & new: US$40.00 (price subject to change: see help) Asin: 0817643893 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description "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 § 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
More information 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 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
The MAPLE programs and web pages make this book unique. |
49. Nonlinear Dynamical Control Systems by Henk Nijmeijer, Arjan van der Schaft | |
Paperback: 492
Pages
(2010-11-02)
list price: US$159.00 -- used & new: US$126.44 (price subject to change: see help) Asin: 1441930914 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review 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
Nonlinear Dynamical Systems from Nijmeier and van der Schaft |
50. Dynamical Systems: Stability, Symbolic Dynamics, and Chaos (Studies in Advanced Mathematics) by Clark Robinson | |
Hardcover: 520
Pages
(1998-11-17)
list price: US$129.95 -- used & new: US$112.03 (price subject to change: see help) Asin: 0849384958 Canada | United Kingdom | Germany | France | Japan | |
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51. Modeling Complex Systems (Graduate Texts in Physics) by Nino Boccara | |
Paperback: 397
Pages
(2010-11-02)
list price: US$124.00 -- used & new: US$98.83 (price subject to change: see help) Asin: 1441923381 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description 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
A good comprehensive presentation of the state of the art |
52. Discrete Dynamical Systems: Theory and Applications by James T. Sandefur | |
Hardcover: 464
Pages
(1990-10-25)
list price: US$46.95 -- used & new: US$266.97 (price subject to change: see help) Asin: 0198533845 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (1)
Excellent textbook on chaos! |
53. Dynamical Systems and Ergodic Theory (London Mathematical Society Student Texts) by Mark Pollicott, Michiko Yuri | |
Paperback: 196
Pages
(1998-02-13)
list price: US$43.00 -- used & new: US$36.37 (price subject to change: see help) Asin: 0521575990 Canada | United Kingdom | Germany | France | Japan | |
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54. In the Wake of Chaos: Unpredictable Order in Dynamical Systems (Science and Its Conceptual Foundations series) by Stephen H. Kellert | |
Paperback: 190
Pages
(1994-12-15)
list price: US$22.50 -- used & new: US$20.22 (price subject to change: see help) Asin: 0226429768 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (2)
Different view
Sanity confronts chaos theory 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 |
55. A Visual Introduction to Dynamical Systems Theory for Psychology - 1990 publication. by Chris Shaw | |
Paperback:
Pages
(1990)
Isbn: 094234409X Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Customer Reviews (1)
The Seminal Book on Chaos Theory in Psychology |
56. Impulsive and Hybrid Dynamical Systems: Stability, Dissipativity, and Control (Princeton Series in Applied Mathematics) by Wassim M. Haddad, VijaySekhar Chellaboina, Sergey G. Nersesov | |
Hardcover: 520
Pages
(2006-07-03)
list price: US$80.00 -- used & new: US$74.36 (price subject to change: see help) Asin: 0691127158 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
57. Handbook of Dynamical Systems, Volume 3 | |
Hardcover: 560
Pages
(2010-10-26)
list price: US$240.00 -- used & new: US$240.00 (price subject to change: see help) Asin: 0444531416 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review 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. |
58. Geometrical Theory of Dynamical Systems and Fluid Flows (Advanced Series in Nonlinear Dynamics) by Tsutomu Kambe | |
Hardcover: 444
Pages
(2009-12-28)
list price: US$99.00 -- used & new: US$77.54 (price subject to change: see help) Asin: 9814282243 Canada | United Kingdom | Germany | France | Japan | |
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59. Randomness and Recurrence in Dynamical Systems (Carus Mathematical Monographs) by Rodney Nillsen | |
Hardcover: 357
Pages
(2010-10-29)
list price: US$62.95 -- used & new: US$62.95 (price subject to change: see help) Asin: 0883850435 Canada | United Kingdom | Germany | France | Japan | |
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60. Non-Smooth Dynamical Systems (Lecture Notes in Mathematics) by Markus Kunze | |
Paperback: 228
Pages
(2000-10-27)
list price: US$59.95 -- used & new: US$18.09 (price subject to change: see help) Asin: 3540679936 Canada | United Kingdom | Germany | France | Japan | |
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