Elements of Applied Bifurcation Theory (Applied Mathematical Sciences, 112) 3rd Edition by Yuri Kuznetsov (PDF)

Description

Providing readers with a solid basis in dynamical systems theory, as well as explicit procedures for application of general mathematical results to particular problems, the focus here is on efficient numerical implementations of the developed techniques. The book is designed for advanced undergraduates or graduates in applied mathematics, as well as for Ph.D. students and researchers in physics, biology, engineering, and economics who use dynamical systems as model tools in their studies. A moderate mathematical background is assumed, and, whenever possible, only elementary mathematical tools are used. This new edition preserves the structure of the first while updating the context to incorporate recent theoretical developments, in particular new and improved numerical methods for bifurcation analysis.

User’s Reviews

Editorial Reviews: Review Review of earlier edition”I know of no other book that so clearly explains the basic phenomena of bifurcation theory.” Math Reviews “The book is a fine addition to the dynamical systems literature. It is good to see, in our modern rush to quick publication, that we, as a mathematical community, still have time to bring together, and in such a readable and considered form, the important results on our subject.” Bulletin of the AMSFrom the reviews of the third edition:”In the third edition of this textbook, the material again has been slightly extended while the main structure of the book was kept. … the clear structure of the book allows applied scientists to use it as a reference book. … Kuznetsov’s book on applied bifurcation theory is still very useful both as a textbook and as a reference work for researchers from the natural sciences, engineering or economics.” (Jörg Härterich, Zentralblatt MATH, Vol. 1082, 2006)“This book deals with the theory of dynamical systems relevant for applications. The material is presented in a systematic and very readable form. It covers recent developments in bifurcation theory, with special attention to efficient numerical implementations. The text aims at an audience of graduate and Ph.D. students in applied mathematics, and researchers in science and engineering, who use dynamical systems and bifurcation analysis as a tool. Each chapter contains useful examples and many illustrations.” (Dirk Roose, Bulletin of the Belgian Mathematical Society, 2007) From the Back Cover This is a book on nonlinear dynamical systems and their bifurcations under parameter variation. It provides a reader with a solid basis in dynamical systems theory, as well as explicit procedures for application of general mathematical results to particular problems. Special attention is given to efficient numerical implementations of the developed techniques. Several examples from recent research papers are used as illustrations. The book is designed for advanced undergraduate or graduate students in applied mathematics, as well as for Ph.D. students and researchers in physics, biology, engineering, and economics who use dynamical systems as model tools in their studies. A moderate mathematical background is assumed, and, whenever possible, only elementary mathematical tools are used. This new edition preserves the structure of the previous editions, while updating the context to incorporate recent theoretical and software developments and modern techniques for bifurcation analysis. Reviews of earlier editions: “I know of no other book that so clearly explains the basic phenomena of bifurcation theory.” – Math Reviews “The book is a fine addition to the dynamical systems literature. It is good to see, in our modern rush to quick publication, that we, as a mathematical community, still have time to bring together, and in such a readable and considered form, the important results on our subject.” – Bulletin of the AMS “It is both a toolkit and a primer” – UK Nonlinear News

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Ver y good

⭐I’ve had a love/hate relationship with this text for the past two years. Originally, I had purchased it to accompany lectures notes for a graduate-level bifurcation theory course, and at the time, I made use of it, albeit not much. Fast forward one year later, and I’ve been referring to this book constantly for the past two months. The following is relevant to Chapters 3 to 5, of which I read most thoroughly.Kuznetsov’s proofs are detailed and do not leave much work for the reader to sort out. Being marketed as an introductory text, they should be. His presentation of normal forms and center manifold reduction is very clear, and in particular, Section 5.4 on calculation of center manifolds is incredibly useful in practice, and the methods therein are applicable to parameter-dependent systems. That being said, there is a distinct lack of examples involving discrete systems, and the presentation of results for the discrete case is also a bit more hand-wavey at times. This is especially true for the center manifold reduction, where Kuznetsov mentions that a similar technique works for discrete-time systems, but does not provide an example of how to apply, or suggest at how to begin to apply the method. Fortunately, this is elaborated upon in a later chapter. However, for this reason, Kuznetsov is a far better REFERENCE than a primary learning resource.On the other hand, I don’t know of any other dynamical systems texts that cover even the codimension one case at a level of sophistication close to this, yet provide adequate examples and are presented at an elementary level suitable to beginners. Wiggins’ “Introduction to Applied Nonlinear Dynamical Systems and Chaos” comes close, except the vast majority of that volume would be impenetrable to many a novice to the field (although the chapter on bifurcation theory is phenomenal).In conclusion, Kuznetsov’s Elements of Applied Bifurcation Theory is an excellent reference, and much of the volume is certainly accessible to a beginning graduate student. The presentation is clear, and the section on explicit calculation of center manifolds indispensable. However, there are at times too few examples illustrating the important techniques.

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