Elements of Applied Bifurcation Theory (Applied Mathematical Sciences) - Hardcover

Kuznetsov, Iu. A.; Kuznetsov, Yuri A.

Hardcover

ISBN 10: 0387944184 ISBN 13: 9780387944180

Publisher: Springer Nature, 1995

Synopsis

This book is about nonlinear dynamical systems and their bifurcations under parameter variation. It aims to provide 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.
Basic results of bifurcation theory, such as Andronov-Hopf, planar homoclinic, period-doubling, and Neimark-Sacker bifurcations, are presented in much detail, including self-contained proofs not available in existing textbooks. Several recent results are also discussed, like generic two-parameter bifurcations of equilibria and fixed points, bifurcations of homoclinic orbits to non-hyperbolic equilibria, and one-parameter bifurcations of limit cycles in systems with reflectional symmetry, which are hardly covered in graduate-level textbooks. The presented material is sufficient to perform quite complex bifurcation analysis of dynamical systems and to understand basic methods, results, and terminology used in modern applied mathematics literature.

About this title

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

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 AMS

From 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)

Edition details

• Publisher: Springer Nature
• Publication date: 1995
• Language: English
• ISBN 10: 0387944184
• ISBN 13: 9780387944180
• Binding: Hardcover
• Number of pages: 598