Elements of Applied Bifurcation Theory

by Yuri A. Kuznetsov

The years that have passed since the publication of the first edition of this book proved that the basic principles used to select and present the material made sense. The idea was to write a simple text that could serve as a seri­ ous introduction to the subject. Of course, the meaning of "simplicity" varies from person to person and from country to country. The word "introduction" contains even more ambiguity. To start reading this book, only a moder­ ate knowledge of linear algebra and calculus is required. Other preliminaries, qualified as "elementary" in modern mathematics, are explicitly formulated in the book. These include the Fredholm Alternative for linear systems and the multidimensional Implicit Function Theorem. Using these very limited tools, a of notions, results, and methods is gradually built that allows one to read (and possibly write) scientific papers on bifurcations of nonlinear dynamical systems. Among other things, progress in the sciences means that mathematical results and methods that once were new become standard and routinely used by the research and development community. Hopefully, this edition of the book will contribute to this process. The book's structure has been kept intact. Most of the changes introduced reflect recent theoretical and software developments in which the author was involved. Important changes in the third edition can be summarized as follows. A new section devoted to the fold-flip bifurcation for maps has appeared in Chapter 9.

Genres: Mathematics

654 pages, Hardcover

First published April 1, 1995

Reviews

[C. Hinsley · Rating 4 out of 5]

Yuri's a great guy and is most known in numerical bifurcation theory for developing much of MATCONT. This book is a good starting point for people getting into bifurcation theory of any kind, containing numerous brief expositions of Soviet dynamical systems results that are hard to find good concise writing about elsewhere. This is because he personally knows many of the mathematicians who developed these results and has been active in the field for a long time. Very easy to read, too. Some of the more intricate work from the Shilnikov-Afraimovich school is missing, such as some of the Belyakov & Bykov bifurcations, but one can just read the original papers about these without much trouble after this textbook; the mathematical methods are similar to those discussed here.

[DJ]

Deeper study of bifurcations that might be good for understanding neurocomputational properties.