Elements of Applied Bifurcation Theory

by Yuri A. Kuznetsov

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.

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.