Elements of Applied Bifurcation Theory (2nd Ed) (Applied Mathematical Sciences

by Brand: Springer-Verlag (Brand)

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 1st edition while updating the context to incorporate recent theoretical developments, in particular new and improved numerical methods for bifurcation analysis. Review of 1st "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

Genres: Mathematics

591 pages, Hardcover

First published April 1, 1995

Reviews

[C. Hinsley]

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.