Elements of Applied Bifurcation Theory

by Yuri A. Kuznetsov

to Dynamical Systems.- Topological Equivalence, Bifurcations, and Structural Stability of Dynamical Systems.- One-Parameter Bifurcations of Equilibria in Continuous-Time Dynamical Systems.- One-Parameter Bifurcations of Fixed Points in Discrete-Time Dynamical Systems.- Bifurcations of Equilibria and Periodic Orbits in n-Dimensional Dynamical Systems.- Bifurcations of Orbits Homoclinic and Heteroclinic to Hyperbolic Equilibria.- Other One-Parameter Bifurcations in Continuous-Time Dynamical Systems.- Two-Parameter Bifurcations of Equilibria in Continuous-Time Dynamical Systems.- Two-Parameter Bifurcations of Fixed Points in Discrete-Time Dynamical Systems.- Numerical Analysis of Bifurcations.

Genres: Mathematics

598 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.