John Guckenheimer

Algorithms for Bifurcations

Dynamical systems theory elucidates geometric structure in the solution of ordinary differential equations. Bifurcation theory describes the changes that occur in these structures as parameters change. Algorithms based upon classical numerical methods and mathematical theory facilitate the visualization of dynamical systems. This chapter reviews the phenomena described by the theory and surveys the algorithms that are used to compute them. Examples are used throughout. Software packages that incorporate algorithms for studying dynamical systems are discussed and their performance is evaluated.

Tentative Outline:

Computation of trajectories
Invariant sets
Local bifurcations
Numerical issues and software packages
Global bifurcations (??)

John Guckenheimer

Jan 16 1998