Canards, Chaos, and Relaxation Oscillations: Dynamical Systems with Multiple Time Scales

John Guckenheimer, Cornell University

Dynamical systems theory describes properties of "generic" dynamical systems but the results change in the presence of multiple time scales. This lecture will give an overview of phenomena that occur in this setting, including "canards," "folded singularities," and the first examples of chaotic dynamical systems. The concept of the slow-fast decompositions will serve as a unifying framework for describing bifurcations of relaxation oscillations. The forced van der Pol equation and models of neural oscillations will be used to illustrate the phenomena.

The P/T Colloquium is
typically held each
Thursday, 3:45–5:00 PM.
Refreshments are served
at 3:15 PM.