Studying relaxation oscillators using geometric singular perturbation theory

Martin Wechselberger
Mathematical Biosciences Institute, The Ohio State University

(October 30, 2002 12:30 PM - 1:30 AM)

Studying relaxation oscillators using geometric singular perturbation theory

Abstract

Relaxation oscillations (RO), a highly nonlinear type of oscillation, are found in many biological, chemical, physical and neuronal problems. The characteristic feature of RO is a repeated switching between fast and slow motions. We will study the well known forced van der Pol oscillator, a model for a triode circuit. This oscillator exhibits all kinds of dynamical behaviour from synchronization up to 'chaos'. We will explain some of these properties by using techniques from dynamical systems, especially geometric singular perturbation theory (GSPT).