PhD Comprehensive Seminar | Kevin Church, Bifurcations in impulsive systems

MC 5417

Candidate

Kevin Church
Applied Mathematics, University of Waterloo

Title

Bifurcations in impulsive systems

Abstract

Impulsive differential equations are frequently used to model phenomena that exhibit changes in state on small time scales relative to the overall system dynamics.  Bifurcation theory is the study of qualitative changes of solutions of dynamical systems due to variation of system parameters.  Classical bifurcation theory of smooth ordinary differential equations and difference equations assumes an autonomy (a lack of explicit time dependence) of the vector field or map in question.  For this reason, different techniques are needed to study bifurcations in general impulsive systems.  The purpose of this seminar is to provide a general background on smooth bifurcation theory and its applications. Following this, we demonstrate the need for a bifurcation theory for impulsive systems.