MC 5417
Candidate
Kevin
Church
Applied
Mathematics,
University
of
À¶Ý®ÊÓƵ
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. ÌýBifurcation theory is the study of qualitative changes of solutions of dynamical systems due to variation of system parameters. ÌýClassical 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. ÌýFor this reason, different techniques are needed to study bifurcations in general impulsive systems. ÌýThe 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. Ìý