Impulsive delay differential equations: invariant manifolds, bifurcations, control and numerics

Kevin Church

The analysis of discontinuous dynamical systems presents some challenges from both a theoretical and applied standpoint. In the infinite-dimensional context of delay equations, these issues are further compounded: for instance, the two-parameter dynamical system associated to such a system can be discontinuous everywhere. With applications in engineering, the life sciences and other areas abound, there is a clear need to develop theoretical and computational techniques that can handle such systems.
In this talk we will present some recent advances in invariant manifold theory for impulsive functional differential equations (FDE) and some applications to bifurcation and control. It will be clear from the applications that one of the main bottlenecks in the analysis of impulsive FDE is the availability of suitable numerical methods. To this end, we will present some current work on spectral methods for Floquet multipliers and continuation of periodic solutions in nonlinear equations.