Impulses in driving semigroups of nonautonomous dynamical systems: Application to cascade systems

Abstract

In this paper we investigate the long time behavior of a nonautonomous dynamical system (cocycle) when its driving semigroup is subjected to impulses. We provide conditions to ensure the existence of global attractors for the associated impulsive skew-product semigroups, uniform attractors for the coupled impulsive cocycle and pullback attractors for the associated evolution processes. Finally, we illustrate the theory with an application to cascade systems.