Attractors for nonautonomous and random dynamical systems perturbed by impulses

Nonautonomous and random dynamical systems perturbed by impulses are considered. The impulses form a flow. Over this flow the perturbed system also has the structure of a new nonautonomous/random dynamical system. The long time behavior of this system is considered. In particular the existence of an attractor is proven. The result can be applied to a large class of dissipative systems given by partial or ordinary differential equations. As an example of this class of problems the Lorenz system is studied. For another problem given by a one-dimensional affine differential equation and perturbed by affine impulses, the attractor can be calculated explicitly.