A survey on impulsive dynamical systems

Abstract

In this survey we provide an introduction to the theory of impulsive dynamical systems in both the autonomous and nonautonomous cases. In the former, we will show two different approaches which have been proposed to analyze such kind of dynamical systems which can experience some abrupt changes in their evolution (impulses). But, unlike the autonomous framework, the nonautonomous one is being developed right now and some progress is being obtained over the recent years. We will provide some results on how the theory of autonomous impulsive dynamical systems can be extended to cover such nonautonomous situations, which are more often to occur in the real world.

Keywords

• impulsive dynamical systems
• global attractors
• nonautonomous dynamical systems
• cocycle attractors
• navier-stokes equation