Description of complex dynamics in a class of impulsive differential equations

Dynamical evolutions involving from equilibrium state to complex motion are prevalent not only in systems depicted by either continuous equations or discrete iterations but also in models governed by hybrid systems. In particular, chaotic motion could be found in hybrid systems whose dimension is even less than three. In this paper, we attempt to provide some concepts to describe various dynamics that occur in the simulations of a class of impulsive differential equations. Furthermore, some specific examples are also provided to illustrate these established concepts.