Study of Local Dissipative Random Dynamical Systems

Abstract

The main objective of this work is to study local dissipation  in stochastic dynamical systems. The main properties of this concept were studied. In addition to presenting the necessary and sufficient conditions that make the random dynamic system a local dissipative. In Theorem 3.2, local dissipation is described in terms of Levinson center, and in Theorem 3.5, it is described in terms of  is a forward prolongation of the random set  and  is a forward limit prolongation of the random set . . Finally in Theorem 3.7 it is described by locally asymptotically condensing.