Random Attractor Of Stochastic Klein-Gordon-Schr(?)dinger Lattice System

It is known that attractor is widely used to describe limit behavior of a large number of dissi-pative systems and it is shown that attractor is a very useful tool, therefore it is of great importance to study the existence of global attractor of dynamical systems generated by dissipative systems. It is also true for stochastic systems. However, in the stochastic case, the global is generally not a deterministic set, but a family of deterministic sets who depends on random parameters, i.e. random attractor.This paper is devoted to the existence of the random attractor of the random dynamical system generated by the KGS with white noises. It consists of three chapters.In the first chapter, we introduce the history and development of dynamical system, random dynamical system and random attractor.The second chapter gives such concepts as metric dynamical systems, random absorbing set, tempered random set, random attractor, and shows sufficient conditions on the existence of unique random attractor.In chapter 3 we devoted the dynamics of the stochastic Klein-Gordon-Schrodinger lattice system. It is shown that the random dynamical system generated by the system has a random attractor, which attracts all tempered random sets.