Random Attractors And Exponential Stability For Second Order Non-autonomous Stochastic Retarded Lattice Systems With Multiplicative White Noise

In this thesis,we mainly study the existence,singleness and exponential stability of random attractors for non-autonomous second-order stochastic lattice systems with multiplicative white noise.This thesis is divided into the following three parts:The first chapter briefly summarize the background and introduce the main research content,then we give the preparatory knowledge that we need to use in this thesis.The second chapter,we first present some conditions for the existence of a random attractor of continuous cocycle and locally coupled stochastic retarded lattice dynamical systems in a space of continuous functions from finite closed interval into a product space of finite weighted spaces of infinite sequences.In chapter three,we consider the existence,structure and exponentially stability of the random attractor for the second order stochastic retarded lattice systems with multiplicative white noise.Firstly,we use O-U process to transform the lattice system with multiplicative white noise into a lattice system without white noise,the solution of the lattice system generates continuous cocycles on infinite sequence space.Then,we estimate the bound and tail of the solution for the transformed system and obtain the existence of the random attractor.Thirdly,we verify that the random attractor is a single point set in the infinite sequence space which exponentially pullback attracts all the solutions of the system.Finally,we further prove the convergence of the single point set random attractor when the delay tends to zero.