Random Attractor For Two Kinds Of Lattice Systems With Infinite White Noise

This dissertation mainly investigate the asymptotic behavior of stochastic lattice differential equations with a different infinite white noise at different each node.In the previous results in the most literature,the stochastic lattice differ-ential equations only considered the behavior with the same noise at all nodes.In fact,it is more reasonable that we use different noise to describe the stochastic disturbance at different each node.Structure of this paper as follows:The first chapter,we introduce the history and the development of random lattice dynamical systems,random attractor,and some preliminary results and definitions and frequently used inequalities,and the main research work for this paper.In the second chapter,we present Ornstein-Uhlenbeck transformation as well as some corresponding properties and an existence theorem for weak solutions to general random evolution equations.In the third chapter,we study the existence of global random attractor for first order stochastic lattice dynamical system with a different infinite additive white noise at different each node.In the fourth chapter,we prove the existence of global random attractor for stochastic FitzHugh-Nagumo dynamical system with a different infinite multi-plicative white noise at different each node.In the fifth chapter,we briefly summarize the conclusions obtained in this paper and put forward problem remaining to be solved.