Pullback Attractor Of Non-autonomous Stochastic Lattice Dynamical Systems With Delay

Lattice systems are very useful mathematical models, and have very im-portant in theoretical significance and application value in many fields such as the physics、chemistry and biology.In the past few decades, the systems have received extensive attention and been researched. At present, some basic theories about attractors of the autonomous deterministic dynamical systems and autonomous random dynamical systems have been well developed, How-ever, the theories on the non-autonomous random dynamical systems need to be further investigated and improved.Therefore,it is very necessary to study the corresponding theory about non-autonomous dynamical systems. In many practical systems, external force term may contain some genetic or memo-ry features,so it is practical to study the non-autonomous random dynamical system in which external force term is with delay.The paper will study the pullback attractor of the equation:The paper is organized as follows:In Chapter1,firstly, we introduce the research background of the equa- tion and present research status of the random dynamical system.Then,some preliminary concepts and results related to random dynamical system are in-troduced.In Chapter2,firstly,we give brief presention and describtion of the above equation, and through the Ornstein-Uhlenbeck process, we transform the orig-inal equations into the equations with random coeffcients in order to facilitate the following discussion on random dynamical system. Then, we study the ex-istence of solution of the equation, Moreover, we establish a continuous cocycle on the spaceXh-In Chapter3,We study the existence of pullback attractor of the above equation. Firstly, by the uniform estimates established for solutions, we get a conclusion that the continuous cocycle has bounded absorbing set, then by uniform estimates of the "tail" of the solution, we prove the asymptotic compactness of stochastic dynamic systems. Finally,we come to prove the existence,uniqueness and the periodicity under certain conditions of pullback attractors of the above equation.