非自治随机格点动力系统的渐近行为

本项目研究非自治随机格点动力系统的渐近行为，首先探讨一般非自治随机格点动力系统存在随机吸引子的充分条件，然后把所得到的结果应用到具体的非自治随机格点动力系统，探讨这些系统的随机吸引子的存在性和连续性。通过引进对应于确定性非自治项的关于时间的动力系统和对应于随机项的遍历度量动力系统，建立由这两个动力系统共同驱动的随机动力系统，从而解决确定性非自治项和随机项对系统的渐近行为产生不同影响所造成的困难。本项目期望能揭示非自治随机格点动力系统的演化规律，为其它科学和技术领域提供理论基础。

This project is to investigate the asymptotic behavior of non-autonomous stochastic lattice dynamical systems (LDSs). We first study some sufficient conditions for the existence of random attractors for general non-autonomous stochastic LDSs. Then we apply the result to specific non-autonomous stochastic LDSs and discuss the existence and continuity of random attractors for these systems. By introducing a dynamical system about time corresponding to the deterministic non-autonomous term and an ergodic metric dynamical system corresponding to the stochastic term, we establish the random dynamical system driven by these two dynamical systems. Then we can overcome the difficulties which the deterministic non-autonomous term and the stochastic term have different influences on the asymptotic behavior. We expect that this project will explore the evolution of non-autonomous stochastic LDSs and lay a theoretical foundation for other fields of science and technology.