随机动力系统涉及常（偏）微分方程、动力系统和随机分析等多分支理论，具有非常重要的理论研究意义和实际应用价值。退化非高斯噪声对应的Malliavin协方差矩阵具有不可逆且计算很困难，导致当前由退化非高斯噪声驱动的随机耗散发展方程的适定性和遍历性研究结论很少，该问题的研究具有重要的研究价值和较大的挑战性。通过建立随机抛物方程的比较原理和大偏差原理等随机动力系统理论来研究随机生物模型的随机行波解是动力系统的前沿课题，具有重要的理论研究价值。本项目主要通过对退化非高斯噪声驱动的几类随机耗散方程不变测度的存在唯一性及指数混合性等基本遍历特性的研究、揭示基于随机动力系统遍历理论的非高斯随机KPP型模型的随机行波解及其波速估计原理，进而研究时间分数阶随机发展方程的适定性和正则性等的基本理论，分析非高斯噪声和时间分数阶的指数等因素对随机动力系统的动力学的影响，探索项目研究中的新现象和新方法。

The theory of random dynamical systems is related to the discipline of ordinary (partial) differential equations, dynamical systems and stochastic analysis. Due to the irreversibility of the Malliavin covariance matrix corresponding to the non-Gauss noise, which is difficult to calculate, there is a few results on the well-posedness and the ergodicity of the stochastic dissipative evolution equations driven by non-Gauss noise. Hence it has important research value with great challenge. It is also important to study the random traveling wave solutions of stochastic models based on the theory of random dynamical system, such as the comparison principle of stochastic parabolic differential equations and the large deviation principle. .. The main task of this project is to study the existence, uniqueness and mixing exponential stability of the invariant measure for some stochastic dissipative equations driven by degenerate non-Gauss noise. By applying the theory of random dynamical systems，we study the existence and asymptotic propagation speed of the random traveling wave for stochastic Fisher-KPP-type model driven by non-Gauss noise. Finally, the well-posedenss and regularity of time-fractional stochastic evolution equations will be explored as well. The effects of the non-Gaussian driving noise, the fractional index and some other factors on the corresponding random dynamic system should be clarified accompanying with some mew research phenomena and new approaches during the whole research process.