Random Perturbation of Invariant Manifolds for Non-Autonomous Dynamical Systems
Random Perturbation of Invariant Manifolds for Non-Autonomous Dynamical Systems
复制标题
非自治动力系统不变流形的随机扰动
DOI：
10.3390/math10060992
复制
发表时间：
2022-03
期刊：
影响因子：
2.4
通讯作者：
Xingjie Yan
中科院分区：
文献类型：
--
作者：
Tao Jiang;Zhongkai Guo;Xingjie Yan
随机不变流形是理解随机不动点附近随机影响下的动力学的有用几何对象。在动力系统的框架下，我们比较了扰动随机非自治偏微分方程和原始随机非自治偏微分方程。主要是在用色噪声代替高斯白色噪声的情况下，得到了随机不变流形的一些路径逼近结果，这是一种Wong-Zakai逼近。
Random invariant manifolds are geometric objects useful for understanding dynamics near the random fixed point under stochastic influences. Under the framework of a dynamical system, we compared perturbed random non-autonomous partial differential equations with original stochastic non-autonomous partial differential equations. Mainly, we derived some pathwise approximation results of random invariant manifolds when the Gaussian white noise was replaced by colored noise, which is a type of Wong–Zakai approximation.