Random Perturbation of Invariant Manifolds for Non-Autonomous Dynamical Systems

Tao Jiang, Zhongkai Guo and Xingjie Yan
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Tao Jiang: Collaborative Innovation Center of China Pilot Reform Exploration and Assessment, Hubei Sub-Center, Hubei University of Economics, Wuhan 430205, China
Zhongkai Guo: School of Mathematics and Statistics, South-Central University for Nationalities, Wuhan 430074, China
Xingjie Yan: Department of Mathematics, China University of Mining and Technology, Xuzhou 221116, China

Mathematics, 2022, vol. 10, issue 6, 1-12

Abstract: 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.

Keywords: random invariant manifold; random non-autonomous partial differential equations; stochastic non-autonomous partial differential equation; invariant manifolds; Wong–Zakai approximation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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