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Random Perturbation of Invariant Manifolds for Non-Autonomous Dynamical Systems

Author

Listed:
  • 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)

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.

Suggested Citation

  • Tao Jiang & Zhongkai Guo & Xingjie Yan, 2022. "Random Perturbation of Invariant Manifolds for Non-Autonomous Dynamical Systems," Mathematics, MDPI, vol. 10(6), pages 1-12, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:6:p:992-:d:774880
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    References listed on IDEAS

    as
    1. Evans, Lawrence Christopher & Stroock, Daniel W., 2011. "An approximation scheme for reflected stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 121(7), pages 1464-1491, July.
    2. Konecny, Franz, 1983. "On Wong-Zakai approximation of stochastic differential equations," Journal of Multivariate Analysis, Elsevier, vol. 13(4), pages 605-611, December.
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