Random periodic paths of stochastic periodic semi-flows through random attractors, synchronizations and Lyapunov exponents

Feng, Chunrong; Luo, Yan

Abstract

This paper discusses the existence and uniqueness of random periodic paths of stochastic periodic semi-flows. Random periodic attractors are introduced and synchronization for stochastic periodic semi-flows is proved under some conditions to find the unique random periodic path. The multiplicative ergodic theorem of stochastic periodic semi-flows is proved to characterize Lyapunov exponents. The Benzi–Parisi–Sutera–Vulpiani climate model is an example to verify the results by estimating the negative Lyapunov exponent constructed by the density function from the Fokker–Planck equation. Numerical approximations are performed with great agreement. A case of gradient systems is considered to be another example of a negative Lyapunov exponent.

Citation

Feng, C., & Luo, Y. (2025). Random periodic paths of stochastic periodic semi-flows through random attractors, synchronizations and Lyapunov exponents. Computational and Applied Mathematics, 44(2), Article 179. https://doi.org/10.1007/s40314-025-03135-9

• Journal Article Type: Article
• Acceptance Date: Jan 29, 2025
• Online Publication Date: Feb 19, 2025
• Publication Date: Mar 1, 2025
• Deposit Date: Apr 8, 2025
• Publicly Available Date: Apr 11, 2025
• Journal: Computational and Applied Mathematics
• Print ISSN: 0101-8205
• Electronic ISSN: 1807-0302
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 44
• Issue: 2
• Article Number: 179
• DOI: https://doi.org/10.1007/s40314-025-03135-9
• Public URL: https://durham-repository.worktribe.com/output/3783495