Slow manifolds for stochastic systems with non-Gaussian stable Lévy noise

2017/02/27 by Shenglan Yuan, Jianyu Hu, Yuan, Shenglan +5 · 1 citation
Environmental Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Dynamical Systems (math.DS) #Ecosystem dynamics and resilience #FOS: Mathematics #stochastic dynamics and bifurcation

paper · pdf · doi:10.48550/arxiv.1702.08213

openalex publication_date 2017/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This work is concerned with the dynamics of a class of slow-fast stochastic dynamical systems with non-Gaussian stable Lévy noise with a scale parameter. Slow manifolds with exponentially tracking property are constructed, eliminating the fast variables to reduce the dimension of these coupled dynamical systems. It is shown that as the scale parameter tends to zero, the slow manifolds converge to critical manifolds in distribution, which helps understand long time dynamics. The approximation of slow manifolds with error estimate in distribution are also considered.

Citations

• Synchronization of Coupled Stochastic Systems Driven by Non-Gaussian\n L 'evy Noises

Cited by

• Invariant foliations for stochastic dynamical systems with multiplicative stable Levy noise

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