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

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.

35 pages, 6 figures. The authors are grateful to Björn Schmalfuß, René Schilling, Georg Gottwald, Jicheng Liu and Jinlong Wei for helpful discussions on stochastic differenial equations driven by Lévy motions

References in corpus (2)

• Normal form transforms separate slow and fast modes in stochastic dynamical systems
• Synchronization of Coupled Stochastic Systems Driven by Non-Gaussian Lévy Noises

Cited by in corpus (1)

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