Stability of the Poincaré maps for a stochastic fast–slow system

Abstract

This work focuses on the existence and the stability of Poincaré maps of a stochastic fast–slow system with multiplicative noise. It shows that the Poincaré maps of the stochastic fast–slow system return, one time or even infinite times, to a small neighborhood of a fixed point of the Poincaré map for a deterministic fast–slow system, which implies the stability of Poincaré maps of the stochastic fast–slow system with the small noise disturbing.