平面系统的随机稳定性

Stochastic stability of two-dimensional systems

本文首先研究了确定性平面系统的双曲极限环在加法噪声扰动下的随机稳定性;其次考察了一类平面“拟Hamilton”系统在随机扰动下的稳定性,并指出结构稳定性系统与非结构稳定性系统的随机稳定性具有显著差异.

In this paper,we first study the stochastic stability of the hyperbolic limit cycles of a deterministic planar system under additive noise.Then we consider the stochastic stability of a class of planar“quasi-Hamilton”systems under nondegenerate stochastic perturbations,and point out that there is a big difference between the structurally stable system and structurally unstable system with respect to stochastic stability.