应用数学和力学2012，Vol.33Issue(5)：526-538,13.DOI:10.3879/j.issn.1000-0887.2012.05.002
有界噪声参激一类三维系统的矩Liapunov指数
Moment Liapunov Exponent of a Three-Dimensional System Under Bounded Noise Excitation
摘要
Abstract
The moment Liapunov exponent of a co-dimension two bifurcation system was evaluated, which was on a three-dimensional central manifold and was subjected to a parametric excitation by a bounded noise. Based on the theory of the stochastic dynamics, the eigenvalue problem governing the moment Liapunov exponent was established. Through a singular perturbation method, the explicit asymptotic expressions or numerical results of the second-order, weak noise expansions of the moment Liapunov are obtained for two cases. Then the effects of the bounded noise and the parameters of the system on the moment Liapunov exponent and the stability index were investigated. It is found that the stochastic stability of the system can be strengthened by the bounded noise.关键词
有界噪声/矩Liapunov指数/稳定指标Key words
bounded noise/ moment Liapunov exponent/ stability index分类
数理科学引用本文复制引用
方次军,杨建华,刘先斌..有界噪声参激一类三维系统的矩Liapunov指数[J].应用数学和力学,2012,33(5):526-538,13.基金项目
国家自然科学基金资助项目(10672074 （）
11072107) （）
高等学校博士学科点专项科研基金资助项目(20093218110003). （20093218110003）
