白噪声参激余维2分岔系统奇点分析及最大Lyapunov指数  

Singular Point Analyses of One-Dimensional Diffusion Processes and Maximal Lyapunov Exponents in Stochastic Bifurcation System

作　　者：蔡祥梅[1] 刘先斌[1] 

机构地区：[1]南京航空航天大学航空宇航学院,南京210016

出　　处：《南京航空航天大学学报》2009年第1期21-24,共4页Journal of Nanjing University of Aeronautics & Astronautics

基　　金：国家自然科学基金(10672074)资助项目

摘　　要：在随机动力系统中,最大Lyapunov指数是定义随机分岔系统概率1意义分岔的重要指标。为了分析白噪声参数激励对三维中心流形上一类余维2分岔系统的影响,本文基于一维扩散过程的奇点理论,通过L Arnold的摄动方法,针对不同的噪声作用项系数矩阵讨论了相应的奇异边界分类情况和最大Lyapunov指数渐近分析式。In a co-dimension two-bifurcation system based on a three-dimensional central manifold subjected to a parametric excitation by a white noise, the asymptotic expansion of the maximal Lyapunov exponent is evaluated. Based on the theory of singular boundaries of one-dimensional diffusion processes and via a perturbation method introduced by L Arnold, the explicit asymptotic expressions of the maximal Lyapunov exponent are obtained for four cases. The different forms of the coefficient matrix included in the noise excitation term are assumed.

关 键 词：随机分岔 最大LYAPUNOV指数 FPK方程 扩散过程 奇异边界 白噪声 

分 类 号：O324[理学—一般力学与力学基础] O317.2[理学—力学]