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

作　　者：方次军[1,2] 杨建华[3] 刘先斌[1] 

机构地区：[1]南京航空航天大学机械结构力学及控制国家重点实验室,南京210016 [2]湖北工业大学理学院,武汉430068 [3]中国矿业大学机电工程学院,江苏徐州221116

出　　处：《应用数学和力学》2012年第5期526-538,共13页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(1067207411072107);高等学校博士学科点专项科研基金资助项目(20093218110003);中国矿业大学青年教师启航计划项目基金资助;中国矿业大学中央高校基本科研业务费资助(2011RC13)

摘　　要：对于一类三维中心流形上受有界噪声参激的余维2分岔系统,计算了它的矩Liapunov指数.根据随机动力系统理论,首先建立了系统矩Liapunov指数求解的特征值问题,然后由奇异摄动法,得到了弱噪声展开的矩Liapunov指数的二阶渐近解析表达式和数值结果.接着进一步研究了有界噪声和系统参数对矩Liapunov指数和稳定指标的影响.结果表明:系统的随机稳定性有被有界噪声加强的可能性.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 

分 类 号：O324[理学—一般力学与力学基础]