三稳态Van der Pol-Duffng振子的随机P分岔  

STOCHASTIC P-BIFURCATION OF TRI-STABLE VAN DER POL-DUFFING OSCILLATOR

作　　者：郝颖[1] 吴志强[1] 

机构地区：[1]天津大学机械工程学院力学系,天津300072

出　　处：《力学学报》2013年第2期257-264,共8页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金(11172198);教育部博士点基金(2009003211005);教育部新世纪优秀人才支持计划(NCET-15-0247)资助项目~~

摘　　要：分析了乘性和加性噪声作用下三稳态Van der Pol--Duffng振子的随机P分岔.首先用随机平均法得到系统的随机微分方程,求得系统响应幅值的稳态概率密度函数.然后应用分岔分析的奇异性理论,求得随机P分岔发生的临界参数条件,得到多种定性不同的稳态概率密度曲线.讨论了2种激励噪声强度和系统阻尼对响应稳态概率密度曲线峰的个数、各峰值相对大小的影响.通过Monte--Carlo数值模拟对理论计算结果进行了验证.该方法可用于其他系统的随机P分岔分析.This paper aims to investigate the stochastic P-blturcatlons m me tn-staole Vau der Pol-Duffing oscillator with additive and multiplicative Gauss noise. By using the stochastic averaging method, the stationary probability density function of amplitude is obtained. Then based on the singularity theory of the deterministic system, the explicit parameter conditions for P-bifurcation are deduced, and eleven types of qualitatively different probability density curves are founded. Finally the effects of three coefficients, one for linear damping and two for random excitation strength, are discussed. The results are verified by Monte-Carlo numerical simulations. The method used here is also suitable for other systems＇ P-bifurcation analysis.

关 键 词：随机P分岔 概率密度函数 奇异性理论 

分 类 号：O324[理学—一般力学与力学基础]