Van der Pol振子在随机激励下的Hopf分叉  

Hopf Bifurcation of Van der Pol Oscillator Under Stochastic Excitations

作　　者：杨槐[1] 朱华[1] 褚亦清 

机构地区：[1]北京理工大学应用力学系,北京100081

出　　处：《北京理工大学学报》1993年第S1期279-285,共7页Transactions of Beijing Institute of Technology

基　　金：国家自然科学基金

摘　　要：研究了Van der Pol振子在宽带随机外部激励和宽带随机参数激励联合作用下的Hopf分叉.文中采用随机平均法将Van del Pol方程的幅值响应过程逼近为一维的Markov扩散过程.利用FPK方程的直接积分,得到了幅值响应的稳态概率密度函数.在此基础上,分析了系统在分叉点附近由于随机扰动的影响带来的系统局域行为的变化.从本文的研究中发现,非线性系统在随机外部激励以及两种不同的随机参数激励作用下,其分叉行为与确定性系统相比会有明显的变化。Studies Hopf bifurcation of the Van der Pol oscillator in the presence of wide-band parametric and external stochastic excitations. The amplitude response process of the Van der Pol equation is approximated in the weak sense by a diffusive Markov process using stochastic averaging. The stationary probability density function of the amplitude response is. obtained by performing a straight-forward integration on the FPK equation. Based on the stationary probability density function , the change of the local behaviour in the neighbourhood of the bifurcation point of a system due to stochastic perturbation is analysed. It is found that the bifurcation behaviour of nonlinear systems under stochastic external and two kinds of parametric excitation differs from that of the relevant determinate systems.

关 键 词：范德波尔方程/随机激励 HOPF分叉 随机分叉 

分 类 号：O324[理学—一般力学与力学基础] O211.[理学—力学] 63