加性噪声激励对双稳态Van der Pol系统联合概率密度的影响  

Influence of additive noise excitation on joint probability density of bi-stable Van der Pol system

作　　者：宋凯令 吴志强[1] Song Kailing;Wu Zhiqiang(Tianjin University School of Mechanical Engineering,300072,Tianjin,China)

机构地区：[1]天津大学机械工程学院,天津300072

出　　处：《应用力学学报》2020年第6期2395-2403,I0006,I0007,共11页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(11372211)。

摘　　要：通过电路实验研究了含超临界Hopf分岔和鞍结分岔的Van der Pol系统在加性高斯白噪声激励下的二维随机动力学行为。研究表明:当确定性系统处在平衡点或极限环区域时,随着噪声激励强度的增加,系统的联合概率密度都会出现拓扑形状的改变;但无论处在平衡点还是极限环区域中,系统的稳态幅值概率密度曲线的拓扑形状都没有发生定性改变。而当确定性系统处于双稳态区域时,系统的稳态幅值概率密度和联合概率密度都发生了随机P分岔。当噪声激励强度变化时,因稳定系数取值的不同,系统的联合概率密度发生定性变化共有三种途径。The two-dimensional stochastic dynamic behavior of Van der Pol system with supercritical Hopfbifurcation and saddle-node bifurcation under additive Gaussian white noise is studied by the circuit experiment.The investigation shows that when the deterministic system is in the balance point or limit cycle region,with the increasing noise intensity,the topological shape of the joint probability density of system will change.However,in both cases,there is no qualitative change in the topological shape of steady-state amplitude probability density curve.When the deterministic system is in the bistable region,both the amplitude probability density and the joint probability density of system have stochastic P-bifurcation.When the excitation intensity changes,there are three different ways to result in the qualitative changes of the joint probability density because of the different values of stability coefficient.

关 键 词：Van der Pol方程 随机激励 联合概率密度 随机P分岔 

分 类 号：O322[理学—一般力学与力学基础]