【摘要】 从联合概率密度的角度分析随机非线性系统的随机分岔行为，现有研究通常需要人为判断概率密度特征有无本质变化，并且此过程无法自动化.该文提出了一种新的计算方法，能够实现随机分岔点的自动计算.以强噪声激励下的双稳态Van der Pol系统为例，分析了阻尼系数变化对随机动力学响应的影响.研究结果表明，随着阻尼系数的增加，系统的联合概率密度会发生三次分岔，呈现四种不同类型的几何特征.该文提出的方法有望应用于其他随机非线性系统的随机分岔行为研究.更多还原

【Abstract】 The analysis of the stochastic bifurcation behaviors of stochastic nonlinear systems often requires artificial judgment based on the joint probability density and cannot be automated. A new calculation method for automatic calculation of random bifurcation points was proposed. The bi-stable Van der Pol system under strong noise excitation was taken as an example, the influences of damping coefficient changes on stochastic dynamic responses were analyzed. The research results show that, the joint probability density of the system bifurcates for 3 times with the increase of the damping coefficient, exhibiting 4 different types of geometric features. The proposed method can hopefully be applied to the study of stochastic bifurcation behaviors of other stochastic nonlinear systems.更多还原