强噪声作用下双稳态Van der Pol系统的随机分岔
Stochastic Bifurcations of Bi-Stable Van der Pol Systems Under Strong Noise
郜心茹 1吴志强 1陈胜利1
作者信息
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.
Abstract
The analysis of the stochastic bifurcation behaviors of stochastic nonlinear systems often requires ar-tificial 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.
关键词
随机P分岔/分岔点/联合概率密度/自动计算Key words
stochastic P-bifurcation/bifurcation point/joint probability density/automatic calculation引用本文复制引用
出版年
2024
国家科技期刊平台
NSTL
万方数据