Stochastic P-bifurcation of tri-stable Van der Pol-Duffing oscillator

被引：0

作者：

机构：

[1] Department of Mechanics, Tianjin University

来源：

Wu, Z. (zhiqwu@tju.edu.cn) | 1600年 / Chinese Society of Theoretical and Applied Mechanics卷 / 45期

关键词：

Probability density function; Singularity theory; Stochastic P-bifurcation;

D O I：

10.6052/0459-1879-12-169

中图分类号：

学科分类号：

摘要：

This paper aims to investigate the stochastic P-bifurcations in the tri-stable Van 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.

引用

页码：257 / 264

页数：7

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