Stochastic P-bifurcations In Tri-stable van der Pol- Duffing Oscillator

Hao Ying; Wu zhiqiang

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Stochastic P-bifurcations In Tri-stable van der Pol- Duffing Oscillator

Hao Ying 1,Wu zhiqiang 2 *

1.School of Mechanical Engineering, Tianjin University, TianJin 300072

2.School of Mechanical Engineering, Tianjin University

*Correspondence author

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Funding: The project supported by the National Natural Science Foundation of China（No.11172198）, Ministry of Education Found for the Dotroal（No.2009003211005）

Opened online:27 December 2012

Accepted by: none

Citation: Hao Ying,Wu zhiqiang.Stochastic P-bifurcations In Tri-stable van der Pol- Duffing Oscillator[OL]. [27 December 2012] http://en.paper.edu.cn/en_releasepaper/content/4503911

This paper aims to investigate the stochastic P-bifurcations in the tri-stable van der Pol-Duffing oscillator with Gauss white 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, 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.

Keywords:stationary probability density function; Stochastic P-bifurcation; Transition sets

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