Stochastic Bifurcations of Bi-Stable Van der Pol Systems Under Strong Noise

GAO Xinru; WU Zhiqiang; CHEN Shengli

doi:10.21656/1000-0887.440375

Volume 45 Issue 12

Dec. 2024

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GAO Xinru, WU Zhiqiang, CHEN Shengli. Stochastic Bifurcations of Bi-Stable Van der Pol Systems Under Strong Noise[J]. Applied Mathematics and Mechanics, 2024, 45(12): 1506-1514. doi: 10.21656/1000-0887.440375

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Stochastic Bifurcations of Bi-Stable Van der Pol Systems Under Strong Noise

doi: 10.21656/1000-0887.440375

Department of Mechanics, Tianjin University, Tianjin 300350, P.R.China

Received Date: 2023-12-29
Rev Recd Date: 2024-04-10

Available Online: 2024-12-27

Abstract

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.
- stochastic P-bifurcation,
- bifurcation point,
- joint probability density,
- automatic calculation

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References(32)

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