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Cite this article: 

Sun, YH., Yang, YG. & Xu, W. Stochastic P-bifurcations of a noisy nonlinear system with fractional derivative element. Acta Mech. Sin. 37, 507–515 (2021).

https://doi.org/10.1007/s10409-020-01020-8

Stochastic P-bifurcations of a noisy nonlinear system with fractional derivative element

Ya-Hui Sun, Yong-Ge Yang, Wei Xu

This paper investigates the stochastic P-bifurcation (SPB) of a fractionally damped oscillator subjected to additive and multiplicative Gaussian white noise. Variable transformation and the stochastic averaging technique are applied to derive the expression of probability density function (PDF) of the system response. Critical conditions of the stochastic bifurcation induced by system parameters are presented based on the change in the number of extreme points of the probability density function. Numerical results are given to show the effectiveness of the proposed approach. Stochastic P-bifurcations for additive and multiplicative noise are studied in detail according to the critical conditions.

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