Eur. Phys. J. B (2022) 95: 34
https://doi.org/10.1140/epjb/s10051-022-00286-0

Regular Article - Statistical and Nonlinear Physics

Stochastic P-bifurcation in a self-sustained tristable oscillator under random excitations

School of Mathematics and Statistics, Shaanxi Normal University, 710119, Xi’an, China

^b ninglijuan@snnu.edu.cn

Received: 24 September 2021
Accepted: 19 January 2022
Published online: 23 February 2022

Abstract

Stochastic P-bifurcation in a self-sustained tristable oscillator subjected to two random excitations is explored. The self-sustained oscillator here has two stable limit cycles and a stable state, which is known for modeling the flutter of airfoils with large span in low-speed wind tunnels. By means of the stochastic averaging method, the stationary probability density function of the system amplitude for characterizing stochastic P-bifurcation is derived. The stationary probability density function can be easily transferred between the unimodal, bimodal and trimodal structure according to the critical parameters displayed in the bifurcation diagram. The effects of two noises and time delay on stochastic P-bifurcation are analyzed theoretically, whose correctness is verified numerically. The involvement of two noises and time delay not only expands the range of bifurcation parameters, but also enriches the bifurcation phenomenon.