TY - JOUR
TI - Stochastic transition behaviors in a tri-stable van der Pol oscillator with fractional delayed element subject to Gaussian white noise
AU - Li Yajie
AU - Wu Zhiqiang
AU - Lan Qixun
AU - Cai Yujie
AU - Xu Huafeng
AU - Sun Yongtao
JN - Thermal Science
PY - 2022
VL - 26
IS - 3
SP - 2713
EP - 2725
PT - Article
AB - The stochastic P-bifurcation behavior of tri stability in a generalized Van  der Pol system with fractional derivative under additive Gaussian white  noise excitation is investigated. Firstly, based on the minimal mean square  error principle, the fractional derivative is found to be equivalent to a  linear combination of damping and restoring forces, and the original system  is simplified into an equivalent integer order system. Secondly, the  stationary probability density function of the system amplitude is obtained  by stochastic averaging, and according to the singularity theory, the  critical parameters for stochastic P-bifurcation of the system are found.  Finally, the nature of stationary probability density function curves of the  system amplitude is qualitatively analyzed by choosing the corresponding  parameters in each region divided by the transition set curves. The  consistency between the analytical solutions and Monte-Carlo simulation  results verifies the theoretical results in this paper.