TY - JOUR
TI - Stochastic bifurcation and bistable behaviors in a modified fractional Rayleigh system driven by recycling noise
AU - Cai Yujie
AU - Li Yajie
AU - Xu Huafeng
AU - Zhang Xiangyun
AU - Chen Shengli
AU - Cheng Feifei
AU - Shi Yue
JN - Thermal Science
PY - 2026
VL - 30
IS - 2
SP - 855
EP - 867
PT - Article
AB - The present study investigates the stochastic response and bifurcation  behavior of system amplitude in a fractional and generalized bi-stable Van  der Pol system driven by Gaussian colored noise. Firstly, the principle of  minimal mean square error and the generalized harmonic balance technique  were employed to demonstrate that the fractional derivative is equivalent  to a linear combination of damping and restoring forces. Consequently, the  original system was simplified to an equivalent integer order Van der Pol  system. Secondly, the system amplitude's stationary probability density  function is acquired by stochastic averaging. According to the principles of  singularity theory, the critical parametric conditions for the stochastic  P-bifurcation of system amplitude can be determined. A qualitative analysis  of the stationary probability density function curves of amplitude is  finally conducted in each area, with the transition set curves serving as a  dividing point. The congruence between the analytical outcomes and the  numerical results derived from the Monte-Carlo simulation substantiates the  theoretical analysis in this paper. The methodology employed and the  results obtained in this paper can enhance the design of the  fractional-order controller to regulate the response of the system.
DO - 10.2298/TSCI2602855C
ER -