TY - JOUR
TI - Non-linear stochastic response and bifurcation analysis of a multistable Rayleigh system with a fractional element subjected to noise excitation
AU - Li Yajie
AU - Wu Zhiqiang
AU - Hao Ying
AU - Sun Yongtao
JN - Thermal Science
PY - 2025
VL - 29
IS - 3
SP - 1861
EP - 1870
PT - Article
AB - The study examines the stochastic bifurcation phenomenon of a generalized and  multistable Rayleigh system subjected to fractional damping driven by  Gaussian white noise. First, the harmonic balance technique is employed to  minimize the error in terms of mean square, thereby deriving the approximate  equal integer-order system from the original system with fractional-order  elements. Subsequently, the stationary probability density function of the  system is determined using the stochastic averaging method. Subsequently,  employing singularity theory, the critical conditions of system parameters  for stochastic P-bifurcation of the original system are identified. Finally,  a qualitative analysis of the stationary probability density function curves  of the system amplitude is conducted in each region delineated by the  boundary set curves. The analytical solutions were found to align with the  numerical findings obtained from Monte-Carlo simulation, thereby  corroborating the theoretical deductions. The methodology and findings  presented in this study have the potential to enhance system response  control through the design of fractional-order controllers.