TY - JOUR
TI - Analysis of the stationary probability density of a generalized and bistable van der Pol system excited by colored noise
AU - Li Yajie
AU - Wu Zhiqiang
AU - Sun Yongtao
AU - Hao Ying
AU - Zhang Xiangyun
AU - Wang Feng
AU - Shi Heping
JN - Thermal Science
PY - 2024
VL - 28
IS - 3
SP - 2189
EP - 2199
PT - Article
AB - The stochastic P-bifurcation behavior of bi-stability in a generalized van  der Pol oscillator with the fractional damping under colored noise and  thermal excitation is investigated. Firstly, using the principle of minimal  mean square error and lin-earization method, the non-linear stiffness terms  can be equivalent to a linear stiffness which is a function of the system  amplitude, and the original system is simplified to an equivalent integer  order van der Pol system. Secondly, the system amplitude stationary  probability density function is obtained by the stochastic averaging, and  then based on the singularity theory, the critical parametric con-ditions  for the system amplitude stochastic P-bifurcation are found. Finally, the  types of the stationary probability density function of the system amplitude  are qualitatively analyzed in each area divided by the transition set  curves. The con-sistency between the analytical results and the numerical  results acquired from Monte-Carlo simulation also testifies the theoretical  analysis in this paper and the method used in this paper can directly guide  the design of the fractional order controller to adjust the response of the  system.