TY - JOUR
TI - Stochastic transition behaviors in a generalized Van der Pol oscillator with fractional damping under 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 - 2021
VL - 25
IS - 3
SP - 2347
EP - 2356
PT - Article
AB - The stochastic P-bifurcation behavior of bi-stability in a generalized Van der Pol oscillator with a fractional damping under multiplicative Gaussian white noise excitation is investigated. Firstly, using the principle of minimal mean square error, 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’s stationary probability density function is obtained by stochastic averaging. Then according to the singularity theory, the critical parametric conditions for the sys-tem amplitude’s stochastic P-bifurcation are found. Finally, the types of the system’s stationary probability density function curves of amplitude are qualitatively analyzed by choosing the corresponding parameters in each area divided by the transition set curves. The consistency between the analytical results and the numerical results obtained from Monte-Carlo simulation verifies 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.