相关白噪声激励下双稳态 Duffing⁃Van der Pol 系统的随机分岔

In this paper，the stochastic bifurcation in a bistable Duffing-Van der Pol oscillator driven by correlated mul⁃ tiplicative and additive Gaussian white noises was studied. By using the stochastic averaging method，the stationary prob⁃ ability density function of amplitude for the Duffing-Van der Pol oscillator and the critical parameter condition for sto⁃ chastic P-bifurcation were obtained. Through the changes in the shape of stationary probability density function，it was found that both the damping coefficients and intensity of the multiplicative and additive noise may induce the stochastic P-bifurcation，but they have significantly different effects on the bifurcation regions. Meanwhile，the theoretical results were verified by Monte-Carlo simulations. Moreover，the largest Lyapunov exponent was calculated by the Wolf's algo⁃ rithm to evaluate the system stability. The results showed that both the increases of the coefficient of negative damping and the noise intensity can drive the system into an unstable state and induce D-bifurcation，and the system stability can be enhanced with increasing the coefficients of positive damping.