Stochastic Bifurcations in a Bistable Duffing-Van der Pol Oscillator with Colored Noise

【摘要】：This paper aims to investigate Gaussian colored noise-induced stochastic bifurcations and the influence of correlation time and noise intensity in a bistable Duffing-van der Pol oscillator.By using the stochastic averaging method,one can obtain the stationary probability density function of amplitude for the Duffing-van der Pol oscillator theoretically and find rich dynamics under the influence of Gaussian colored noise.Stochastic bifurcations are discussed through a qualitative change of the stationary probability distribution,which indicates that system parameters,noise intensity and noise correlation time can be treated as bifurcation parameters respectively,They also imply that the effects of multiplicative noise are rather different from that of additive noise.The results of direct numerical simulation verify the effectiveness of the theoretical analysis.Moreover,the largest Lyapunov exponent calculations indicate that the P-bifurcation and D-bifurcation have no direct connection.