Stochastic bifurcation in a Duffing-van der Pol system

Stochastic bifurcation of a Duffing-van der Pol system subject to a deterministic harmonic excitation and bounded noise is studied by using the generalized cell mapping method with diagraphes. System parameters are chosen in the range of two co-existing attractors and a chaotic saddle, during their evolution. It is found that stochastic bifurcation mostly occurs when a stochastic attractor collides with a stochastic saddle. In our study, two kinds of discontinuous bifurcations are found according to the abrupt increase or disappearance of the attractor when it collides with the saddle in the basin interior or on the boundary. Our study also reveals that the bifurcation value is different from that of D-bifurcation which is defined by the change of the sign of the top Lyapunov exponent.