Stochastic bifurcation in a duffing-van der pol system

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