Stochastic bifurcations in the SD (smooth and discontinuous) oscillator under bounded noise excitation

Stochastic bifurcations of the SD (smooth and discontinuous) oscillator with additive and/or multiplicative bounded noises are studied by the generalized cell mapping method using digraph analysis algorithm. From the global viewpoint, stochastic bifurcation can be described as a sudden change in shape and size of a random attractor as the system parameter varies. The evolutionary process of stochastic bifurcation in the SD oscillator is shown in detail. Meanwhile, we show the phenomenon that under stochastic excitation the shape and size of random attractor and random saddle change along with the direction of unstable manifold. A plane stochastic bifurcation diagram is included.