摘要
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.
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 bifur- cation can be described as a sudden change in shape and size of a random attractor as the system parameter valies. The evolu- tionary process of stochastic bifurcation in the SD oscillator is shown in detail. Meanwhile, we show the phenomenon that un- der 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.
基金
supported by the National Natural Science Foundation of China (Grant Nos.10932009 and 11172233)
the Natural Science Foundation of Shaanxi Province (Grant No.2012JQ1004)
the Northwestern Polytechnical University Foundation for Fundamental Research (Grant Nos.JC201266 and JC20110228)
