Investigation of the bifurcation of stochastic van der Pol system

The Chebyshev polynomial approximation is used to investigate the stochastic bifurcation of van der Pol system with two-sided barriers. The numerical results show that there is not only diverse phenomena of period-doubing bifurcation in the system, but also exist, the grazing bifurcation which is unique for the non-smooth system. The grazing bifurcation is investigated emphatically, and the influence of the random factor on the grazing bifurcation in the stochastic non-smooth dynamics system is analyzed. It is shown that the Chebyshev polynomial approximation is a valid method for the investigation of non-smooth systems.