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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.
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Keywords:
- non-smooth dynamic system/
- stochastic van der Pol system/
- grazing bifurcation/
- two-sided barriers
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