双边约束条件下随机van der Pol系统的分岔研究

利用随机光滑动力系统的Chebyshev正交多项式逼近方法，研究了双边约束条件下随机van der Pol系统的分岔现象.数值研究表明，双边约束随机van der Pol系统中不仅存在着丰富的倍周期分岔现象，还存在非光滑系统中所特有的擦边分岔.着重研究了随机非光滑系统中的擦边分岔，分析了随机因素对非光滑动力系统中擦边分岔的影响.研究表明，Chebyshev多项式逼近也是研究随机非光滑系统动力学行为的一种有效方法. 关键词： 非光滑动力系统 随机 van der Pol系统 擦边分岔 双边约束

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.