Grazing phenomena of stochastic Duffing-Van der Pol one-sided constraint system

Chebyshev polynomial approximation is chosen to convert the Duffing-Van der Pol system with a random parameter to an equivalent deterministic system. The system behavior system nearby the grazing condition is researched with numerical method for determining. The result shows that there is a grazing area in the stochastic system occurring in the process of the system motion from grazing to chaos. It demonstrates that when the controls parameter completely passes the area the motion of stochastic system get chaos as the deterministic. In the area, the behavior of the stochastic system transforms from grazing to chaos repeated.