具有刚性约束随机非线性动力系统擦边现象的研究

Grazing Phenomena of Stochastic Duffing-van der Pol one-Sided Constranint System

利用Chebyshev多项式逼近法在单边约束条件下将带有随机参数的Duffing-van der Pol系统转化为与之等价的确定性系统,然后利用确定性系统的数值方法,研究了系统在擦边附近的动力学行为。研究表明,随机非光滑动力系统由擦边到混沌运动过程中,存在一个擦边区间。当控制参数完全经过这个区间时,随机系统才变为和确定性系统类似的混沌运动,而在这个区间内,随机系统经过一个由擦边运动到混沌再到擦边运动的反复过程。同时作者还发现,随机非光滑动力系统在擦边附近存在由随机因素诱发的倍周期分岔现象。

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.