随机Duffing单边约束系统的倍周期分岔

通过引进平均约束面和平均跃变方程对随机约束系统的约束条件进行处理，把研究随机光滑系统倍周期分岔的Chebyshev多项式逼近的方法运用到随机非光滑系统中，数值研究表明随机Duffing单边约束系统同样存在丰富的倍周期分岔现象，Chebyshev多项式逼近是研究带有约束的随机非光滑动力系统的有效方法. 关键词：非光滑动力系统随机Duffing系统Chebyshev多项式倍周期分岔

Period-doubling bifurcation of stochastic Duffing one-sided constraint system

The conditions of constraint are treated by means of the mean constraint plane and the mean jump equation, in which the method of the Chebyshev polynomial approximation, previously used to explore period-doubling bifurcation of stochastic smooth systems, is applied to stochastic non-smooth systems. Numerical simulations show that period-doubling bifurcation exists in stochastic Duffing one-sided constraint system just as in smooth stochastic Duffing system, and furthermore, the Chebyshev polynomial approximation is an effective method in exploring the dynamical behavior of stochastic non-smooth system.