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.