Stochastic response of a vibro-impact system by path integration based on generalized cell mapping method

The generalized cell mapping method is extended to study the response of a vibro-impact system with white noise excitation. The transient and steady-state responses of a Duffing-van der Pol vibro-impact system under white noise excitation are obtained by using this method. The accuracy of the method is verified by comparison with Monte Carlo simulation results. In addition, stochastic P-bifurcation for different parameters is considered, and several special forms are observed in this paper.