Response of a stochastic Duffing–Van der Pol elastic impact oscillator

The response of a Duffing–Van der Pol elastic impact system with one random parameter is investigated. The system is transformed to two high dimension deterministic systems according to Laguerre polynomial approximation, through which the response can be derived from deterministic numerical method. It is found that the behavior of the system changes from chaos to periodic through inverse period-doubling bifurcation when the spring stiffness of elastic impact force increases, and the idea that all the bifurcation points are advanced by random factor is presented. Numerical results show that the Laguerre polynomial approximation is an effective approach to solving the problems of elastic impact systems with random parameters.