Numerical Research on Stochastic Duffing System

AbstractIn this paper, the numerical simulation method is applied to investigate the nonlinear stochastic bifurcation systems. In order to obtain a better understanding of the relationship between the Lyapunov exponents and stochastic bifurcation, the Duffing system under stochastic external excitations is examined by way of the stochastic process simulation.The simulation results are compared with the results of some other analytical methods, such as the stochastic averaging method, the perturbation method and the Laplace asymptotic evaluation method. It is shown that these analytical methods are all valid if the intensity of the noise is small. And the numerical method can be applied to the case of arbitrary noise intensity