On chaotic motion of some stochastic nonlinear dynamic system

In this paper we discussed the chaotic motion of a forced vibration system which contains nonlinear items such as cubic excitation, square damping force and bounded stochastic excitation.x¨-αx-γx3=εδcos(Ωt+Ψ)-μx˙+νx˙2.With Melnikov approach we obtained the necessary conditions for chaotic motion of the stochastic system in the mean-value sense and in the mean-square-value sense. As the stochastic excitation is bounded noise, we can add the stochastic items in the Runge–Kutta method and the conclusion we obtained by theoretic conclusions can be approved by the numerical simulation.