On chaotic motion of some stochastic nonlinear dynamic system

摘要

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 - alpha x - gamma x(3) = epsilon[delta cos(Omega t + Psi) - mu x + nu x(2)]. With Melnikov approach we obtained the necessary conditions for chaotic motion of the stochastic system in the meanvalue 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. (c) 2005 Elsevier Ltd. All rights reserved.