Stationary probability density of a class of non-linear dynamical systems to stochastic excitation

The response of a dynamical system to Gaussian white-noise excitations may be represented by the Markov process whose probability density is governed by the well-known Fokker-Plank equation. In this paper a general procedure is developed to obtain the solution for Fokker-Plank equation in the state of statistical stationary. The dynamical systems considered are generally non-linear. This paper also demonstrates that the stationary joint probability density of the coordinates and velocity may possess the form of a separate product for the systems both non-linear damping and non-linear restoring forces.