The study on stationary solution of a stochastically complex dynamical system

The main topic of this paper is the study of the stationary solution of a stochastically complex dynamical system. The stochastic averaging method of quasi-Hamiltonian system, an important tool for the analysis of dynamical properties of stochastically real dynamical system, is used at the first time to investigate a complex dynamical system. The theoretic formulas of the stationary solution associated with system energy and its analytic characters are given. Moreover, the numerical results about them are also provided in illustrative figures.