Analysis of Stochastic Equilibria for Nonlinear Discrete Systems with Parametrical Noise

摘要

Stochastically forced discrete dynamical systems are considered. Using first approximation systems, we study dynamics of deviations of stochastic solutions from deterministic equilibria. Necessary and sufficient conditions of the existence of stable stationary solutions of equations for mean-square deviations are derived. Stationary values of these mean-square deviations are used for the estimations of the dispersion of random states nearby stable equilibria. Constructive application of the suggested technique to the analysis of stochastic equilibria is demonstrated.