Mean-square analysis of stochastic cycles in nonlinear discrete-time systems with parametric noise

Abstract

We study a discrete-time nonlinear dynamical system forced by parametric noise. A method of mean-square analysis of the dispersion of random solutions near deterministic cycle is elaborated. A problem of the existence of the stable periodic solution of the closed system for second moments is studied in detail. This problem is reduced to the estimation of the spectral radius of some positive operator. A constructive method of the spectral majorants is suggested. The accuracy of our mathematical technique is demonstrated in the analysis of stochastically forced periodic regimes for the Henon model.