Impact of the Parametric Noise on Map-based Dynamical Systems

Discrete-time nonlinear dynamical systems with general parametric stochastic disturbances are considered. For such systems, a problem of the probabilistic analysis of the random states dispersion around attractors is studied. For the constructive approximation of probabilistic distributions, the method of the stochastic sensitivity is developed. Matrix equations for the asymptotics of moments of deviations from equilibria are derived. The suggested mathematical theory is applied to the analysis of the general logistic-type model with parametric random noises.