ANALYSIS OF LIMIT CYCLES RESPONSE ON PARAMETRIC NOISE IN ONE-DIMENSIONAL DISCRETE-TIME SYSTEMS

Abstract

We study cycles of the discrete-time nonlinear dynamical system under parametric random disturbances. A dynamics of deviations of the random solutions from the deterministic cycle is analyzed with the help of first approximation linear systems. A closed system for second moments of these deviations is obtained and explicit formulas for the stable periodic solution are given. Constructive abilities of our mathematical technique are demonstrated for parametrical analysis of stochastically forced periodic regimes in the Ricker population model with Allee effect. A threshold noise intensity corresponding to the onset of stochastic extinction is estimated.