Stochastic sensitivity of regular and multi-band chaotic attractors in discrete systems with parametric noise

Abstract

We consider a response of nonlinear dynamic systems on random disturbances. A stochastic sensitivity of regular and chaotic attractors of discrete systems with parametric noise is studied. Cases of equilibria, cycles, one- and multi-band chaotic attractors are considered, and explicit parametric formulas for the stochastic sensitivity of these attractors are derived. We give a constructive application of this theory to the analysis of the dispersion of random states near chaotic attractors on the example of the logistic map. It is shown how this technique can be effectively used in the analysis of noise-induced crisis bifurcation of merging chaotic bands.