Abstract
Abstract A response of chaotic discrete-time dynamical systems on parametric random disturbances is considered. For two-dimensional stochastic systems with non-invertible maps, a dispersion of random states near chaotic attractors is studied. To analyse the dispersion near the border of the chaotic attractor, we elaborate an asymptotic approach based on the stochastic sensitivity technique. In this analysis, critical curves defining parts of this border are used. An application of this theory to the study of the dispersion of random states near borders of chaotic attractors is given on the example of the Sprott model. Constructive abilities of the elaborated approach for the analysis of noise-induced escape from the basin of the chaotic attractor are demonstrated.
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