Escape from attracting sets in randomly perturbed systems

Christian S. Rodrigues, Celso Grebogi, and Alessandro P.S. de Moura

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Submission date: 20. Oct. 2010
published in: Physical review / E, 82 (2010) 4, art-no. 046217 
DOI number (of the published article): 10.1103/PhysRevE.82.046217
Bibtex
PACS-Numbers: 05.45.Ac, 61.43.Hv, 02.50.Ey
Keywords and phrases: Randomly perturbed dynamics, stochastic stability

Abstract:
The dynamics of escape from an attractive state due to random perturbations is of central interest to many areas in science. Previous studies of escape in chaotic systems have rather focused on the case of unbounded noise, usually assumed to have Gaussian distribution. In this paper, we address the problem of escape induced by bounded noise. We show that the dynamics of escape from an attractor’s basin is equivalent to that of a closed system with an appropriately chosen "hole". Using this equivalence, we show that there is a minimum noise amplitude above which escape takes place, and we derive analytical expressions for the scaling of the escape rate with noise amplitude near the escape transition. We verify our analytical predictions through numerical simulations of two well-known two-dimensional maps with noise.