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Escape from attracting sets in randomly perturbed systems

Authors
  • Rodrigues, Christian S.
  • Grebogi, Celso
  • de Moura, Alessandro P. S.
Type
Published Article
Publication Date
Oct 25, 2010
Submission Date
Apr 19, 2010
Identifiers
DOI: 10.1103/PhysRevE.82.046217
Source
arXiv
License
Yellow
External links

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 a two-dimensional map with noise.

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