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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
62/2010

Escape from attracting sets in randomly perturbed systems

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

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.

Received:
Oct 20, 2010
Published:
Oct 21, 2010
PACS:
05.45.Ac, 61.43.Hv, 02.50.Ey
Keywords:
Randomly perturbed dynamics, stochastic stability

Related publications

inJournal
2010 Repository Open Access
Christian S. Rodrigues, Celso Grebogi and Alessandro P. S. De Moura

Escape from attracting sets in randomly perturbed systems

In: Physical review / E, 82 (2010) 4, p. 046217