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Escape from attracting sets in randomly perturbed systems | | Christian S. Rodrigues
; Celso Grebogi
; Alessandro P. S. de Moura
; | | Date: |
19 Apr 2010 | | 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. | | Source: | arXiv, 1004.3125 | | Services: | Forum | Review | PDF | Favorites | |
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