MiS Preprint Repository
We have decided to discontinue the publication of preprints on our preprint server end of 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.
Escape from attracting sets in randomly perturbed systems
Christian S. Rodrigues, Celso Grebogi and Alessandro P.S. de MouraAbstract
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:
- 20.10.10
- Published:
- 21.10.10
- PACS:
- 05.45.Ac, 61.43.Hv, 02.50.Ey
- Keywords:
- Randomly perturbed dynamics, stochastic stability