Escape from attracting sets in randomly perturbed systems

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

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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.

Original languageEnglish
Article number046217
Number of pages5
JournalPhysical Review. E, Statistical, Nonlinear and Soft Matter Physics
Volume82
Issue number4
DOIs
Publication statusPublished - 20 Oct 2010

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Perturbed System
escape
Escape Rate
Random Perturbation
Chaotic System
Gaussian distribution
Attractor
Equivalence
Scaling
Verify
Numerical Simulation
Closed
Prediction
normal density functions
equivalence
scaling
perturbation
predictions

Keywords

  • noise-induced escape
  • chaos
  • maps
  • bifurcations
  • invariant
  • rates
  • model

Cite this

Escape from attracting sets in randomly perturbed systems. / Rodrigues, Christian S.; Grebogi, Celso; de Moura, Alessandro P. S.

In: Physical Review. E, Statistical, Nonlinear and Soft Matter Physics, Vol. 82, No. 4, 046217, 20.10.2010.

Research output: Contribution to journalArticle

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