10.1137/120887965
Berglund, Nils
Nils
Berglund
Gentz, Barbara
Barbara
Gentz0000-0001-7490-2929
ON THE NOISE-INDUCED PASSAGE THROUGH AN UNSTABLE PERIODIC ORBIT II: GENERAL CASE
Society For Industrial And Applied Mathematics
2014
2014-05-12T12:21:05Z
2019-05-10T09:00:56Z
journal_article
https://pub.uni-bielefeld.de/record/2675698
https://pub.uni-bielefeld.de/record/2675698.json
Consider a dynamical system given by a planar differential equation, which exhibits an unstable periodic orbit surrounding a stable periodic orbit. It is known that under random perturbations, the distribution of locations where the system's first exit from the interior of the unstable orbit occurs typically displays the phenomenon of cycling: The distribution of first-exit locations is translated along the unstable periodic orbit proportionally to the logarithm of the noise intensity as the noise intensity goes to zero. We show that for a large class of such systems, the cycling profile is given, up to a model-dependent change of coordinates, by a universal function given by a periodicized Gumbel distribution. Our techniques combine action-functional or large-deviation results with properties of random Poincare maps described by continuous-space discrete-time Markov chains.