ON THE NOISE-INDUCED PASSAGE THROUGH AN UNSTABLE PERIODIC ORBIT II: GENERAL CASE
Berglund, Nils
Gentz, Barbara ; https://orcid.org/0000-0001-7490-2929
stochastic resonance
cycling
Gumbel distribution
phase slip
synchronization
large deviations
limit cycle
boundary
characteristic
first-exit time
stochastic exit problem
diffusion exit
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.
Society For Industrial And Applied Mathematics
2014
info:eu-repo/semantics/article
doc-type:article
text
https://pub.uni-bielefeld.de/record/2675698
Berglund N, Gentz B. ON THE NOISE-INDUCED PASSAGE THROUGH AN UNSTABLE PERIODIC ORBIT II: GENERAL CASE. <em>SIAM Journal on Mathematical Analysis</em>. 2014;46(1):310-352.
eng
info:eu-repo/semantics/altIdentifier/doi/10.1137/120887965
info:eu-repo/semantics/altIdentifier/issn/0036-1410
info:eu-repo/semantics/altIdentifier/wos/000333591800011
info:eu-repo/semantics/closedAccess