---
res:
bibo_abstract:
- '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.@eng'
bibo_authorlist:
- foaf_Person:
foaf_givenName: Nils
foaf_name: Berglund, Nils
foaf_surname: Berglund
- foaf_Person:
foaf_givenName: Barbara
foaf_name: Gentz, Barbara
foaf_surname: Gentz
foaf_workInfoHomepage: http://www.librecat.org/personId=184956
orcid: 0000-0001-7490-2929
bibo_doi: 10.1137/120887965
bibo_issue: '1'
bibo_volume: 46
dct_date: 2014^xs_gYear
dct_identifier:
- UT:000333591800011
dct_isPartOf:
- http://id.crossref.org/issn/0036-1410
dct_language: eng
dct_publisher: Society For Industrial And Applied Mathematics@
dct_subject:
- stochastic resonance
- cycling
- Gumbel distribution
- phase slip
- synchronization
- large deviations
- limit cycle
- boundary
- characteristic
- first-exit time
- stochastic exit problem
- diffusion exit
dct_title: 'ON THE NOISE-INDUCED PASSAGE THROUGH AN UNSTABLE PERIODIC ORBIT II:
GENERAL CASE@'
...