ON THE NOISE-INDUCED PASSAGE THROUGH AN UNSTABLE PERIODIC ORBIT II: GENERAL CASE

Berglund N, Gentz B (2014)
SIAM Journal on Mathematical Analysis 46(1): 310-352.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor/in
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Abstract / Bemerkung
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.
Stichworte
stochastic resonance; cycling; Gumbel distribution; phase slip; synchronization; large deviations; limit cycle; boundary; characteristic; first-exit time; stochastic exit problem; diffusion exit
Erscheinungsjahr
2014
Zeitschriftentitel
SIAM Journal on Mathematical Analysis
Band
46
Ausgabe
1
Seite(n)
310-352
ISSN
0036-1410
Page URI
https://pub.uni-bielefeld.de/record/2675698

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Berglund N, Gentz B. ON THE NOISE-INDUCED PASSAGE THROUGH AN UNSTABLE PERIODIC ORBIT II: GENERAL CASE. SIAM Journal on Mathematical Analysis. 2014;46(1):310-352.
Berglund, N., & Gentz, B. (2014). ON THE NOISE-INDUCED PASSAGE THROUGH AN UNSTABLE PERIODIC ORBIT II: GENERAL CASE. SIAM Journal on Mathematical Analysis, 46(1), 310-352. doi:10.1137/120887965
Berglund, N., and Gentz, B. (2014). ON THE NOISE-INDUCED PASSAGE THROUGH AN UNSTABLE PERIODIC ORBIT II: GENERAL CASE. SIAM Journal on Mathematical Analysis 46, 310-352.
Berglund, N., & Gentz, B., 2014. ON THE NOISE-INDUCED PASSAGE THROUGH AN UNSTABLE PERIODIC ORBIT II: GENERAL CASE. SIAM Journal on Mathematical Analysis, 46(1), p 310-352.
N. Berglund and B. Gentz, “ON THE NOISE-INDUCED PASSAGE THROUGH AN UNSTABLE PERIODIC ORBIT II: GENERAL CASE”, SIAM Journal on Mathematical Analysis, vol. 46, 2014, pp. 310-352.
Berglund, N., Gentz, B.: ON THE NOISE-INDUCED PASSAGE THROUGH AN UNSTABLE PERIODIC ORBIT II: GENERAL CASE. SIAM Journal on Mathematical Analysis. 46, 310-352 (2014).
Berglund, Nils, and Gentz, Barbara. “ON THE NOISE-INDUCED PASSAGE THROUGH AN UNSTABLE PERIODIC ORBIT II: GENERAL CASE”. SIAM Journal on Mathematical Analysis 46.1 (2014): 310-352.