Hunting French ducks in a noisy environment

Berglund N, Gentz B, Kuehn C (2012)
Journal of Differential Equations 252(9): 4786-4841.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Berglund, Nils; Gentz, BarbaraUniBi ; Kuehn, Christian
Abstract / Bemerkung
We consider the effect of Gaussian white noise on fast-slow dynamical systems with one fast and two slow variables, containing a folded node singularity. In the absence of noise, these systems are known to display mixed-mode oscillations, consisting of alternating large- and small-amplitude oscillations. We quantify the effect of noise and obtain critical noise intensities beyond which the small-amplitude oscillations become hidden by fluctuations. Furthermore we prove that the noise can cause sample paths to jump away from so-called canard solutions with high probability before deterministic orbits do. This early-jump mechanism can drastically influence the local and global dynamics of the system by changing the mixed-mode patterns. (C) 2012 Elsevier Inc. All rights reserved.
Stichworte
Singular perturbation; Invariant manifold; Dynamic; Fast-slow system; bifurcation; Folded node; Canard; Mixed-mode oscillation; Random; dynamical system; Concentration of sample paths; First-exit time
Erscheinungsjahr
2012
Zeitschriftentitel
Journal of Differential Equations
Band
252
Ausgabe
9
Seite(n)
4786-4841
ISSN
0022-0396
Page URI
https://pub.uni-bielefeld.de/record/2489130

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Berglund N, Gentz B, Kuehn C. Hunting French ducks in a noisy environment. Journal of Differential Equations. 2012;252(9):4786-4841.
Berglund, N., Gentz, B., & Kuehn, C. (2012). Hunting French ducks in a noisy environment. Journal of Differential Equations, 252(9), 4786-4841. doi:10.1016/j.jde.2012.01.015
Berglund, N., Gentz, B., and Kuehn, C. (2012). Hunting French ducks in a noisy environment. Journal of Differential Equations 252, 4786-4841.
Berglund, N., Gentz, B., & Kuehn, C., 2012. Hunting French ducks in a noisy environment. Journal of Differential Equations, 252(9), p 4786-4841.
N. Berglund, B. Gentz, and C. Kuehn, “Hunting French ducks in a noisy environment”, Journal of Differential Equations, vol. 252, 2012, pp. 4786-4841.
Berglund, N., Gentz, B., Kuehn, C.: Hunting French ducks in a noisy environment. Journal of Differential Equations. 252, 4786-4841 (2012).
Berglund, Nils, Gentz, Barbara, and Kuehn, Christian. “Hunting French ducks in a noisy environment”. Journal of Differential Equations 252.9 (2012): 4786-4841.