From Random Poincar, Maps to Stochastic Mixed-Mode-Oscillation Patterns

Berglund N, Gentz B, Kuehn C (2015)
Journal of Dynamics and Differential Equations 27(1): 83-136.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Berglund, Nils; Gentz, BarbaraUniBi ; Kuehn, Christian
Abstract / Bemerkung
We quantify the effect of Gaussian white noise on fast-slow dynamical systems with one fast and two slow variables, which display mixed-mode oscillations owing to the presence of a folded-node singularity. The stochastic system can be described by a continuous-space, discrete-time Markov chain, recording the returns of sample paths to a Poincar, section. We provide estimates on the kernel of this Markov chain, depending on the system parameters and the noise intensity. These results yield predictions on the observed random mixed-mode oscillation patterns. Our analysis shows that there is an intricate interplay between the number of small-amplitude oscillations and the global return mechanism. In combination with a local saturation phenomenon near the folded node, this interplay can modify the number of small-amplitude oscillations after a large-amplitude oscillation. Finally, sufficient conditions are derived which determine when the noise increases the number of small-amplitude oscillations and when it decreases this number.
Stichworte
Concentration of sample paths; system; Random dynamical; Mixed-mode oscillation; Fast-slow system; Folded node; Markov chain
Erscheinungsjahr
2015
Zeitschriftentitel
Journal of Dynamics and Differential Equations
Band
27
Ausgabe
1
Seite(n)
83-136
ISSN
1040-7294
Page URI
https://pub.uni-bielefeld.de/record/2731199

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Berglund N, Gentz B, Kuehn C. From Random Poincar, Maps to Stochastic Mixed-Mode-Oscillation Patterns. Journal of Dynamics and Differential Equations. 2015;27(1):83-136.
Berglund, N., Gentz, B., & Kuehn, C. (2015). From Random Poincar, Maps to Stochastic Mixed-Mode-Oscillation Patterns. Journal of Dynamics and Differential Equations, 27(1), 83-136. doi:10.1007/s10884-014-9419-5
Berglund, N., Gentz, B., and Kuehn, C. (2015). From Random Poincar, Maps to Stochastic Mixed-Mode-Oscillation Patterns. Journal of Dynamics and Differential Equations 27, 83-136.
Berglund, N., Gentz, B., & Kuehn, C., 2015. From Random Poincar, Maps to Stochastic Mixed-Mode-Oscillation Patterns. Journal of Dynamics and Differential Equations, 27(1), p 83-136.
N. Berglund, B. Gentz, and C. Kuehn, “From Random Poincar, Maps to Stochastic Mixed-Mode-Oscillation Patterns”, Journal of Dynamics and Differential Equations, vol. 27, 2015, pp. 83-136.
Berglund, N., Gentz, B., Kuehn, C.: From Random Poincar, Maps to Stochastic Mixed-Mode-Oscillation Patterns. Journal of Dynamics and Differential Equations. 27, 83-136 (2015).
Berglund, Nils, Gentz, Barbara, and Kuehn, Christian. “From Random Poincar, Maps to Stochastic Mixed-Mode-Oscillation Patterns”. Journal of Dynamics and Differential Equations 27.1 (2015): 83-136.

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