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Pré-Publication, Document De Travail Année : 2013

From random Poincaré maps to stochastic mixed-mode-oscillation patterns

Résumé

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 Poincaré 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. An unexpected result of the analysis is that in certain cases, noise may increase the number of small-amplitude oscillations between consecutive large-amplitude oscillations.
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Dates et versions

hal-00921881 , version 1 (22-12-2013)
hal-00921881 , version 2 (14-11-2014)

Identifiants

  • HAL Id : hal-00921881 , version 1

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Nils Berglund, Barbara Gentz, Christian Kuehn. From random Poincaré maps to stochastic mixed-mode-oscillation patterns. 2013. ⟨hal-00921881v1⟩
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