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Pré-Publication, Document De Travail Année : 2013

Weakly coupled two slow- two fast systems, folded node and mixed mode oscillations

Résumé

We study Mixed Mode Oscillations (MMOs) in systems of two weakly coupled slow/fast oscillators. We focus on the existence and properties of a folded singularity called FSN II that allows the emergence of MMOs in the presence of a suitable global return mechanism. As FSN II corresponds to a transcritical bifurcation for a desingularized reduced system, we prove that, under certain non-degeneracy conditions, such a transcritical bifurcation exists. We then apply this result to the case of two coupled systems of FitzHugh- Nagumo type. This leads to a non trivial condition on the coupling that enables the existence of MMOs.

Dates et versions

hal-00786195 , version 1 (08-02-2013)

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Maciej Krupa, Benjamin Ambrosio, M. A. Aziz-Alaoui. Weakly coupled two slow- two fast systems, folded node and mixed mode oscillations. 2013. ⟨hal-00786195⟩
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