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

Abstract : 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.
Type de document :
Pré-publication, Document de travail
2013
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https://hal.archives-ouvertes.fr/hal-00786195
Contributeur : Benjamin Ambrosio <>
Soumis le : vendredi 8 février 2013 - 09:34:44
Dernière modification le : mardi 5 février 2019 - 11:41:16

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  • HAL Id : hal-00786195, version 1
  • ARXIV : 1302.1800

Citation

Maciej Krupa, B. 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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