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.
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https://hal.archives-ouvertes.fr/hal-00786195
Contributor : Benjamin Ambrosio <>
Submitted on : Friday, February 8, 2013 - 9:34:44 AM
Last modification on : Tuesday, February 5, 2019 - 11:41:16 AM

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

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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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