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arXiv · 1302.1800

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

M. Krupa·B. Ambrosio·M. A. Aziz-Alaoui
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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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M. Krupa, B. Ambrosio, M. A. Aziz-Alaoui. 2014-03-03. Weakly coupled two slow- two fast systems, folded node and mixed mode oscillationsM. https://doi.org/10.1088/0951-7715%2F27%2F7%2F1555

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