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We study Mixed Mode Oscillations (MMOs) in systems of two weakly coupledslow/fast oscillators. We focus on the existence and properties of a foldedsingularity called FSN II that allows the emergence of MMOs in the presence ofa suitable global return mechanism. As FSN II corresponds to a transcriticalbifurcation for a desingularized reduced system, we prove that, under certainnon-degeneracy conditions, such a transcritical bifurcation exists. We thenapply 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 theexistence of MMOs.

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