Weakly coupled two slow- two fast systems, folded node and mixed mode oscillationsM
Dynamical Systems
2015-06-15 v2
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.
Cite
@article{arxiv.1302.1800,
title = {Weakly coupled two slow- two fast systems, folded node and mixed mode oscillationsM},
author = {M. Krupa and B. Ambrosio and M. A. Aziz-Alaoui},
journal= {arXiv preprint arXiv:1302.1800},
year = {2015}
}