Dynamics of three coupled excitable cells with D3 symmetry

Abstract

We study the solutions of a system of three coupled excitable cells with D3 symmetry. The system has two parameters, one controls the local dynamics of each cell and the other the strength of the coupling. We find and describe self-sustained collective oscillations. Periodic solutions appear in global bifurcations, typically after the collapse of fixed points heteroclinically connected. The symmetries of these periodic solutions are the same as the ones expected in periodic solutions which appear in local (Hopf) bifurcations.