Splay states and two-cluster states in ensembles of excitable units

Abstract

Focusing on systems of sinusoidally coupled active rotators, we study the emergence and stability of periodic collective oscillations for systems of identical excitable units with repulsive all-to-all interaction. Special attention is put on splay states and two-cluster states. Recently, it has been shown that one-parameter families of such systems, containing the parameter values at which the Watanabe–Strogatz integrability takes place, feature an instantaneous non-local exchange of stability between splay and two-cluster states. Here, we illustrate how in the extended families that circumvent the Watanabe–Strogatz dynamics, this abrupt transition is replaced by the “gradual transfer” of stability between the 2-cluster and the splay states, mediated by mixed-type solutions. We conclude our work by recovering the same kind of dynamics and transfer of stability in an ensemble of voltage-coupled Morris–Lecar neurons.