Splay states and two-cluster states in ensembles of excitable units
Institut für Physik, Humboldt-Universität zu Berlin, 12489, Berlin, Germany
Accepted: 23 April 2021
Published online: 5 July 2021
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.
© The Author(s) 2021
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