Event-based Synchronization in Biology: Dynamics of Pulse Coupled Oscillators

The principles of event-based control appear to be abackbone of many self-coordinating natural systems. Populations offlashing fireflies and cells of the cardiac pacemakers are believed toreach synchrony via event-based interactions, known as the pulsecoupling. Synchronization via pulse coupling is also widely used inwireless sensor networks, allowing to avoid the packet exchange. Inspite of serious attention to networks of coupled oscillators, thereis a lack of results on their synchronization under general topologyand phase-response curves. The most general, to the best of theauthors’ knowledge, result of this type (Wang et al., 2012) establishessynchronization of oscillators with a delay-advance phase-responsecurve under the assumption of strongly connected network topology. Inthis paper we relax the latter assumption to the existence of an orientedspanning tree, which is also necessary for the synchronization, beingcommonly adopted in multi-agent control