Event-based synchronization in biology: Dynamics of pulse coupled oscillators

The principles of event-based control appear to be a backbone of many self-coordinating natural systems. Populations of flashing fireflies and cells of the cardiac pacemakers are believed to reach synchrony via event-based interactions, known as the pulse coupling. Synchronization via pulse coupling is also widely used in wireless sensor networks, allowing to avoid the packet exchange. In spite of serious attention to networks of coupled oscillators, there is a lack of results on their synchronization under general topology and phase-response curves. The most general, to the best of the authors' knowledge, result of this type (Wang et al., 2012) establishes synchronization of oscillators with a delay-advance phase-response curve under the assumption of strongly connected network topology. In this paper we relax the latter assumption to the existence of an oriented spanning tree, which is also necessary for the synchronization, being commonly adopted in multi-agent control.