Synchronization of pulse-coupled oscillators on (strongly) connected graphs

Abstract

The synchronization of pulse-coupled oscillators (PCOs) interacting on general (strongly) connected graphs is addressed. It is shown that the network synchronizes if the phases are contained in an arc of length less than π, for every (strongly) connected interaction topology. Moreover, global synchronization is feasible in the all-to-all, strongly rooted, and connected bidirectional cases. Examples, counter-examples, and numerical simulations are given to illustrate the analytical findings.