Synchronization of Pulse-Coupled Oscillators on (Strongly) Connected Graphs

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 $\pi$, 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.