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Driven by increased applications in biological networks and wireless sensornetworks, synchronization of pulse-coupled oscillators (PCOs) has gainedincreased popularity. However, most existing results address the localsynchronization of PCOs with initial phases constrained in a half cycle, andresults on global synchronization from any initial condition are very sparse.In this paper, we address global PCO synchronization from an arbitrary phasedistribution under chain or directed tree graphs. Our results differ fromexisting global synchronization studies on decentralized PCO networks in twokey aspects: first, our work allows heterogeneous coupling functions, and weanalyze the behavior of oscillators with perturbations on their naturalfrequencies; secondly, rather than requiring a large enough coupling strength,our results hold under any coupling strength between zero and one, which iscrucial because a large coupling strength has been shown to be detrimental tothe robustness of PCO synchronization to disturbances.

On the Global Synchronization of Pulse-coupled Oscillators Interacting on Chain and Directed Tree Graphs