  In this paper, we propose a novel stochastic binary resetting algorithm for
networks of pulse-coupled oscillators (or, simply, agents) to reach global
synchronization. The algorithm is simple to state: Every agent in a network
oscillates at a common frequency. Upon completing an oscillation, an agent
generates a Bernoulli random variable to decide whether it sends pulses to all
of its out-neighbors or it stays quiet. Upon receiving a pulse, an agent resets
its state by following a binary phase update rule. We show that such an
algorithm can guarantee global synchronization of the agents almost surely as
long as the underlying information flow topology is a rooted directed graph.
The proof of the result relies on the use of a stochastic hybrid dynamical
system approach. Toward the end of the paper, we present numerical
demonstrations for the validity of the result and, also, numerical studies
about the times needed to reach synchronization for various information flow
topologies.
