A Stochastic Binary Vertex-Triggering Resetting Algorithm for Global Synchronization of Pulse-Coupled Oscillators

Abstract

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-neighbours 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 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">global</i> 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 units of time needed to reach synchronization for networks with various information flow topologies.