Synchronization as Aggregation: Cluster Kinetics of Pulse-Coupled Oscillators

TL;DR

This paper analyzes how pulse-coupled oscillators synchronize over time by studying the evolution of cluster sizes, providing exact results on the process of cluster coalescence leading to full synchronization.

Contribution

It introduces a novel application of aggregation theory to quantify the dynamics of cluster formation in pulse-coupled oscillators.

Findings

Derived exact time-dependent distribution of cluster sizes.

Quantified the coalescence process from disorder to synchrony.

Provided insights into the kinetics of synchronization.

Abstract

We consider models of identical pulse-coupled oscillators with global interactions. Previous work showed that under certain conditions such systems always end up in sync, but did not quantify how small clusters of synchronized oscillators progressively coalesce into larger ones. Using tools from the study of aggregation phenomena, we obtain exact results for the time-dependent distribution of cluster sizes as the system evolves from disorder to synchrony.