Synchronization of Heterogeneous Kuramoto Oscillators with Arbitrary Topology

TL;DR

This paper develops an optimization-based method to determine conditions for synchronization in heterogeneous Kuramoto oscillators with arbitrary network topology, improving upon existing bounds by leveraging system-specific features.

Contribution

It introduces a novel optimization approach to compute bounds for synchronization, considering topology and frequency distribution of heterogeneous oscillators.

Findings

Provided conditions guarantee synchronization and positive invariance.

The optimization approach yields tighter bounds than previous analytical methods.

Illustrated improvements through numerical examples.

Abstract

We study synchronization of coupled Kuramoto oscillators with heterogeneous inherent frequencies and general underlying connectivity. We provide conditions on the coupling strength and the initial phases which guarantee the existence of a Positively Invariant Set (PIS) and lead to synchronization. Unlike previous works that focus only on analytical bounds, here we introduce an optimization approach to provide a computational-analytical bound that can further exploit the particular features of each individual system such as topology and frequency distribution. Examples are provided to illustrate our results as well as the improvement over previous existing bounds.