Asymptotic synchronization of Kuramoto oscillators with time delay and non-universal interaction

TL;DR

This paper investigates how synchronization emerges in a network of Kuramoto oscillators with time delays, establishing conditions for asymptotic synchronization and providing numerical insights into the effects of network structure and delays.

Contribution

The paper proves asymptotic frequency synchronization in Kuramoto models with time delays on strongly connected digraphs and derives exponential synchronization estimates for all-to-all networks.

Findings

Uniform bound on phase diameter established

Asymptotic frequency synchronization proven under certain conditions

Numerical simulations illustrate effects of network structure and delays

Abstract

We study the emergence of synchronization in the Kuramoto model on a digraph in the presence of time delays. Assuming the digraph is strongly connected, we first establish a uniform bound on the phase diameter and subsequently prove the asymptotic frequency synchronization of the oscillators under suitable assumptions on the initial configurations. In the case of an all-to-all connection, we obtain an exponential synchronization estimate. Additionally, we present numerical simulations, providing further insights into the synchronization and oscillatory behaviors of the oscillator frequencies depending on the network structure and the magnitude of the time delay.