Synchronization of Phase-coupled Oscillators with Distance-dependent Delay

TL;DR

This paper explores how distance-dependent delays in a Kuramoto model of phase-coupled oscillators influence synchronization, revealing that non-uniform delays promote incoherence and alter phase transition behaviors.

Contribution

It introduces a generalized Kuramoto model with distance-dependent delay on a lattice, analyzing the effects of finite interaction velocity on synchronization patterns.

Findings

Distance-dependent delay promotes incoherence.

Non-uniform delay removes reentrant synchronization behavior.

A phase diagram for coupling and delay is developed.

Abstract

By means of numerical integration we investigate the coherent and incoherent phases in a generalized Kuramoto model of phase-coupled oscillators with distance-dependent delay. Preserving the topology of a complete graph, we arrange the nodes on a square lattice while introducing finite interaction velocity, which gives rise to non-uniform delay. It is found that such delay facilitates incoherence and removes reentrant behavior found in models with uniform delay. A coupling-delay phase diagram is obtained and compared with previous results for uniform delay.