Synchronization of networks with variable local properties

TL;DR

This paper investigates how local network properties like clustering and path length influence the synchronization transition of Kuramoto oscillators on scale-free networks, emphasizing the importance of exploring the entire phase diagram.

Contribution

It provides a detailed finite size scaling analysis showing the impact of local network properties on synchronization, highlighting differences between onset and complete synchronization.

Findings

Synchronization onset depends smoothly on local properties.

Complete synchronization is highly affected by network structure.

The study emphasizes exploring the full phase diagram.

Abstract

We study the synchronization transition of Kuramoto oscillators in scale-free networks that are characterized by tunable local properties. Specifically, we perform a detailed finite size scaling analysis and inspect how the critical properties of the dynamics change when the clustering coefficient and the average shortest path length are varied. The results show that the onset of synchronization does depend on these properties, though the dependence is smooth. On the contrary, the appearance of complete synchronization is radically affected by the structure of the networks. Our study highlights the need of exploring the whole phase diagram and not only the stability of the fully synchronized state, where most studies have been done up to now.