Heterogeneity in oscillator networks: Are smaller worlds easier to synchronize?

TL;DR

This paper investigates how the distribution of connectivity in oscillator networks affects their ability to synchronize, revealing that more homogeneous networks can synchronize more easily despite having larger average distances.

Contribution

It demonstrates that network homogeneity enhances synchronizability, challenging the common belief that smaller network distances facilitate synchronization.

Findings

Homogeneous networks are more synchronizable than heterogeneous ones.

Synchronizability correlates with connectivity homogeneity rather than network distance.

Results suggest natural neural networks favor homogeneity for better synchronization.

Abstract

Small-world and scale-free networks are known to be more easily synchronized than regular lattices, which is usually attributed to the smaller network distance between oscillators. Surprisingly, we find that networks with a homogeneous distribution of connectivity are more synchronizable than heterogeneous ones, even though the average network distance is larger. We present numerical computations and analytical estimates on synchronizability of the network in terms of its heterogeneity parameters. Our results suggest that some degree of homogeneity is expected in naturally evolved structures, such as neural networks, where synchronizability is desirable.