Effects of degree-frequency correlations on network synchronization: universality and full phase-locking

TL;DR

This paper introduces a model examining how degree-frequency correlations influence network synchronization, revealing a universal, fully phase-locked synchronized state independent of network topology, and analyzing various correlation effects.

Contribution

The study uncovers a universal synchronized state in networks with degree-frequency correlations and provides a comprehensive analysis of synchronization dynamics under different correlation patterns.

Findings

Universal synchronized state independent of network topology

All oscillators become simultaneously phase-locked

Different correlation patterns lead to distinct synchronization behaviors

Abstract

We introduce a model to study the effect of degree-frequency correlations on synchronization in networks of coupled oscillators. Analyzing this model, we find several remarkable characteristics. We find a stationary synchronized state that is (i) universal, i.e., the degree of synchrony, as measured by a global order parameter, is independent of network topology, and (ii) fully phase-locked, i.e., all oscillators become simultaneously phase-locked despite having different natural frequencies. This state separates qualitatively different behaviors for two other classes of correlations where, respectively, slow and fast oscillators can remain unsynchronized. We close by presenting analysis of the dynamics under arbitrary degree-frequency correlations.