The synchronization transition in correlated oscillator populations

TL;DR

This paper investigates how correlations between native frequencies of coupled oscillators on sparse networks affect the synchronization transition, revealing shifts in critical points and changes in universality classes.

Contribution

It demonstrates that oscillator frequency correlations significantly influence synchronization behavior and critical phenomena in networked Kuramoto models.

Findings

Negative correlations lower the critical coupling for synchronization.

Positive correlations increase the critical coupling and can alter the universality class.

Synchronization behavior depends on both network architecture and oscillator placement.

Abstract

The synchronization transition of correlated ensembles of coupled Kuramoto oscillators on sparse random networks is investigated. Extensive numerical simulations show that correlations between the native frequencies of adjacent oscillators on the network systematically shift the critical point as well as the critical exponents characterizing the transition. Negative correlations imply an onset of synchronization for smaller coupling, whereas positive correlations shift the critical coupling towards larger interaction strengths. For negatively correlated oscillators the transition still exhibits critical behaviour similar to the all-to-all coupled Kuramoto system, while positive correlations change the universality class of the transition depending on the correlation strength. Crucially, the paper demonstrates that the synchronization behaviour is not only determined by the coupling architecture, but is also strongly influenced by the oscillator placement on the coupling network.