Networks of noisy oscillators with correlated degree and frequency dispersion

TL;DR

This paper studies how correlations between network connectivity and oscillator frequency diversity influence synchronization, revealing that increased correlation raises the synchronization threshold and can decouple it from network connectivity.

Contribution

It introduces a novel analysis of how correlated degree and frequency dispersion affect synchronization in stochastic oscillator networks, highlighting counterintuitive effects.

Findings

Increased correlation raises the critical coupling strength for synchronization.

Critical coupling can depend solely on average connectivity, independent of network structure.

Stronger correlations are needed when noise is present to observe similar effects.

Abstract

We investigate how correlations between the diversity of the connectivity of networks and the dynamics at their nodes affect the macroscopic behavior. In particular, we study the synchronization transition of coupled stochastic phase oscillators that represent the node dynamics. Crucially in our work, the variability in the number of connections of the nodes is correlated with the width of the frequency distribution of the oscillators. By numerical simulations on Erd\"os-R\'enyi networks, where the frequencies of the oscillators are Gaussian distributed, we make the counterintuitive observation that an increase in the strength of the correlation is accompanied by an increase in the critical coupling strength for the onset of synchronization. We further observe that the critical coupling can solely depend on the average number of connections or even completely lose its dependence on the network connectivity. Only beyond this state, a weighted mean-field approximation breaks down. If noise is present, the correlations have to be stronger to yield similar observations.