Correlated disorder in the Kuramoto model: Effects on phase coherence, finite-size scaling, and dynamic fluctuations

TL;DR

This paper investigates how correlated quenched disorder in natural frequencies and coupling strengths affects phase coherence, critical synchronization, and finite-size scaling in a mean-field Kuramoto model, revealing universality with the traditional model.

Contribution

It introduces a correlated disorder in the Kuramoto model and analyzes its impact on synchronization and critical behavior, showing universality with the traditional model for p<1.

Findings

Critical width for synchronization is independent of the fraction p of positively coupled oscillators.

The model shares the same universality class as the traditional Kuramoto model with deterministic frequencies for p<1.

Correlation in disorder does not alter the critical width or universality class for p<1.

Abstract

We consider a mean-field model of coupled phase oscillators with quenched disorder in the natural frequencies and coupling strengths. A fraction $p$ of oscillators are positively coupled, attracting all others, while the remaining fraction $1-p$ are negatively coupled, repelling all others. The frequencies and couplings are deterministically chosen in a manner which correlates them, thereby correlating the two types of disorder in the model. We first explore the effect of this correlation on the system's phase coherence. We find that there is a a critical width $\gamma_c$ in the frequency distribution below which the system spontaneously synchronizes. Moreover, this $\gamma_c$ is independent of $p$. Hence, our model and the traditional Kuramoto model (recovered when $p=1$) have the same critical width $\gamma_c$. We next explore the critical behavior of the system by examining the finite-size scaling and the dynamic fluctuation of the traditional order parameter. We find that the model belongs to the same universality class as the Kuramoto model with deterministically (not randomly) chosen natural frequencies for the case of $p<1$.