Entrainment transition in populations of random frequency oscillators

TL;DR

This paper investigates the phase transition to synchronization in populations of oscillators with random frequencies, revealing dimension-dependent behaviors and finite size effects in different coupling regimes.

Contribution

It provides new insights into the nature of entrainment transitions, including finite size effects and dimension-dependent scaling laws, in both global and local coupling scenarios.

Findings

Sample-dependent finite size effects with correlation size exponent 5/2.

Mean-field behavior observed for dimensions greater than 4.

Scaling laws for correlation length in lower dimensions.

Abstract

The entrainment transition of coupled random frequency oscillators is revisited. The Kuramoto model (global coupling) is shown to exhibit unusual sample-dependent finite size effects leading to a correlation size exponent $\bar\nu=5/2$. Simulations of locally coupled oscillators in $d$-dimensions reveal two types of frequency entrainment: mean-field behavior at $d>4$, and aggregation of compact synchronized domains in three and four dimensions. In the latter case, scaling arguments yield a correlation length exponent $\nu=2/(d-2)$, in good agreement with numerical results.