The universality of synchrony: critical behavior in a discrete model of stochastic phase coupled oscillators

TL;DR

This paper introduces a simple discrete model demonstrating universal synchronization behavior in stochastic phase oscillators, exhibiting critical phenomena consistent with the XY universality class.

Contribution

The paper presents the simplest discrete model showing synchronization and critical behavior in stochastic phase-coupled oscillators, including numerical characterization of phase transitions.

Findings

Global oscillatory behavior at critical coupling

Signatures of XY universality class in phase transition

Critical dimensions identified as 2 and 4

Abstract

We present the simplest discrete model to date that leads to synchronization of stochastic phase-coupled oscillators. In the mean field limit, the model exhibits a Hopf bifurcation and global oscillatory behavior as coupling crosses a critical value. When coupling between units is strictly local, the model undergoes a continuous phase transition which we characterize numerically using finite-size scaling analysis. In particular, the onset of global synchrony is marked by signatures of the XY universality class, including the appropriate classical exponents $\beta$ and $\nu$, a lower critical dimension $d_{lc} = 2$, and an upper critical dimension $d_{uc}=4$.