Critical behavior and synchronization of discrete stochastic phase coupled oscillators

TL;DR

This paper introduces a simple discrete stochastic phase-coupled oscillator model that exhibits critical synchronization behavior, including a supercritical Hopf bifurcation and XY universality class phase transition, analyzed across multiple dimensions.

Contribution

It provides a detailed characterization of synchronization transitions in a discrete stochastic oscillator model, including critical exponents and universality class, with numerical analysis across various dimensions.

Findings

Global oscillatory behavior at critical coupling

Onset of synchrony follows XY universality class

Critical dimensions identified as d_{lc} = 2 and d_{uc} = 4

Abstract

Synchronization of stochastic phase-coupled oscillators is known to occur but difficult to characterize because sufficiently complete analytic work is not yet within our reach, and thorough numerical description usually defies all resources. We present a discrete model that is sufficiently simple to be characterized in meaningful detail. In the mean field limit, the model exhibits a supercritical 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, we explicitly rule out multistability and show that that the onset of global synchrony is marked by signatures of the XY universality class. Our numerical results cover dimensions d=2, 3, 4, and 5 and lead to the appropriate XY classical exponents \beta and \nu, a lower critical dimension d_{lc} = 2, and an upper critical dimension d_{uc}=4.