Effects of Disorder on Synchronization of Discrete Phase-Coupled Oscillators

TL;DR

This paper investigates how disorder in transition rates affects synchronization in populations of stochastic three-state oscillators, revealing a single phase transition to synchrony regardless of disorder level.

Contribution

It provides an exactly solvable model and systematic analysis of synchronization behavior in disordered oscillator populations, including analytical and numerical results.

Findings

Single phase transition to synchrony at a critical coupling strength

Disorder does not prevent the emergence of macroscopic synchrony

Analytical and numerical methods confirm robustness of synchronization

Abstract

We study synchronization in populations of phase-coupled stochastic three-state oscillators characterized by a distribution of transition rates. We present results on an exactly solvable dimer as well as a systematic characterization of globally connected arrays of N types of oscillators (N=2, 3, 4) by exploring the linear stability of the nonsynchronous fixed point. We also provide results for globally coupled arrays where the transition rate of each unit is drawn from a uniform distribution of finite width. Even in the presence of transition rate disorder, numerical and analytical results point to a single phase transition to macroscopic synchrony at a critical value of the coupling strength. Numerical simulations make possible the further characterization of the synchronized arrays.