Phase transitions towards frequency entrainment in large oscillator lattices

TL;DR

This paper studies how large networks of coupled oscillators undergo phase transitions leading to frequency entrainment, revealing two distinct transitions and self-organized criticality in the process.

Contribution

It demonstrates the existence of two phase transitions in large oscillator lattices and characterizes the critical behavior and self-organized criticality between them.

Findings

Largest cluster of entrained oscillators becomes macroscopic at first transition.

Global frequency entrainment occurs at second transition.

System exhibits self-organized criticality between the two transitions.

Abstract

We investigate phase transitions towards frequency entrainment in large, locally coupled networks of limit cycle oscillators. Specifically, we simulate two-dimensional lattices of pulse-coupled oscillators with random natural frequencies, resembling pacemaker cells in the heart. As coupling increases, the system seems to undergo two phasetransitions in the thermodynamic limit. At the first, the largest cluster of frequency entrained oscillators becomes macroscopic. At the second, global entrainment settles. Between the two transitions, the system has features indicating self-organized criticality.