On Synchronization in a Lattice Model of Pulse-Coupled Oscillators

TL;DR

This paper investigates how pulse-coupled oscillators on a lattice synchronize, revealing conditions for full synchronization and exploring spatial structures and self-organized criticality through simulations.

Contribution

It identifies the synchronization condition in lattice models and compares it to globally coupled systems, providing new insights into spatial patterns and criticality.

Findings

Synchronization condition matches that of globally coupled populations

Different spatial structures emerge when the condition is not fully met

Hints at self-organized criticality in the system

Abstract

We analyze the collective behavior of a lattice model of pulse-coupled oscillators. By means of computer simulations we find the relation between the intrinsic dynamics of each member of the population and their mutual interaction that ensures, in a general context, the existence of a fully synchronized regime. This condition turns out to be the same than the obtained for the globally coupled population. When the condition is not completely satisfied we find different spatial structures. This also gives some hints about self-organized criticality.