Mechanisms of synchronization and pattern formation in a lattice of pulse-coupled oscillators

TL;DR

This paper investigates how synchronization and pattern formation occur in a one-dimensional ring of pulse-coupled oscillators, revealing the stability conditions that lead to different dynamic behaviors.

Contribution

It provides exact stability analysis for a simplified unidirectionally coupled oscillator lattice, elucidating the mechanisms behind synchronization and pattern formation.

Findings

Stability of fixed points determines system behavior.

Exact results for a one-dimensional ring model.

Different behaviors linked to stability conditions.

Abstract

We analyze the physical mechanisms leading either to synchronization or to the formation of spatio-temporal patterns in a lattice model of pulse-coupled oscillators. In order to make the system tractable from a mathematical point of view we study a one-dimensional ring with unidirectional coupling. In such a situation, exact results concerning the stability of the fixed of the dynamic evolution of the lattice can be obtained. Furthermore, we show that this stability is the responsible for the different behaviors.