Comment on ``Mechanisms of synchronization and pattern formation in a lattice of pulse-coupled oscillators'' by Diaz-Guilera et al., Phys. Rev. E 57, 3820 (1998)

TL;DR

This paper critiques a previous study on synchronization in pulse-coupled oscillators, highlighting that their linear stability analysis is flawed and does not accurately reflect the true dynamics of the system.

Contribution

The paper provides a critical analysis of the stability method used by Diaz-Guilera et al., demonstrating its limitations and discussing the actual dynamics of the oscillator system.

Findings

The linear stability analysis does not accurately predict system behavior.

Many assumptions in the original analysis are generally incorrect.

The true dynamics differ significantly from the linear stability predictions.

Abstract

In a recent paper, Diaz-Guilera et al. [Phys. Rev. E 57, 3820 (1998)] analyze the mechanisms of synchronization and pattern formation in a lattice of pulse-coupled oscillators. In essence, their analysis consists in the study of the stability of the fixed points of several linear return maps which are obtained from the original system by means of matrix manipulations. We show that although the model they consider is very specific and actually unable to account even for a linear phase response curve, their method does not give correct information on the original system since many of the assumptions involved are in general not correct. To clarify these aspects, several issues concerning the real dynamics are also discussed.