Stability of Spatio-Temporal Structures in a Lattice Model of Pulse-Coupled Oscillators

TL;DR

This paper investigates the stability of spatio-temporal patterns and synchronization in a lattice model of pulse-coupled oscillators, combining analysis of individual dynamics and interactions.

Contribution

It introduces a linear stability analysis framework for understanding the emergence and stability of structures in pulse-coupled oscillator lattices.

Findings

Identification of conditions for stable spatio-temporal structures

Demonstration of synchronized regimes under certain parameters

Analytical results on the stability of observed patterns

Abstract

We analyze the collective behavior of a lattice model of pulse-coupled oscillators. By studying the intrinsic dynamics of each member of the population and their mutual interactions we observe the emergence of either spatio-temporal structures or synchronized regimes. We perform a linear stability analysis of these structures.