---
abstract: 'The property of desynchronization in an all-to-all network of homogeneous impulse-coupled oscillators is studied. Each impulse-coupled oscillator is modeled as a hybrid system with a single timer state that self-resets to zero when it reaches a threshold, at which event all other impulse-coupled oscillators adjust their timers following a common reset law. In this setting, desynchronization is considered as each impulse-coupled oscillator’s timer having equal separation between successive resets. We show that, for the considered model, desynchronization is an asymptotically stable property. For this purpose, we recast desynchronization as a set stabilization problem and employ Lyapunov stability tools for hybrid systems. Furthermore, several perturbations are considered showing that desynchronization is a robust property. Perturbations on both the continuous and discrete dynamics are considered. Numerical results are presented to illustrate the main contributions.'
author:
- 'Sean Phillips and Ricardo G. Sanfelice[^1]'
bibliography:
- 'Biblio.bib'
- 'RGS.bib'
- 'SAP.bib'
---

Introduction
============

Impulse-coupled oscillators are multi-agent systems with state variables consisting of timers that evolve continuously until a state-dependent event triggers an instantaneous update of their values. Networks of such oscillators have been employed to model the dynamics of a wide range of biological and engineering systems. In fact, impulse-coupled 