Synchronization of Integrate and Fire oscillators with global coupling

TL;DR

This paper investigates how large assemblies of globally coupled Integrate and Fire oscillators synchronize their relaxations through pulse interactions, revealing conditions for synchronized states and effects of disorder.

Contribution

It demonstrates that pulse effects alone can synchronize oscillators in different modes, regardless of the evolution function's convexity or concavity, and explores disorder's role.

Findings

Synchronization occurs in two forms: in phase or in stable avalanches.

Synchronization is independent of the evolution function's convexity or concavity.

Disorder can facilitate synchronization and remove degeneracies.

Abstract

In this article we study the behavior of globally coupled assemblies of a large number of Integrate and Fire oscillators with excitatory pulse-like interactions. On some simple models we show that the additive effects of pulses on the state of Integrate and Fire oscillators are sufficient for the synchronization of the relaxations of all the oscillators. This synchronization occurs in two forms depending on the system: either the oscillators evolve ``en bloc'' at the same phase and therefore relax together or the oscillators do not remain in phase but their relaxations occur always in stable avalanches. We prove that synchronization can occur independently of the convexity or concavity of the oscillators evolution function. Furthermore the presence of disorder, up to some level, is not only compatible with synchronization, but removes some possible degeneracy of identical systems and allows new mechanisms towards this state.