Non-universal results induced by diversity distribution in coupled excitable systems

TL;DR

This paper investigates how the diversity distribution affects collective firing in coupled excitable systems, revealing that Lorentzian distributions do not exhibit the transition common to other distributions, challenging their typical use.

Contribution

It demonstrates that the transition to collective firing depends on the diversity distribution, showing Lorentzian distributions do not produce this transition, unlike other well-defined distributions.

Findings

Transition occurs for any diversity distribution with well-defined moments.

Lorentzian distribution does not exhibit the transition.

Challenges the common assumption of Lorentzian distributions in oscillator models.

Abstract

We consider a system of globally coupled active rotators near the excitable regime. The system displays a transition to a state of collective firing induced by disorder. We show that this transition is found generically for any diversity distribution with well defined moments. Singularly, for the Lorentzian distribution (widely used in Kuramoto-like systems) the transition is not present. This warns about the use of Lorentzian distributions to understand the generic properties of coupled oscillators.