Comment on "The Winfree model with non-infinitesimal phase-response curve: Ott-Antonsen theory" [Chaos 30, 073139 (2020)]

TL;DR

This paper investigates the relationship between the nonlinear coupling function Q and the phase-response curve (PRC) in an extended Winfree model, using numerical simulations to compare their qualitative similarities.

Contribution

It clarifies the practical differences between the coupling function Q and the actual PRC, correcting a previous misconception in the literature.

Findings

PRC and Q functions are qualitatively similar in all cases examined

Numerical simulations confirm the similarity between PRC and Q functions

Clarifies the distinction between coupling functions and phase-response curves

Abstract

In a recent paper [Chaos 30, 073139 (2020)] we analyzed an extension of the Winfree model with nonlinear interactions. The nonlinear coupling function Q was mistakenly identified with the non-infinitesimal phase-response curve (PRC). Here, we asses to what extent Q and the actual PRC differ in practice. By means of numerical simulations, we compute the PRCs corresponding to the Q functions previously considered. The results confirm a qualitative similarity between the PRC and the coupling function Q in all cases.