Phase transformation and synchrony for a network of coupled Izhikevich neurons

TL;DR

This paper develops a phase model for Izhikevich neurons using the Ott-Antonsen ansatz, enabling a tractable mean-field description and linking it to existing models through conformal mapping.

Contribution

It introduces an equivalent phase model for Izhikevich neurons and applies the Ott-Antonsen ansatz to derive mean-field dynamics, connecting different theoretical frameworks.

Findings

Derived mean-field dynamics using the Kuramoto order parameter.

Established the validity of conformal mapping between models.

Provided a new phase model for Izhikevich neurons.

Abstract

A number of recent articles have employed the Lorentz ansatz to reduce a network of Izhikevich neurons to a tractable mean-field description. In this letter, we construct an equivalent phase model for the Izhikevich model and apply the Ott-Antonsen ansatz, to derive the mean field dynamics in terms of the Kuramoto order parameter. In addition, we show that by defining an appropriate order parameter in the voltage-firing rate framework, the conformal mapping of Montbri\'o et al., which relates the two mean-field descriptions, remains valid.