Phase transformation and synchrony for a network of coupled Izhikevich neurons
Neurons and Cognition
2026-01-06 v1
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.
Keywords
Cite
@article{arxiv.2407.20055,
title = {Phase transformation and synchrony for a network of coupled Izhikevich neurons},
author = {Áine Byrne},
journal= {arXiv preprint arXiv:2407.20055},
year = {2026}
}