Clarification and complement to "Mean-field description and propagation of chaos in networks of Hodgkin-Huxley and FitzHugh-Nagumo neurons"

TL;DR

This paper clarifies the mathematical foundations and proves the propagation of chaos for mean-field models of neuron networks, also extending the modeling to ion channels and neurotransmitter dynamics.

Contribution

It provides a rigorous analysis of the well-posedness and chaos propagation in mean-field neuron models, extending previous work to include stochastic ion channel and neurotransmitter equations.

Findings

Proved well-posedness of the limit equations.

Established propagation of chaos for the models.

Extended modeling to stochastic ion channels and neurotransmitters.

Abstract

In this note, we clarify the well-posedness of the limit equations to the mean-field $N$-neuron models proposed in Baladron et al. and we prove the associated propagation of chaos property. We also complete the modeling issue in Baladron et al. by discussing the well-posedness of the stochastic differential equations which govern the behavior of the ion channels and the amount of available neurotransmitters.