Clarification and Complement to "Mean-Field Description and Propagation of Chaos in Networks of Hodgkin-Huxley and FitzHugh-Nagumo Neurons"

J Math Neurosci. 2015 Dec;5(1):31. doi: 10.1186/s13408-015-0031-8. Epub 2015 Sep 1.

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. in J. Math. Neurosci. 2:10, 2012) and we prove the associated propagation of chaos property. We also complete the modeling issue in (Baladron et al. in J. Math. Neurosci. 2:10, 2012) by discussing the well-posedness of the stochastic differential equations which govern the behavior of the ion channels and the amount of available neurotransmitters.