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.

中文翻译：

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澄清和补充“霍奇金-赫克斯利和费兹休-纳古莫神经元网络中的平均场描述和混沌的传播”。

在本说明中，我们阐明了（Baladron et al。in J. Math。Neurosci。2:10，2012）中提出的平均场N-神经元模型的极限方程的适定性，并证明了相关的传播混乱的财产。我们还讨论了控制离子通道行为和可用神经递质数量的随机微分方程的适定性，从而完成了（Baladron等人，J。Math。Neurosci。2:10，2012）中的建模问题。 。