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

被引：43

作者：

Bossy, Mireille ^{[1
]}

Faugeras, Olivier ^{[2
]}

Talay, Denis ^{[1
]}

机构：

[1] INRIA Sophia Antipolis Mediterranee, TOSCA Lab, Sophia Antipolis, France

[2] INRIA Sophia Antipolis Mediterranee, NeuroMathComp Lab, Sophia Antipolis, France

来源：

JOURNAL OF MATHEMATICAL NEUROSCIENCE | 2015年 / 5卷

基金：

欧洲研究理事会;

关键词：

Mean-field limits; Propagation of chaos; Stochastic differential equations; Neural networks; Neural assemblies; Hodgkin-Huxley neurons; FitzHugh-Nagumo neurons;

D O I：

10.1186/s13408-015-0031-8

中图分类号：

Q [生物科学];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

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.

引用

页数：23