A Microscopic Spiking Neuronal Network for the Age-Structured Model

被引：4

作者：

Quininao, Cristobal ^{[1
,2
]}

机构：

[1] Univ Catolica, Fac Ciencias Biol, Dept Ecol, Avda Libertador Bernardo OHiggins 340, Santiago, Chile

[2] Univ Tarapaca, Inst Alta Invest, Antofagasta 1520, Arica, Chile

来源：

ACTA APPLICANDAE MATHEMATICAE | 2016年 / 146卷 / 01期

关键词：

Chaos propagation; Mean-field limits; Neuronal networks; Age structured model; Poisson coupling; LIMIT;

D O I：

10.1007/s10440-016-0056-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce a microscopic spiking network consistent with the age-structured/renewal equation proposed by Pakdaman, Perthame and Salort. It is a jump process interacting through a set of global activity variables with random delays. We show the well-posedness of the particle system and the mean-field equation. Moreover, by studying the tightness of the empirical measure, we prove the propagation of chaos property. Eventually, we quantify the rate of convergence by using the coupling method.

引用

页码：29 / 55

页数：27

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