On a Kinetic Fitzhugh-Nagumo Model of Neuronal Network

被引：38

作者：

Mischler, S. ^{[1
,2
]}

Quininao, C. ^{[3
,4
]}

Touboul, J. ^{[4
,5
]}

机构：

[1] Univ Paris 09, Pl Marechal Lattre de Tassigny, F-75775 Paris 16, France

[2] CNRS, IUFCEREMADE, UMR 7534, Pl Marechal Lattre de Tassigny, F-75775 Paris 16, France

[3] Univ Paris 06, Lab Jacques Louis Lions, CNRS, UMR 7598, 4 Pl Jussieu, F-75005 Paris, France

[4] CIRB Coll France, Math Neurosci Team, 11 Pl Marcelin Berthelot, F-75005 Paris, France

[5] CIRB Coll France, INRIA Paris Rocquencourt, Mycenae Team, 11 Pl Marcelin Berthelot, F-75005 Paris, France

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2016年 / 342卷 / 03期

关键词：

MATHEMATICAL-THEORY; DYNAMICS; OSCILLATIONS; INTEGRATE; EQUATION; SYSTEM;

D O I：

10.1007/s00220-015-2556-9

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We investigate existence and uniqueness of solutions of a McKean-Vlasov evolution PDE representing the macroscopic behaviour of interacting Fitzhugh-Nagumo neurons. This equation is hypoelliptic, nonlocal and has unbounded coefficients. We prove existence of a solution to the evolution equation and non trivial stationary solutions. Moreover, we demonstrate uniqueness of the stationary solution in the weakly nonlinear regime. Eventually, using a semigroup factorisation method, we show exponential nonlinear stability in the small connectivity regime.

引用

页码：1001 / 1042

页数：42

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