On a Kinetic Fitzhugh-Nagumo Model of Neuronal Network

被引：35
|
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
收藏
页码：1001 / 1042
页数：42
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