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Journal Articles Communications in Mathematical Physics Year : 2016

On a Kinetic Fitzhugh–Nagumo Model of Neuronal Network

Abstract

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 semi-group factorisation method , we show exponential nonlinear stability in the small connectivity regime .
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Origin : Files produced by the author(s)
Origin : Files produced by the author(s)
Origin : Files produced by the author(s)
Origin : Files produced by the author(s)
Origin : Files produced by the author(s)
Origin : Files produced by the author(s)
Origin : Files produced by the author(s)
Origin : Files produced by the author(s)
Origin : Files produced by the author(s)
Origin : Files produced by the author(s)

Dates and versions

hal-01108872 , version 1 (23-01-2015)
hal-01108872 , version 2 (02-03-2015)
hal-01108872 , version 3 (06-11-2015)
hal-01108872 , version 4 (18-01-2016)

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Stéphane Mischler, Cristóbal Quiñinao, Jonathan Touboul. On a Kinetic Fitzhugh–Nagumo Model of Neuronal Network. Communications in Mathematical Physics, 2016, 342 (3), pp.1001-1042. ⟨10.1007/s00220-015-2556-9⟩. ⟨hal-01108872v4⟩
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