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Pré-Publication, Document De Travail Année : 2015

On a kinetic FitzHugh-Nagumo model of neuronal network

Résumé

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.
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Dates et 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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  • HAL Id : hal-01108872 , version 1

Citer

Stéphane Mischler, Cristóbal Quiñinao, Jonathan Touboul. On a kinetic FitzHugh-Nagumo model of neuronal network. 2015. ⟨hal-01108872v1⟩
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