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 semigroup factorisation method, we show exponential nonlinear stability in the small connectivity regime.
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https://hal.archives-ouvertes.fr/hal-01108872
Contributor : Cristóbal Quiñinao <>
Submitted on : Monday, March 2, 2015 - 12:54:18 PM
Last modification on : Tuesday, March 19, 2019 - 11:52:02 AM
Long-term archiving on: Monday, June 1, 2015 - 5:15:52 PM

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  • HAL Id : hal-01108872, version 2
  • ARXIV : 1503.00492

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Stéphane Mischler, Cristóbal Quiñinao, Jonathan Touboul. On a kinetic FitzHugh-Nagumo model of neuronal network. 2015. ⟨hal-01108872v2⟩

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