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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https://hal.archives-ouvertes.fr/hal-01108872
Contributor : Cristóbal Quiñinao <>
Submitted on : Monday, January 18, 2016 - 7:29:39 PM
Last modification on : Thursday, July 4, 2019 - 11:00:07 AM
Long-term archiving on : Tuesday, April 19, 2016 - 12:31:25 PM

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

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