On a kinetic FitzHugh-Nagumo model of neuronal network
Analysis of PDEs
2016-02-17 v1 Functional Analysis
Spectral Theory
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.
Keywords
Cite
@article{arxiv.1503.00492,
title = {On a kinetic FitzHugh-Nagumo model of neuronal network},
author = {Stéphane Mischler and Cristóbal Quiñinao and Jonathan Touboul},
journal= {arXiv preprint arXiv:1503.00492},
year = {2016}
}