3 papers
math.NA2020
Asymptotic preserving schemes for the FitzHugh-Nagumo transport equation with strong local interactions
Joachim Crevat, Francis Filbet
This paper is devoted to the numerical approximation of the spatially-extended FitzHugh-Nagumo transport equation with strong local interactions based on a particle method. In this…
math.AP2019
Asymptotic limit of a spatially-extended mean-field FitzHugh-Nagumo model
Joachim Crevat
We consider a spatially extended mean-field model of a FitzHugh-Nagumo neural network, with a rescaled interaction kernel. Our main purpose is to prove that its asymptotic limit in…
math.AP2018
Rigorous derivation of the nonlocal reaction-diffusion FitzHugh-Nagumo system
Joachim Crevat, Grégory Faye, Francis Filbet
We introduce a spatially extended transport kinetic FitzHugh-Nagumo model with forced local interactions and prove that its hydrodynamic limit converges towards the classical nonlo…