Large coupling in a FitzHug-Nagumo neural network: quantitative and strong convergence results - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2022

Large coupling in a FitzHug-Nagumo neural network: quantitative and strong convergence results

Résumé

We consider a spatially extended mesoscopic FitzHugh-Nagumo model with interactions and prove that in the regime where strong and local interactions dominate, the probability density of the potential throughout the network concentrates into a Dirac distribution whose center of mass solves the classical non-local reaction-diffusion FitzHugh-Nagumo system. In [2], we proved that the profile of concentration is Gaussian by providing a weak convergence result. Our main purpose here consists in strengthening this result by deriving two quantitative and strong convergence estimates: the first one in a L1 functional framework and the second in a weighted L2 functional setting. Our approach is based on relative entropy techniques in the first case and on propagation of regularity in the second.
Fichier principal
Vignette du fichier
FHN_strong.pdf (560.54 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03619446 , version 1 (25-03-2022)
hal-03619446 , version 2 (07-04-2022)
hal-03619446 , version 3 (12-10-2022)
hal-03619446 , version 4 (11-06-2023)

Identifiants

Citer

Alain Blaustein. Large coupling in a FitzHug-Nagumo neural network: quantitative and strong convergence results. 2022. ⟨hal-03619446v1⟩
158 Consultations
139 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More