Pré-Publication, Document De Travail Année : 2026

A Fokker-Planck equation with superlinear drift at infinity for Integrate-and-Fire model

Résumé

The Integrate-and-Fire model is a Fokker-Planck equation arising in neuroscience. It describes the evolution of the probability density of the neuronal membrane potential and fitting has shown that the inclusion of a em superlinear drift provides the most realistic description. To make sense of this, we propose to set the equation on the full line, the neural activity being described by the flux at infinity. This framework serves as a model extension of the classical Noisy Integrate-and-Fire model, with a fixed firing potential. We first establish the well-posedness of the solution, establish the boundary condition at infinity which is the major difficulty. Then, state rigorously the entropy dissipation property. Finally, using Doeblin’s method, we prove the exponential convergence of the solution toward the unique stationary state in full generality.

Fichier principal
Vignette du fichier
FPSL_hal_version.pdf (477.39 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Licence

Dates et versions

hal-05476616 , version 1 (26-01-2026)

Licence

Identifiants

Citer

Benoît Perthame, Clément Rieutord, Delphine Salort. A Fokker-Planck equation with superlinear drift at infinity for Integrate-and-Fire model. 2025. ⟨hal-05476616⟩
151 Consultations
58 Téléchargements

Altmetric

Partager

  • More