On the exponential convergence rate for a non-gradient Fokker-Planck equation in Computational Neuroscience

2016/03/23 by J. A. Espichán Carrillo, J-A Carrillo, Simona Mancini +5
Biochemistry, Genetics and Molecular Biology · Mathematics · Neuroscience · Physics and Astronomy · #Analysis of PDEs (math.AP) #Diffusion and Search Dynamics #FOS: Mathematics #Neural dynamics and brain function #math.AP #stochastic dynamics and bifurcation

paper · pdf · doi:10.48550/arxiv.1603.07192

arxiv created 2016/03/23 · openalex publication_date 2016/03/23 · arxiv updated 2016/03/24 · openalex created_date 2023/01/08 · openalex updated_date 2026/07/28

Abstract

This paper concerns the proof of the exponential rate of convergence of the solution of a Fokker-Planck equation, with a drift term not being the gradient of a potential function and endowed by Robin type boundary conditions. This kind of problem arises, for example, in the study of interacting neurons populations. Previous studies have numerically shown that, after a small period of time, the solution of the evolution problem exponentially converges to the stable state of the equation.

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