Nicolas ZADEH et Pierre RECHO

GdT Math-Bio Sud-Est

星期四, 14 十一月, 2024 - 从 10:00 到 12:00

Résumé :

10h : Nicolas ZADEH (Université Libre de Bruxelles): Kinetic description and numerical study of a network of resonate and fire neurons

Abstract: An important feature of some neurons is their ability to display resonant-like properties. The resonate and fire (RF) model (Izhikevich, 2001) allows for a simple description of such neurons, for a meager computational cost. We will first present a mean-field description of a network of interconnected RF neurons, following the kinetic formalism.

Then a numerical approximation finite differences scheme designed to tackle the equation will be seen, having mass and positivity preservation properties. Some simulations giving validity to the mean-field approach conclude the talk.

11h : Pierre RECHO (LiPhy, UGA): A mechanical interpretation of the Fisher-KPP equation

Abstract: In ecology, the Fisher-KPP equation is often motivated by the proliferation of a population of randomly moving individuals in an environment with finite ressources. In this talk, I will show that this equation also appears as the limit of a Stefan problem originating from an active gel model of a proliferating cell monolayer with a free boundary. The advancement of the leading edge still relies on cell proliferation and protrusive activity at the tissue margin but the effective diffusion coefficient has now a direct mechanical interpretation.

Institution de l'orateur :

Université Libre de Bruxelles, resp. LiPhy UGA

Thème de recherche :

Probabilités

Salle :

B29