Séminaire Analyse-Proba (Delphine Salort , mardi 16 décembre)

Le prochain séminaire Analyse-Proba aura lieu mardi 9 décembre à 10h30 en A711. Delphine Salort (LJLL - Sorbonne Université) nous parlera de :

Asymptotic dynamic of neural models with partial diffusion

Abstract
In many biological contexts, one observes Brownian motions that are restricted to certain variables or random movements that differ from classical Brownian motion. Among these mod- els are those involving large populations of interacting neurons. In such models, the variability of neuronal ion channels, which are also subject to random fluctuations, is modeled by diffusion in the conductance variable, while the membrane potential variable remains non-diffusive. Other models focus exclusively on the membrane potential (without conductance) and include an adaptation variable that responds to stimuli received by the neurons. In this case, diffusion is applied to the membrane potential, while the adaptation variable remains non-diffusive. All these phenomena can lead to changes in propagation speed and, in some cases, a significant loss of regularity properties. In this talk, we will explain, using two toy models from neuroscience, how to study the asymptotic properties of these equations and deduce the exponential convergence of the solution toward the stationary state in L^1.