Scale transitions for models with spatial structure

Description

Models that incorporate spatial dynamics additional to their time evolution arise in various areas of mathematical neuroscience and related fields, e.g., Hodgkin-Huxley type membrane models for axons and in cardiac tissue, Wilson-Cowan / Amari-type neural field models or reaction-diffusion models of chemical reactions system in inhomogeneous media as occurs inside a living cell. Originally, these models were introduced as deterministic equations approximating an inherently noisy (or stochastic) real-world process. Later these models were either extended to incorporate also stochastic effects or a rigorous derivation from smaller scale stochastic models was attempted. These derivation attempts also lead to new classes of models. In my talk I will present typical mathematical set-ups and corresponding methods useful for rigorously obtaining a limit theorem describing a scale transition in spatio-temporal models. I will discuss the interpretations, implications and possible limitations of these approaches. On the one hand, this will be a review of previous work from the literature. On the other hand I will also present some concrete recent results obtained in our work in connection of scale transitions of discrete Markov Chain models describing excitable membranes or neural fields.

Period	04 Jul 2012
Event title	Random Models in Neuroscience
Event type	Conference
Location	FranceShow on map