Organizers: Mathieu Desroches, University of Montpellier, mathieu.desroches at inria.fr; Yangyang Wang, Brandeis University, yangyangwang at brandeis.edu; Pascal Chossat, University of Montpellier,, pascal.chossat at inria.fr
Description
This session will focus on “Dynamical Modelling in Neuroscience”, presenting exemples on how mathematics can contribute to shed light onto brain dynamics. The session includes eight talks offering a recent panorama of this topic from multiple angles and viewpoints, with a variety of mathematical methods applied to neuroscience questions. The objective is to showcase the (reasonable or unreasonable) effectiveness of dynamical systems in neural modeling. Amongst the topics to be presented in the session will be symmetry (how symmetric structures in neural models can shape the activity and constrain possible dynamics), bifurcation theory (high-codimension bifurcations and organising centres in population behaviour), ion channel mutations (linking microscopic alterations to macroscopic epileptiform activity), synchronization phenomena in networks of neural oscillators (key to understanding coherence in brain rhythms), exact mean-field limits (their relevance to large-scale neural population models) and McKean-Vlasov equations (describing collective behaviour in networks). These talks illustrate the development of dynamical models pertinent to understanding brain activity across multiple spatial and temporal scales, with both theoretical underpinnings, numerical components, and with links to experimental data.