Speaker
Pierre Roux, École Centrale de Lyon, Institut Camille Jordan
Abstract
Since patterned activity in a neural network often arises from the interplay between a large number of cells susceptible to noise, understanding the underlying mechanism can be very challenging. In this talk, I will present the so-called Nonlinear Noisy Leaky Integrate and Fire (NNLIF) model, a non-linear non-local Fokker-Planck-type equation appearing as the mean-field limit of a stochastic particle system modelling finitely many neurons with simple assumptions. This mean-field model allows us to get insight into the evolution of the probability distribution of the neurons in the (virtually infinite) network, namely by studying the convergence to stationary states (desynchronisation), the emergence of periodic solutions (self-sustained oscillation) and finite-time blow-up (synchronisation).