Abstract

In this talk, I will present some results regarding the dynamics of a network of stochastic spiking neurons akin to the "generalised linear model". This network is an elaboration of the one introduced in [De Masi et al. 2014] by generalising the dynamics of the individual neurons. This allows to capture most of the known intrinsic neuronal spiking, like bursting for example, and thus to study the effect of the neuron dynamics on the macroscopic one.

The model presents some challenges. It is a nonlinear Piecewise Deterministic Markov process with explosive flow and unbounded total rate function. I will present some theoretical results regarding the linearised equation (well posedness, ergodicity) and will highlight the difficulties associated to the nonlinear one. In particular, I will prove the existence of invariant distributions for the nonlinear process. Some numerical applications will be provided.