Sue Ann Campbell
Title: Mean Field Analysis and the Dynamics of Large Networks of Neurons
Abstract: We use mean field analysis to study emergent behaviour in networks of all-to-all coupled, pulse-coupled neurons. The individual neurons are represented using a class of two-dimensional integrate and fire model. The mean field model is derived using a population density approach, moment closure assumptions and a quasi-steady state approximation. The resulting model is a system of switching ordinary differential equations, which exhibits a variety of smooth and nonsmooth bifurcations. We show that the results of the mean field analysis are a reasonable prediction of the behaviour seen in numerical simulations of large networks and discuss how the presence of parameter heterogeneity and noise affects the results.