A statistical neurodynamics for networks of synaptically coupled nonlinear integrate-and-fire neurons

Project description

A network of globally coupled quadratic integrate-and-fire neurons with conductance based synapses has recently been shown to admit to an exact mean field description using the Ott-Antonsen (OA) ansatz [1,2]. The resulting neuronal population model is ideally suited as a model for understanding local field potentials.

This PhD project will initially treat finite-size effects around the asynchronous state using a Bogolyubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy with an appropriate moment-closure approximation [3].

It will then move on to consider a path-integral formalism to derive a perturbation expansion in the inverse system size to determine the evolution of system covariances [4].

The final part of the project will consider generalisations of the OA ansatz to allow the treatment of more general nonlinear integrate-and-fire neurons, and in particular piece-wise linear models with adaptation [5].