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].
Project published references
[1] S Coombes and Á Byrne 2019 , Nonlinear Dynamics in Computational Neuroscience, PoliTO Springer Series, Ed. A Torcini and F Corinto, Springer, 1-16
[2] Á Byrne, M J Brookes and S Coombes 2017 , Journal of Computational Neuroscience, Vol 43, 143-158
[3] E J Hildebrand, M A Buice and C C Chow 2007 , Physical Review Letters, 98:054101
[4] S Qiu and C C Chow 2018 , Physical Review E, Vol 98, 062414
[5] R Nicks, L Chambon and S Coombes 2018 , Physical Review E, Vol 97, 032213
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