
Paul Bressloff
Mathematical Institute, University of Oxford, UK
Wednesday 2 December 2009
16.00
Seminar Room B10 (Basement)
Alexandra House, 17 Queen Square, London, WC1N 3AR
Stochastic neurodynamics, master equations and the systemsize expansion
There are a growing number of examples where noise appears to play a role in generating spontaneous oscillatory and wavelike phenomena in largescale cortical and subcortical networks. Examples include retinal waves and spontaneous oscillations in early cortical development, breathing rhythms, neuronal avalanches with powerlawlike behaviour, and spontaneous waves in epileptiform tissue. In this talk we consider a master equation formulation of stochastic neurodynamics in a recurrent network of synaptically coupled homogeneous neuronal populations each consisting of N identical neurons. The state of the network is specified by the fraction of active or spiking neurons in each population, and transition rates are chosen so that in the thermodynamic or meanfield limit we recover standard ratebased models. We derive the lowest order corrections to these rate equations for large but finite N using the Van Kampen systemsize expansion, and show how this is related to the pathintegral approach of Buice and Cowan. We then briefly describe applications of the master equation approach to studying noiseinduced oscillations and metastable states in recurrent networks.