Departmental Colloquium


Neurons exchange information via discharges propagated by membrane potential  which trigger firing of the many connected neurons. How to describe large assemblies of such neurons? How can such a network generate a collective activity? 

Such questions can be tackled using nonlinear partial-integro-differential equations which are classically used to describe neuronal assemblies. Among them, the Wilson-Cowan equations are the best known and describe globally brain spiking rates. Another classical model is the integrate-and-fire equation based on Fokker-Planck equations. The spike times distribution, which encodes more directly the neuronal information, can also be described directly thanks to structured population. 

We will compare and analyze these models. A striking observation is that solutions to the I\&F can blow-up in finite time, a form of synchronization that can be regularized with a refractory stage. We can also show that for small or large connectivities  the ‘elapsed time model’ leads to desynchronization. For intermediate regimes, sustained periodic activity occurs compatible with observations. A common tool is the use of the relative entropy method.

The talk will be followed by reception in the Huxley Common Room (649A) at 6pm.