PDEs for neural assemblies; analysis, simulations and behavior - Prof. Benoit Perthame (Laboratoire J.-L. Lions, Sorbonne Universit'e)

作者:   来源:  时间:2021-04-22

Distinguished Lecture Series in Mathematics 系列数学前沿学术讲座

题目:PDEs for neural assemblies; analysis, simulations and behavior

报告人:Prof. Benoit Perthame(Laboratoire J.-L. Lions, Sorbonne Universit'e)

报告时间:2021年4月22日(周四)下午 16:30-18:00 



              Meeting ID: 974 1241 3730
              Passcode: 321050

摘要: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.