Rongzheng Xie

An Introduction to Two-Dimensional Spiking Neuron Models

Formulating a model of individual neurons that is both biologically realistic and mathematically tractable is an important problem in mathematical neuroscience. A number of significant models have been introduced in the literature (i.e. H-H model, F-N model). In my presentation, I will first introduce a two-dimensional spiking neuron model due to Izhikevich that combine continuous dynamics with an instantaneous reset. Then I will state a result about global asymptotic stability of regular spiking, to conclude that this model is capable of reproducing a variety of spiking patterns and also have the advantage of being mathematically tractable. Finally, a will briefly dis- cuss my research proposal to study a PDE model for Neurones to compare it with Izhikevich’s one.