This course focuses on mathematical concepts and techniques used in computational neuroscience. It is designed to provide students with necessary mathematical background for formulating, simulating, and analyzing models of individual neurons and neural networks. The course will serve as an introduction to the theory of nonlinear differential equations and applied dynamical systems in the context of neuronal modeling. The topics to be covered include a review of basic facts about the electrophysiology of neural cells, analysis of the conductance based models, neural excitability, bursting, models for synaptically coupled cells, and compartmental models, as well as a number of mathematical techniques such as phase plane analysis, fast-slow decomposition, and elements of the bifurcation theory. The students will learn basic models of excitable membranes such as Hodgkin-Huxley, Morris-Lecar, and FitzHugh-Nagumo models.
Course material created by Professor Georgi Medvedev.
Target audience: Graduate
Institution: Drexel University