Much of our understanding of the neurocomputational properties of brain cells comes from the pioneering studies of Hodgkin and Huxley in the late 40s. They build a detailed model of the membrane potential dynamics of neurons based on the conductivity of various ion channels. Later work on dynamical systems showed that different responses of cells with similar electrophysiology to input currents is due to different bifurcation mechanisms of excitability.

In this course we study the Hodgkin-Huxley (HH) model of neurons and introduce the analytical treatment of non-linear dynamical systems. We will then drive and study a typical reduced HH model analytically and determine different regimes of activity in such a system.