### An introduction to the Wilson-Cowan model

Logan Chariker

Abstract:
This talk will be an introduction to the Wilson-Cowan model, which has been
highly influential in mathematical neuroscience, as it is one of the first
attempts to understand the dynamics of large, densely-coupled systems
of neurons using very simple model neurons and interactions as well as
mean-field methods from statistical mechanics. These methods yield a
simple set of differential equations for the dynamics that are
relatively easy to analyze compared to those of more biophysically
detailed models. Despite ignoring much of the complex dynamics of
more detailed systems, the Wilson-Cowan model still makes predictions
applicable to certain situations. For example, the W-C equations
predict limit cycle behavior which is reminiscent of oscillatory
activity measured in the real brain during epileptic seizures. No prior
knowledge of neuroscience will be assumed, and a treatment of the relevant
biology and other neuron models will be given for context.