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.