Evolution of the Wilson-Cowan equations

Abstract

The Wilson-Cowan equations were developed to provide a simplified yet powerful description of neural network dynamics. As such, they embraced nonlinear dynamics, but in an interpretable form. Most importantly, it was the first mathematical formulation to emphasize the significance of interactions between excitatory and inhibitory neural populations, thereby incorporating both cooperation and competition. Subsequent research by many has documented the Wilson-Cowan significance in such diverse fields as visual hallucinations, memory, binocular rivalry, and epilepsy. The fact that these equations are still being used to elucidate a wide range of phenomena attests to their validity as a dynamical approximation to more detailed descriptions of complex neural computations.