The research was conducted by Wilson in the early 1970s while he was at the University of Chicago. In in 1972 and 1973, Wilson published two papers presenting the Wilson-Cowan equations as a simplified yet powerful description of the activity in neural networks containing both excitatory (activating) and inhibitory (suppressive) nerve cells.
The papers documented new criteria to describe neurons using their firing rates of electrical impulses per second rather than a much more detailed description of each neural impulse. This, in turn, permitted an extensive study of the variety of spatial and temporal patterns that could be formed by networks of interacting firing rate neurons. (Some of these patterns have provided explanations of the visual hallucinations produced by various drugs.) The success of the Wilson-Cowan firing rate description is exemplified by the fact that the two original papers have been cited more than 4,000 times in scientific literature.
One key behavior of excitatory-inhibitory networks demonstrated by the Wilson-Cowan equations was the generation of neural oscillations. As reported in ScienceDaily, a recent article in the journal Chaos: An Interdisciplinary Journal of Nonlinear Science by L. Alonso of Rockefeller University used the Wilson-Cowan equations to show that a very large number of distinct neural oscillations can be generated in these simple excitatory-inhibitory networks, and some of these are chaotic. These neural oscillations are thought to provide an explanation for the brain waves that can be recorded from the scalp and they may prove useful in understanding how the brain binds disparate information from different cortical areas in cognition.