Nonlinear equations of reaction-diffusion type for neural populations (Q2266677)

The \textit{H. R. Wilson} and \textit{J. D. Cowan} integrodifferential model [Kybernetik 13, 55-80 (1973; Zbl 0281.92003)] for spatially interacting excitatory and inhibitory neural populations is reduced in this paper by means of some simplifying approximations to partial differential equations of the reaction-diffusion type. According to the relative importance of parameters a variety of equations have been derived. Basing on certain bifurcation properties of the integrodifferential model, the applicativity of the simplified one is discussed. The latter may prove useful in the interpretation of certain EEG phenomena.