Abstract
My purpose here is to describe a variety of wave-like phenomena which depend, for their existence, on the nonlinear nature of the underlying laws governing the dynamics of the medium. It will be assumed that these underlying laws can be expressed in terms of field equations of reaction-diffusion type, although some of the methods which have been developed for such systems have also been extended to other types of evolutionary laws. I make no claim that reaction-diffusion systems have a direct bearing on acceptable models for large scale neural nets. But they exhibit patterns and waves suggestive of phenomena expected in such nets, and it is hoped that their theory, which is moderately well developed, may provide a fruitful source of methods for the mathematical analysis of the neural models. Indeed, some parts of the theory, dealing for example with small-amplitude phenomena, have already been extended to the latter context (Ermentrout 1980; Ermentrout and Cowan 1979, 1980a, 1980b).
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Fife, P.C. (1982). Sigmoidal Systems and Layer Analysis. In: Amari, Si., Arbib, M.A. (eds) Competition and Cooperation in Neural Nets. Lecture Notes in Biomathematics, vol 45. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46466-9_2
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