, Volume 25, Issue 1, pp 111-120

A field theory of neural nets: I: Derivation of field equations

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Abstract

A model is described in which neural activity is represented by a field quantity ϕ, with the neurons as the sources of ϕ. It is shown that, with certain physically realistic assumptions, ϕ satisfies a moderately nonlinear differential equation. It is also found that this equation is isotropic and of second order if and only if the neuronal connectivity has a dependence on distance,p, of the formp −1 e −1/2βp .