Use of a neural field model to derive equilibrium values for the weights of recurrent synapses

Amari's field-theoretic model to neural networks is used in a situation in which the weights of the recurrent synapses vary with time according to a Hebbian law. Assuming equilibrium, an equation relating the weight of a recurrent synapse between two neurons to the area of the overlap between the receptive fields of the two neurons is derived. When all receptive fields are circular and have the same radius an equation is derived for the spatial variation of the weights of the recurrent synapses made by a neuron, showing a decay with distance.<
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