Abstract
In this paper a simple two-layer neural network's model, similar to that studied by D. Amit and N. Brunel,11 is investigated in the frames of the mean-field approximation. The distributions of the local fields are analytically derived and compared to those obtained in Ref. 11. The dynamic properties are discussed and the basin of attraction in some parametric space is found. A procedure for driving the system into a basin of attraction by using a regulation imposed on the network is proposed. The effect of outer stimulus is shown to have a destructive influence on the attractor, forcing the latter to disappear if the distribution of the stimulus has high enough variance or if the stimulus has a spatial structure with sufficient contrast. The techniques, used in this paper, for obtaining the analytical results can be applied to more complex topologies of linked recurrent neural networks.
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