Conditions for the emergence of spatial asymmetric states in attractor neural network

In this paper we show that during the retrieval process in a binary symmetric Hebb neural network, spatial localized states can be observed when the connectivity of the network is distance-dependent and when a constraint on the activity of the network is imposed, which forces different levels of activity in the retrieval and learning states. This asymmetry in the activity during the retrieval and learning is found to be sufficient condition in order to observe spatial localized states. The result is confirmed analytically and by simulation.