Hopfield model with self-coupling.

We have studied analytically the retrieval performance of a Hopfield model in the presence of self-coupling in the synaptic matrix. We find, contrary to expectations from some earlier studies based on the counting of fixed points, that negative self-coupling causes deterioration in the retrieval performance of the network. On the other hand, it is possible to enhance the retrieval performance by having a positive self-coupling of appropriate magnitude.