Associative memory on a small-world neural network

We study a model of associative memory based on a neural network with small-world structure. The efficacy of the network to retrieve one of the stored patterns exhibits a phase transition at a finite value of the disorder. The more ordered networks are unable to recover the patterns, and are always attracted to non-symmetric mixture states. Besides, for a range of the number of stored patterns, the efficacy has a maximum at an intermediate value of the disorder. We also give a statistical characterization of the spurious attractors for all values of the disorder of the network.Received: 12 January 2004, Published online: 28 May 2004PACS: 84.35. + i Neural networks - 89.75.Hc Networks and genealogical trees - 87.18.Sn Neural networks