Synchronous versus sequential updating in the three-state Ising neural network with variable dilution

The Q=3-state Ising neural network with synchronous updating and variable dilution is discussed starting from the appropriate Hamiltonians. The thermodynamic and retrieval properties are examined using replica mean-field theory. The appearance and properties of two-cycles are discussed. Capacity-temperature phase diagrams are derived for several values of the pattern activity and different gradations of dilution, and the information content is calculated. It is found that the asymptotic behaviour is rather similar to that for sequential updating. The retrieval region is enhanced marginally, but the spin-glass region is visibly enlarged. Only the presence of self-coupling can enlarge the retrieval region substantially. The dynamics of the network is studied for general Q and both synchronous and sequential updating using an extension of the generating function technique. The differences with the signal-to-noise approach are outlined. Typical flow diagrams for the Q=3 overlap order parameter are presented.