The synchronous BEG neural network with variable dilution
  The thermodynamic and retrieval properties of the Blume-Emery-Griffiths neural network with synchronous updating and variable dilution are studied using replica mean-field theory. Several forms of dilution are allowed by pruning the different types of couplings present in the Hamiltonian. The appearance and properties of two-cycles are discussed. Capacity-temperature phase diagrams are derived for several values of the pattern activity. The results are compared with those for sequential updating. The effect of self-coupling is studied. Furthermore, the optimal combination of dilution parameters giving the largest critical capacity is obtained. 
D. Boll\'e and J. Busquets Blanco