  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.
