  The parallel dynamics of the fully connected Blume-Emery-Griffiths neural
network model is studied at zero temperature for arbitrary using a
probabilistic approach. A recursive scheme is found determining the complete
time evolution of the order parameters, taking into account all feedback
correlations. It is based upon the evolution of the distribution of the local
field, the structure of which is determined in detail. As an illustrative
example, explicit analytic formula are given for the first few time steps of
the dynamics. Furthermore, equilibrium fixed-point equations are derived and
compared with the thermodynamic approach. The analytic results find excellent
confirmation in extensive numerical simulations.
