  Using a probabilistic approach we study the parallel dynamics of fully
connected Q-Ising neural networks for arbitrary Q. A Lyapunov function is shown
to exist at zero temperature. A recursive scheme is set up to determine the
time evolution of the order parameters through the evolution of the
distribution of the local field. As an illustrative example, an explicit
analysis is carried out for the first three time steps. For the case of the Q=3
model these theoretical results are compared with extensive numerical
simulations. Finally, equilibrium fixed-point equations are derived and
compared with the thermodynamic approach based upon the replica-symmetric
mean-field approximation.
