  The parallel dynamics of the fully connected Blume-Emery-Griffiths neural
network model is studied for arbitrary temperature. By employing a
probabilistic signal-to-noise approach, a recursive scheme is found determining
the time evolution of the distribution of the local fields and, hence, the
evolution of the order parameters. A comparison of this approach is made with
the generating functional method, allowing to calculate any physical relevant
quantity as a function of time. Explicit analytic formula are given in both
methods for the first few time steps of the dynamics. Up to the third time step
the results are identical. Some arguments are presented why beyond the third
time step the results differ for certain values of the model parameters.
Furthermore, fixed-point equations are derived in the stationary limit.
Numerical simulations confirm our theoretical findings.
