Parallel dynamics of fully connected Q-Ising neural networks

摘要

Using a probabilistic approach we study the parallel dynamics of fullyconnected Q-Ising neural networks for arbitrary Q. A Lyapunov function is shownto exist at zero temperature. A recursive scheme is set up to determine thetime evolution of the order parameters through the evolution of thedistribution of the local field. As an illustrative example, an explicitanalysis is carried out for the first three time steps. For the case of the Q=3model these theoretical results are compared with extensive numericalsimulations. Finally, equilibrium fixed-point equations are derived andcompared with the thermodynamic approach based upon the replica-symmetricmean-field approximation.