RETRIEVAL AND CHAOS IN LAYERED Q-ISING NEURAL NETWORKS

Using a probabilistic approach, we study the parallel dynamics of the Q-Ising layered networks for arbitrary Q. By introducing auxiliary the rmal fields, we express the stochastic dynamics within the pin functio n formulation of the deterministic dynamics. Evolution equations are d erived for arbitrary Q at both zero and finite temperatures. An explic it analysis of the fixed-point equations is carried out for both Q = 3 and Q --> infinity. The retrieval properties are discussed in terms o f the gain parameter, the storage capacity, and the temperature. Using the time evolution of the distance between two network configurations , we investigate the possibility of microscopic chaos. Chaotic behavio r is always present for arbitrary finite Q. However, in the limit Q -- > infinity the existence of chaos depends on the parameters of the sys tem.