Journal of Statistical Physics, Vol. 74, Nos. 3/4, 1994. p. 583-606.
Using a probabilistic approach, we study the parallel dynamics of the Q-Ising layered networks for arbitrary Q. By introducing auxiliary thermal fields, we express the stochastic dynamics within the gain function formulation of the deterministic dynamics. Evolution equations are derived for arbitrary Q at both zero and finite temperatures. An explicit analysis of the fixed-point equations is carried out for both Q = 3 and Q ->oo.co. The retrieval properties are discussed in terms of 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 behavior is always present for arbitrary finite Q. However, in the limit Q->oo oo the existence of chaos depends on the parameters of the system.