Retrieval and chaos in layeredQ-Ising neural networks

Using a probabilistic approach, we study the parallel dynamics of theQ-Ising layered networks for arbitraryQ. By introducing auxiliary thermal fields, we express the stochastic dynamics within the gain function formulation of the deterministic dynamics. Evolution equations are derived for arbitraryQ at both zero and finite temperatures. An explicit analysis of the fixed-point equations is carried out for bothQ=3 andQ. 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 finiteQ. However, in the limitQ the existence of chaos depends on the parameters of the system.