DYNAMIC BEHAVIOR OF CYCLIC AUTOMATA NETWORKS

We study the principal dynamical aspects of the cyclic automata on fin ite graphs. We give bounds in the transient time and periodicity depen ding essentially on the graph structure. It is shown that there exist non-polynomial periods e(Omega)(root(\V\)), where \V\ denotes the numb er of sites in the graph. To obtain these results we introduce some ma thematical tools as continuity, firing paths, jumps and efficiency, wh ich are interesting by themselves because they give a strong mathemati cal framework to study such discrete dynamical systems.