Dynamic behavior of cyclic automata networks

We study the principal dynamical aspects of the cyclic automata on finite graphs. We give bounds in the transient time and periodicity depending essentially on the graph structure. It is shown that there exist non-polynomial periods e^{Ω(√ |V|)}, where |V| denotes the number of sites in the graph. To obtain these results we introduce some mathematical tools as continuity, firing paths, jumps and efficiency, which are interesting by themselves because they give a strong mathematical framework to study such discrete dynamical systems.