Cyclic automata networks on finite graphs

Abstract

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 important to point out that there exist non-polynomial periods eΩ(√ |V| ), where V denotes the number of sites in the graph. To obtain these results we introduce some mathematical tool as continuity, firing paths, jump and efficiency, which are interesting by themselves because they give a strong mathematical framework to study such discrete dynamical systems.