Parallel dynamical systems over special digraph classes

Abstract

In a previous work, for parallel dynamical systems over digraphs corresponding to the simplest Boolean functions AND and OR, we proved that only fixed or eventually fixed points appear, as it occurs over undirected dependency graphs. Nevertheless, for general Boolean functions, it was shown that any period can appear, depending on the Boolean function that infers the global evolution operator of the system and on the structure of the dependency digraph. Motivated by these results, in this work, we analyse the orbit structure of parallel discrete dynamical systems over some special digraph classes.