Sequential Dynamical Systems over Permutations

In this chapter we will give the formal definition of sequential dynamical systems (SDS). We will study SDS where the update order is a permutation of the vertex set of the underlying graph. In Chapter 7 we will extend our analysis to update orders that are words over the vertex set, that is, systems where vertices can be updated multiple times within a system update. Since most graphs in this chapter are combinatorial graphs (Section 3.1.1), we will, by abuse of terminology, refer to combinatorial graphs simply as graphs unless ambiguity may arise.