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.
KeywordsPhase Space Symmetric Function Periodic Point Cayley Graph Vertex Function
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