The emergence of the concepts of cellular automata (CA) (Wolfram, 1983, 1984, 1986) and Boolean (BN) network (Kauffman, 1969), between the end of the 60s and early 80s, for the formalization of computational processes and genetic regulation, respectively, was a first step in the development of modeling of evolutionary phenomena using networks. This type of modeling has been useful to solve various problems in other Sciences such as Chemistry (see Kier & Seybold, 2009; Kier, Seybold & Cheng 2005; Scalise & Schulman, 2015), Physics (see Chopard & Droz, 1998), Biology (see Deutsch & Dormann, 2004, Toroczkai & Güçlü, 2007), Ecology (see Dieckman, Law & Metz, 2000; Hofbauer & Sigmund, 2003; Hogeweg, 1988), even of Social Sciences like Psychology or Sociology (see Abraham, 2015; Kempe, Kleminberg & Tardos, 2005).
This new paradigm of modeling has evolved in recent years, giving rise to the concept of graph dynamical system (GDS), which generalizes the previous ones, since it contemplates that the relationships among elements of the system can be arbitrary. That is, the graph representing the relations among elements of the system, called dependency graph, could be arbitrary. In this generalization, the smallest units of aggregation of the phenomenon are called nodes (or vertices), in relation to their membership in the graph, relieving the term of cells in a CA and entities in a BN.
In this talk, we discuss some of the advances in the study of the periodic structure of a GDS when the evolution operator is a maxterm or minterm Boolean function.