An introduction to the theory of Finite Dynamical Systems

We are interested in complex networks of interacting entities (such as genes, neurons, persons, computers, etc.), where each entity has a finitely valued state and a function which updates the value of the state. Since entities influence each other, this local update function depends on the states of some of the entities. Such a network is called a Finite Dynamical System (FDS). The main problem when studying an FDS is to determine its dynamics given a limited knowledge of it; for instance, we may only know the interaction graph, i.e. which entities influence each other. In this talk, we will review some of the seminal results in the theory of FDSs and focus on the maximisation of images and periodic points for a given interaction graph.