Systèmes dynamiques finis

In many branches of current science, graphs, and dynamic processes on these graphs, are considered. Finite Dynamical Systems - also called Automata Networks - allow for an unmistakable representation of such processes. They are, for example, classical models for the dynamics of biological networks (neural and gene networks), social networks (epidemic diffusion), or communication networks (network coding).

The aim of this course is to give an introduction to these systems by focusing on the fundamental theoretical results that allow to deduce certain dynamical properties (number of fixed points, speed of convergence) according to the interaction graph only. The proof technics will be varied and will offer the opportunity to use classic results in Discrete Mathematics, essentially coming from Graph, Information and Set Theory.

• Lecture 1
• Lecture 2