A practical guide to analyzing discrete models

In this paper, we survey valuable results to analyze discrete models frequently appearing in social and natural sciences. We review some well-known results and tools to analyze these systems, trying to make them as practical as possible so that not only mathematicians but also physicists, economists or biologists can use them to explore their models. Applying these methods requires some basic knowledge of computational tools and basic programming. The reviewed topics vary from the local stability of equilibrium points to the characterization of topological and physically observable chaos.