9.1. Introduction

Several phenomena are modeled by what is commonly called spatio-temporal dynamics. These are processes for which information localization in space plays a specific role. Each of the disciplines like economy, sociology, ecology, etc. has the opportunity to consider or not this type of information. For example, since the end of the 19 ^th century and with the works of Von Th nen, we have seen the emergence of spatial economy, where the localization of socio-economic players is part of the models. Many other examples will be given throughout this chapter, but we can already envision networks of cities, forests considered as tree networks, or even a eukaryotic cell whose operation is based on a compartmentalization of biochemical processes. We could imagine that space is simply one more variable that we would need to consider, but "things" are a little bit more complicated: space plays a particular role in modeling.

Modeling a natural phenomenon often comes down to formalizing, in a specific and simplified language, the mathematics of what we usually describe in discursive and more complex form. The art of modeling is finding the best compromise between the simplicity of the mathematical form and the respect of prominent and identity elements of the phenomenon studied. This compromise wins the joint support of mathematicians and specialists of a natural discipline with respect to the relevance of a mathematical language based approach. However, there is a problem with reaching a compromise from a mathematical language:...