de Mathématiques de Luminy
Remy Elisabeth, Ruet Paul.
On differentiation and homeostatic behaviours of Boolean dynamical systems.
We study rules proposed by the biologist R. Thomas relating the structure of a concurrent system of interacting genes (represented by a signed directed graph called a regulatory graph) with its dynamical properties. We prove that the results in  are stable under projection, and this enables us to relax the assumptions under which they are valid. More precisely, we relate here the presence of a positive (resp. negative) circuit in a regulatory graph to a more general form of biological differentiation (resp. of homeostasis).