Scientific publications
Other affiliations: Centre National de la Recherche Scientifique · Université Joseph Fourier · Andrology Gerontechnology Inflammation Modelisation · Unité de Modélisation Mathématique et Informatique des Systèmes Complexes
Jacques Demongeot* (Corresponding author)
Other affiliations: Université Joseph Fourier · Andrology Gerontechnology Inflammation Modelisation
Comptes Rendus Mathématique
This Note deals with the mathematical notions of entropy and stability rate in interaction graphs of genetic networks, in the particular context of the genetic threshold Boolean random regulatory networks (getBrens). It is proved that in certain circumstances of particular connectance, the entropy of the invariant measure of the dynamical system can be considered both as a complexity and a stability index, by exploiting the link between these two notions, fundamental to characterize the resistance of a biological system against endogenous or exogenous perturbations, as in the case of the n -switches. Examples of biological networks are then given showing the practical interest of the mathematical notions of complexity and stability in the case of the control of the morphogenesis.
