Robustness of Dynamical Systems Attraction Basins Against State Perturbations: Theoretical Protocol and Application in Systems Biology

This paper aims at giving a general and precise method to achieve a good understanding of discrete dynamical systems by focusing on their attraction basins. This work is the result of a previous one which has permitted to show that the structural changes introduced by fixed boundary conditions on regulatory networks could directly and strongly influence the properties of their attraction basins. In this paper, we give an exhaustive stochastic study protocol to understand what happens on attraction basins of dynamical systems when the latter are subjected to state perturbations. Then, we give an application of this protocol by giving the results obtained on a specific system which is a model of the Arabidopsis thaliana flowerpsilas morphogenesis, depending on a specific boundary condition.