Modeling and analyzing the long-time behavior of random chemostat models

Tomas Caraballo (1) , María J Garrido-Atienza (1) , Javier López-De-La-Cruz (1) , Alain Rapaport (2)

1 EDAN - Departamento de Ecuaciones Differenciales y Analysis numérico [Sevilla]
2 MISTEA - Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie

In this work, the simplest chemostat model, perturbing the input flow by means of the Ornstein-Uhlenbeck process, will be presented. We will make use of the techniques involved in the theory of random dynamical systems to provide some results concerning the existence and uniqueness of global solution just like the existence and uniqueness of random pullback attractor, which will allow us to obtain detailed information about the long-time behavior of our model. In particular, some conditions on the different parameters of our model will be given to ensure the persistence of the microbial biomass. Finally, several numerical simulations comparing the results with the ones obtained when perturbing the input flow by using the standard Wiener process will be also shown.

Mots clés: Chemostat model; brownian motion; standard Wiener process; Ornstein-Uhlenbeck process; random attractor; input flow; random dynamical system

Domaines: Systèmes dynamiques [math.DS]; Biotechnologies

Tomas Caraballo, María J Garrido-Atienza, Javier López-De-La-Cruz, Alain Rapaport. Modeling and analyzing the long-time behavior of random chemostat models. IFAC International Conference on Mathematical Modelling - MATHMOD 2018, Feb 2018, Vienna, Austria. IFAC, pp.37-38, 2018, Mathematical Modelling - 9th MATHMOD 2018. ⟨10.11128/arep.55.a55229⟩. ⟨hal-01716603⟩