ASYMPTOTIC BEHAVIOR OF A CHEMOSTAT MODEL WITH CONSTANT RECYCLE SLUDGE CONCENTRATION

Amine Hamra (1) , Karim Yadi (1)

1 LSDA - Laboratoire Systèmes Dynamiques et Applications

In this work, we study a several species aerobic chemostat model with constant recycle sludge concentration in continuous culture. We reduce the number of parameters by considering a dimensionless model. First, the existence of a global positive uniform attractor for the model with dierent removal rates is proved using the theory of dissipative dynamical systems. Hence, we investigate the asymptotic behavior of the model under small perturbations using methods of singular perturbation theory and we prove that, in the case of two species in competition, the unique equilibrium which is positive is globally asymptotically stable. Finally, we establish the link between the open problem of the chemostat with dierent removal rates and monotone functional responses, and our model when two species compete on the same nutrient. We give some numerical simulations to illustrate the results.

Domaines: Systèmes dynamiques [math.DS]

Amine Hamra, Karim Yadi. ASYMPTOTIC BEHAVIOR OF A CHEMOSTAT MODEL WITH CONSTANT RECYCLE SLUDGE CONCENTRATION. 2016. ⟨hal-01320600⟩