Authors: Radhouane Fekih-Salem ^1,2; Tewfik Sari ³

• 1 Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l'Ingénieur [Tunis]
• 2 Institut Supérieur d’Informatique de Mahdia
• 3 Information – Technologies – Analyse Environnementale – Procédés Agricoles

The objective of this study is to analyze a model of the chemostat involving the attachment and detachment dynamics of planktonic and aggregated biomass in the presence of a single resource. Considering the mortality of species, we give a complete analysis for the existence and local stability of all steady states for general monotonic growth rates. The model exhibits a rich set of behaviors with a multiplicity of coexistence steady states, bi-stability, and occurrence of stable limit cycles. Moreover, we determine the operating diagram which depicts the asymptotic behavior of the system with respect to control parameters. It shows the emergence of a bi-stability region through a saddle-node bifurcation and the occurrence of coexistence region through a transcritical bifurcation. Finally, we illustrate the importance of the mortality on the destabilization of the microbial ecosystem by promoting the washout of species.