Mathematical analysis of a three-tiered microbial food-web model with new input substrates

Sarra Nouaoura (1) , Nahla Abdellatif (1, 2) , Radhouane Fekih-Salem (1, 3) , Tewfik Sari (4)

1 LR-LAMSIN-ENIT - Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l'Ingénieur [Tunis]
2 ENSI - École Nationale des Sciences de l'Informatique [Manouba]
3 ISIMa - Institut Supérieur d’Informatique de Mahdia
4 UMR ITAP - Information – Technologies – Analyse Environnementale – Procédés Agricoles

In this work, we generalise a reduced anaerobic digestion model describing the anaerobic mineralisation of chlorophenol in a three-tiered food-web. The aim of the study is to take into account, the phenol and the hydrogen inflowing concentrations S ph,in and S H2,in , in addition of the chlorophenol input substrate. This case present interesting behaviours. We prove that the system can have eight types of steady-states, instead of only three types of steady-states as in the case S ph,in = S H2,in = 0. We give conditions for the existence and stability of the steady-states of the system without mortality terms. By means of operating diagrams, we illustrate the asymptotic behavior of the model.

Mots clés: Anaerobic digestion; Microbial ecology; Local stability; Operating diagram

Domaines: Systèmes dynamiques [math.DS]; Equations aux dérivées partielles [math.AP]; Biodiversité; Biotechnologies; Sciences de l'ingénieur [physics]

Sarra Nouaoura, Nahla Abdellatif, Radhouane Fekih-Salem, Tewfik Sari. Mathematical analysis of a three-tiered microbial food-web model with new input substrates. 9 ème édition du colloque Tendances dans les Applications Mathématiques en Tunisie Algérie et Maroc, Feb 2019, Tlemcen, Algeria. ⟨hal-02912850⟩