Mathematical analysis of a two-tiered microbial food-web model for the anaerobic digestion process

Mathematical analysis of a two-tiered microbial food-web model for the anaerobic digestion process

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In this research paper, we presented a four-dimensional mathematical system modeling the anaerobic mineralization of phenol in a two-step microbial food-web.The inflowing concentrations of the hydrogen and the phenol are considered in our model.We considered the case of general class of turbo air m3f24-1-n nonlinear growth kinetics, instead of Monod kinetics.Due to some conservative relations, the proposed model was reduced to a two-dimensional system.The stability of the steady states was carried out.

Based on the species growth rates and the three main operating parameters of the model, represented by the dilution rate and input concentrations of here the phenol and the hydrogen, we showed that the system can have up to four steady states.We gave the necessary and sufficient conditions ensuring the existence and the stability for each feasible equilibrium state.We showed that in specific cases, the positive steady state exists and is stable.We gave numerical simulations validating the obtained results.