Comparative analysis of two chemostat models including substrate and biomass inhibitions

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We consider the acetogenesis and hydrogenotrophic methanogenesis phases of the anaerobic digestion model and we include the inhibition of methanogenics, first by volatile fatty acids (VFAs) then by acetogenics. We investigate mathematically the dynamics of two chemostat models described by systems of four nonlinear ordinary differential equations. We established the conditions of existence and stability of equilibrium points in each of the models with respect to the dilution rate. The operating diagrams allowed to reveal the similarities and the differences between regions of stability of the two models and to present the consequent transcritical bifurcations between boundary and positive equilibrium. Models are equivalent for low inlet substrate concentration and significantly different for high concentration. When inhibition is by acetogens and for high concentrations of inlet substrate, the upstream species tends to eliminate the downstream species from the vessel.