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• W2921741176 abstract "Understanding and exploiting the flocculation process is a major challenge in the mathematical theory of the chemostat. Here, we study a model of the chemostat involving the flocculating and deflocculating dynamics of planktonic and attached biomass competing for a single nutrient. In our study, the mortality (or maintenance) of species is taken into account and not neglected as in previous studies. The model is a three-dimensional system of ordinary differential equations. Using general monotonic functional responses, we give a complete analysis for the existence and local stability of all steady states. The theoretical analysis of the model involving the mortality is a difficult problem since the model is not reduced to a planar system as in the case where the dilution rates of the substrate and the biomass are equal. With the same dilution rates, it is well known that the model can have a positive steady state which is unique and stable as long as it exists. Without mortality, and different dilution rates, the system may have a multiplicity of positive steady states that can only appear or disappear through saddle-node or transcritical bifurcations. In contrast to the case without mortality, under the joined effect of flocculation and mortality, the model may undergo supercritical Hopf bifurcations or homoclinic bifurcations, with the appearance or the disappearance of a stable periodic orbit. Therefore coexistence may occur around a positive steady state and also around periodic oscillations." @default.
• W2921741176 created "2019-03-22" @default.
• W2921741176 creator A5022408069 @default.
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• W2921741176 date "2019-01-01" @default.
• W2921741176 modified "2023-09-27" @default.
• W2921741176 title "Properties of the Chemostat Model with Aggregated Biomass and Distinct Removal Rates" @default.
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• W2921741176 doi "https://doi.org/10.1137/18m1171801" @default.
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