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Operating diagram of a flocculation model in the chemostat

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-02160798
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Submitted on : Wednesday, August 5, 2020 - 10:38:24 PM
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Radhouane Fekih-Salem, Tewfik Sari. Operating diagram of a flocculation model in the chemostat. Revue Africaine de Recherche en Informatique et Mathématiques Appliquées, In press, CARI 2018, Volume 31 - 2019 - CARI 2018, pp.45-58. ⟨10.46298/arima.5593⟩. ⟨hal-02160798v3⟩

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