Emergence of coexistence and limit cycles in the chemostat model with flocculation for a general class of functional responses

Abstract : We consider a model of two microbial species in a chemostat competing for a single-resource, involving the floc-culation of the most competitive species which is present in two forms: isolated and attached. We first show that the model with one species and a non-monotonic growth rate of isolated bacteria may exhibit bi-stability and allows the appearance of unstable limit cycles through a sub-critical Hopf bifurcations due to the joined effect of inhibition and flocculation. We then show that the model with two species presents an even richer set of possible behaviors: coexistence, bi-stability and occurrence of stable limit cycles through a super-critical Hopf bifurcations. All these features cannot occur in the classical chemostat model, where generically at most one competitor can survive on a single resource.
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https://hal.inria.fr/hal-01121201
Contributeur : Radhouane Fekih-Salem <>
Soumis le : vendredi 27 février 2015 - 17:05:56
Dernière modification le : dimanche 4 mars 2018 - 11:54:01
Document(s) archivé(s) le : jeudi 28 mai 2015 - 10:40:31

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Radhouane Fekih-Salem, Alain Rapaport, Tewfik Sari. Emergence of coexistence and limit cycles in the chemostat model with flocculation for a general class of functional responses. 2015. 〈hal-01121201〉

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