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 flocculation 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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Applied Mathematical Modelling, Elsevier, 2016, 40 (17-18), pp.7656-7677. 〈10.1016/j.apm.2016.03.028〉
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R. Fekih-Salem, A. Rapaport, T. Sari. Emergence of coexistence and limit cycles in the chemostat model with flocculation for a general class of functional responses. Applied Mathematical Modelling, Elsevier, 2016, 40 (17-18), pp.7656-7677. 〈10.1016/j.apm.2016.03.028〉. 〈hal-01294253〉

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