research product . 2016

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

Fekih Salem, R.; Rapaport, A.; Sari, T.;
Open Access
  • Published: 01 Jan 2016
  • Publisher: Elsevier Inc.
  • Country: France
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 b...
Subjects
arXiv: Quantitative Biology::Populations and Evolution
free text keywords: AGRICULTURE, MODELE MATHEMATIQUE, CHEMOSTAT, FLOCULATION, HOPF BIFURCATION, MATHEMATICAL MODELS, FLOCCULATION
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