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

•A flocculation model of two microbial species in a chemostat is presented.•Flocculation mechanism and substrate inhibition can lead to oscillations.•The bifurcation analysis is performed according to control parameters.•We show the occurrence of limit cycles through Hopf bifurcations. We consider a...

Full description

Saved in:
Bibliographic Details
Published in:Applied mathematical modelling 2016-09, Vol.40 (17-18), p.7656-7677
Main Authors: Fekih-Salem, R., Rapaport, A., Sari, T.
Format: Article
Language:English
Subjects:
Bi-stability
Chemostat
Coexistence
Flocculation
Hopf bifurcation
Limit cycle
Mathematics
Optimization and Control
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:•A flocculation model of two microbial species in a chemostat is presented.•Flocculation mechanism and substrate inhibition can lead to oscillations.•The bifurcation analysis is performed according to control parameters.•We show the occurrence of limit cycles through Hopf bifurcations. 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.
ISSN:0307-904X
1872-8480
DOI:10.1016/j.apm.2016.03.028