Stability analysis of mathematical model of competition in a chain of chemostats in series with delay

•We construct a chain of two interconnected chemostats, assuming competitive exclusion.•The first chemostat cultivates the unadvantaged competitor. The second cultivates two ones.•The output of the first chemostat is the input of the second one.•We carry out a stability analysis by constructing a Ly...

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Bibliographic Details
Published inApplied Mathematical Modelling Vol. 76; pp. 311 - 329
Main Authors Mazenc, Frédéric, Niculescu, Silviu–Iulian, Robledo, Gonzalo
Format Journal Article
LanguageEnglish
Published New York Elsevier Inc 01.12.2019
Elsevier BV
Elsevier
Subjects
Automatic Control Engineering
Chains
Chemostat
Competition
Competitive exclusion
Computer Science
Delay
Delay equations
Differential equations
Lyapunov functions
Mathematical models
Microorganisms
Nonlinear systems
Stability analysis
Competitive exclusion
Lyapunov functions
Chemostat
Delay equations
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Summary:•We construct a chain of two interconnected chemostats, assuming competitive exclusion.•The first chemostat cultivates the unadvantaged competitor. The second cultivates two ones.•The output of the first chemostat is the input of the second one.•We carry out a stability analysis by constructing a Lyapunov functional. We study a nonlinear system of differential delay equations describing a model of a chain of two chemostats, where one contains two microbial species in competition for a single limiting nutrient and receives an external input of the less advantaged competitor, which is cultivated in an external chemostat. We obtain sufficient conditions ensuring coexistence of all the species in competition which consist in upper delay bounds.
ISSN:0307-904X
1088-8691
0307-904X
1872-8480
DOI:10.1016/j.apm.2019.06.006