Global asymptotic behavior of a chemostat model with two perfectly complementary resources and distributed delay

Bingtuan Li, Gail S K Wolkowicz, Yang Kuang

Research output: Contribution to journalArticle

39 Citations (Scopus)

Abstract

A model of the chemostat involving two species of microorganisms competing for two perfectly complementary, growth-limiting nutrients is considered. The model incorporates distributed time delay in the form of integral differential equations in order to describe the time involved in converting nutrient to biomass. The delays are included in the nutrient and species concentrations simultaneously. A general class of monotone increasing functions is used to describe nutrient uptake. Sufficient conditions based on biologically meaningful parameters in the model are given that predict competitive exclusion for certain parameter ranges and coexistence for others. We prove that the global asymptotic attractivity of steady states of the model is similar to that of the corresponding model without time delays. However, our results indicate that when the inherent delays are in fact large, ignoring them may result in incorrect predictions.

Original languageEnglish (US)
Pages (from-to)2058-2086
Number of pages29
JournalSIAM Journal on Applied Mathematics
Volume60
Issue number6
DOIs
StatePublished - May 2000

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Chemostat Model
Chemostats
Distributed Delay
Nutrients
Asymptotic Behavior
Resources
Time delay
Distributed Time Delay
Competitive Exclusion
Attractivity
Chemostat
Integral-differential Equation
Model
Monotone Function
Microorganisms
Increasing Functions
Biomass
Coexistence
Time Delay
Differential equations

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Global asymptotic behavior of a chemostat model with two perfectly complementary resources and distributed delay. / Li, Bingtuan; Wolkowicz, Gail S K; Kuang, Yang.

In: SIAM Journal on Applied Mathematics, Vol. 60, No. 6, 05.2000, p. 2058-2086.

Research output: Contribution to journalArticle

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