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

41 Scopus citations

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 1 2000

ASJC Scopus subject areas

  • Applied Mathematics

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