Bifurcation analysis of a chemostat model with a distributed delay

Shigui Ruan, Gail S K Wolkowicz

Research output: Contribution to journalArticle

57 Citations (Scopus)

Abstract

A chemostat model of a single species feeding on a limiting nutrient supplied at a constant rate is proposed. The model incorporates a general nutrient uptake function and a distributed delay. The delay indicates that the growth of the species depends on the past concentration of nutrient. Using the average time delay as a bifurcation parameter, it is proven that the model undergoes a sequence of Hopf bifurcations. Stability criteria for the bifurcating periodic solutions are derived. It is also found that the periodic solutions become unstable if the dilution rate is increased. Computer simulations illustrate the results.

Original languageEnglish (US)
Pages (from-to)786-812
Number of pages27
JournalJournal of Mathematical Analysis and Applications
Volume204
Issue number3
DOIs
StatePublished - Dec 15 1996
Externally publishedYes

Fingerprint

Chemostat Model
Chemostats
Distributed Delay
Bifurcation Analysis
Nutrients
Periodic Solution
Hopf bifurcation
Stability criteria
Rate Constant
Stability Criteria
Hopf Bifurcation
Dilution
Time Delay
Time delay
Computer Simulation
Bifurcation
Limiting
Unstable
Computer simulation
Model

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Bifurcation analysis of a chemostat model with a distributed delay. / Ruan, Shigui; Wolkowicz, Gail S K.

In: Journal of Mathematical Analysis and Applications, Vol. 204, No. 3, 15.12.1996, p. 786-812.

Research output: Contribution to journalArticle

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