Equilibrium distribution of species among vessels of a gradostat: A singular perturbation approach

Hal Smith

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

The distribution of concentrations of two competing microbial species among the vessels of an n-vessel gradostat at equilibrium is studied for the standard mathematical model of the gradostat. As the equilibrium concentrations cannot be explicitly computed, a continuum limit, as the number of vessels becomes large, is considered which yields a singularly perturbed boundary value problem. Standard singular perturbation techniques yield information on equilibrium species concentration distributions which agree well with numerical calculations for even moderate values of n.

Original languageEnglish (US)
Pages (from-to)31-48
Number of pages18
JournalJournal Of Mathematical Biology
Volume30
Issue number1
DOIs
StatePublished - Oct 1991

Keywords

  • Coexistence equilibrium
  • Continuum limit
  • Singular perturbation

ASJC Scopus subject areas

  • Modeling and Simulation
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics

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