Equilibrium distribution of species among vessels of a gradostat

A singular perturbation approach

Research output: Contribution to journalArticle

2 Citations (Scopus)

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 - 1991

Fingerprint

Equilibrium Distribution
Singular Perturbation
Vessel
mathematical models
biogeography
Perturbation techniques
Boundary value problems
Competing Species
Singularly Perturbed Boundary Value Problem
Theoretical Models
Continuum Limit
Perturbation Technique
Mathematical models
Numerical Calculation
Standard Model
methodology
Mathematical Model

Keywords

  • Coexistence equilibrium
  • Continuum limit
  • Singular perturbation

ASJC Scopus subject areas

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

Cite this

Equilibrium distribution of species among vessels of a gradostat : A singular perturbation approach. / Smith, Hal.

In: Journal of Mathematical Biology, Vol. 30, No. 1, 1991, p. 31-48.

Research output: Contribution to journalArticle

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