### 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 language | English (US) |
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Pages (from-to) | 31-48 |

Number of pages | 18 |

Journal | Journal of Mathematical Biology |

Volume | 30 |

Issue number | 1 |

DOIs | |

State | Published - 1991 |

### Fingerprint

### 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.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Equilibrium distribution of species among vessels of a gradostat

T2 - A singular perturbation approach

AU - Smith, Hal

PY - 1991

Y1 - 1991

N2 - 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.

AB - 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.

KW - Coexistence equilibrium

KW - Continuum limit

KW - Singular perturbation

UR - http://www.scopus.com/inward/record.url?scp=0010428950&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0010428950&partnerID=8YFLogxK

U2 - 10.1007/BF00168005

DO - 10.1007/BF00168005

M3 - Article

VL - 30

SP - 31

EP - 48

JO - Journal of Mathematical Biology

JF - Journal of Mathematical Biology

SN - 0303-6812

IS - 1

ER -