### Abstract

A mathematical model of the exploitative competition between two microbial species in a general multivessel gradostat is considered. Sufficient conditions for the two species to coexist in the gradostat are derived using the theory of monotone dynamical systems and global bifurcation theory. Numerical computations required to verify the hypotheses of the coexistence results suggest that coexistence is more likely as the number of vessels increases.

Original language | English (US) |
---|---|

Pages (from-to) | 1451-1471 |

Number of pages | 21 |

Journal | SIAM Journal on Applied Mathematics |

Volume | 51 |

Issue number | 5 |

State | Published - Oct 1991 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*SIAM Journal on Applied Mathematics*,

*51*(5), 1451-1471.

**Competition in an n-vessel gradostat.** / Smith, Hal; Tang, Betty; Waltman, Paul.

Research output: Contribution to journal › Article

*SIAM Journal on Applied Mathematics*, vol. 51, no. 5, pp. 1451-1471.

}

TY - JOUR

T1 - Competition in an n-vessel gradostat

AU - Smith, Hal

AU - Tang, Betty

AU - Waltman, Paul

PY - 1991/10

Y1 - 1991/10

N2 - A mathematical model of the exploitative competition between two microbial species in a general multivessel gradostat is considered. Sufficient conditions for the two species to coexist in the gradostat are derived using the theory of monotone dynamical systems and global bifurcation theory. Numerical computations required to verify the hypotheses of the coexistence results suggest that coexistence is more likely as the number of vessels increases.

AB - A mathematical model of the exploitative competition between two microbial species in a general multivessel gradostat is considered. Sufficient conditions for the two species to coexist in the gradostat are derived using the theory of monotone dynamical systems and global bifurcation theory. Numerical computations required to verify the hypotheses of the coexistence results suggest that coexistence is more likely as the number of vessels increases.

UR - http://www.scopus.com/inward/record.url?scp=0026237726&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0026237726&partnerID=8YFLogxK

M3 - Article

VL - 51

SP - 1451

EP - 1471

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

SN - 0036-1399

IS - 5

ER -