### Abstract

A chemostat model of n species of microorganisms competing for two perfectly complementary, growth-limiting nutrients is considered. Sufficient conditions are given for there to be a single winning species and for two species to coexist, driving the others to extinction. In the case when n = 3, it is shown that every solution converges to one of the single-species or two-species steady states, and hence the dynamics of the model is completely-determined. The results generalize those of Hsu, Cheng, and Hubbell [SIAM J. Appl. Math., 41 (1981), pp. 422-444] as well as Butler and Wolkowicz [Math. Biosci., 83 (1987), pp. 1-48] who considered two species.

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

Pages (from-to) | 336-366 |

Number of pages | 31 |

Journal | SIAM Journal on Applied Mathematics |

Volume | 62 |

Issue number | 1 |

State | Published - 2001 |

Externally published | Yes |

### Fingerprint

### Keywords

- Chemostat
- Coexistence
- Competition for two resources
- Competitive exclusion principle
- Competitive system
- Global asymptotic behavior

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*SIAM Journal on Applied Mathematics*,

*62*(1), 336-366.

**How many species can two essential resources support?** / Li, Bingtuan; Smith, Hal.

Research output: Contribution to journal › Article

*SIAM Journal on Applied Mathematics*, vol. 62, no. 1, pp. 336-366.

}

TY - JOUR

T1 - How many species can two essential resources support?

AU - Li, Bingtuan

AU - Smith, Hal

PY - 2001

Y1 - 2001

N2 - A chemostat model of n species of microorganisms competing for two perfectly complementary, growth-limiting nutrients is considered. Sufficient conditions are given for there to be a single winning species and for two species to coexist, driving the others to extinction. In the case when n = 3, it is shown that every solution converges to one of the single-species or two-species steady states, and hence the dynamics of the model is completely-determined. The results generalize those of Hsu, Cheng, and Hubbell [SIAM J. Appl. Math., 41 (1981), pp. 422-444] as well as Butler and Wolkowicz [Math. Biosci., 83 (1987), pp. 1-48] who considered two species.

AB - A chemostat model of n species of microorganisms competing for two perfectly complementary, growth-limiting nutrients is considered. Sufficient conditions are given for there to be a single winning species and for two species to coexist, driving the others to extinction. In the case when n = 3, it is shown that every solution converges to one of the single-species or two-species steady states, and hence the dynamics of the model is completely-determined. The results generalize those of Hsu, Cheng, and Hubbell [SIAM J. Appl. Math., 41 (1981), pp. 422-444] as well as Butler and Wolkowicz [Math. Biosci., 83 (1987), pp. 1-48] who considered two species.

KW - Chemostat

KW - Coexistence

KW - Competition for two resources

KW - Competitive exclusion principle

KW - Competitive system

KW - Global asymptotic behavior

UR - http://www.scopus.com/inward/record.url?scp=0036228880&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036228880&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0036228880

VL - 62

SP - 336

EP - 366

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

SN - 0036-1399

IS - 1

ER -