### Abstract

The dynamics of competitive maps and semiflows defined on the product of two cones in respective Banach spaces is studied. It is shown that exactly one of three outcomes is possible for two viable competitors. Either one or the other population becomes extinct while the surviving population approaches a steady state, or there exists a positive steady state representing the coexistence of both populations.

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

Pages (from-to) | 4083-4094 |

Number of pages | 12 |

Journal | Transactions of the American Mathematical Society |

Volume | 348 |

Issue number | 10 |

State | Published - 1996 |

### Fingerprint

### Keywords

- Competitive systems
- Discrete order-preserving semigroup
- Ejective fixed points
- Order-preserving semiflow
- Positive fixed points

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Transactions of the American Mathematical Society*,

*348*(10), 4083-4094.

**Competitive exclusion and coexistence for competitive systems on ordered danach spaces.** / Hsu, S. B.; Smith, Hal; Waltman, Paul.

Research output: Contribution to journal › Article

*Transactions of the American Mathematical Society*, vol. 348, no. 10, pp. 4083-4094.

}

TY - JOUR

T1 - Competitive exclusion and coexistence for competitive systems on ordered danach spaces

AU - Hsu, S. B.

AU - Smith, Hal

AU - Waltman, Paul

PY - 1996

Y1 - 1996

N2 - The dynamics of competitive maps and semiflows defined on the product of two cones in respective Banach spaces is studied. It is shown that exactly one of three outcomes is possible for two viable competitors. Either one or the other population becomes extinct while the surviving population approaches a steady state, or there exists a positive steady state representing the coexistence of both populations.

AB - The dynamics of competitive maps and semiflows defined on the product of two cones in respective Banach spaces is studied. It is shown that exactly one of three outcomes is possible for two viable competitors. Either one or the other population becomes extinct while the surviving population approaches a steady state, or there exists a positive steady state representing the coexistence of both populations.

KW - Competitive systems

KW - Discrete order-preserving semigroup

KW - Ejective fixed points

KW - Order-preserving semiflow

KW - Positive fixed points

UR - http://www.scopus.com/inward/record.url?scp=21444453892&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21444453892&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:21444453892

VL - 348

SP - 4083

EP - 4094

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 10

ER -