### 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) |
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Pages (from-to) | 4083-4094 |

Number of pages | 12 |

Journal | Transactions of the American Mathematical Society |

Volume | 348 |

Issue number | 10 |

State | Published - Dec 1 1996 |

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

## Fingerprint Dive into the research topics of 'Competitive exclusion and coexistence for competitive systems on ordered danach spaces'. Together they form a unique fingerprint.

## Cite this

Hsu, S. B., Smith, H., & Waltman, P. (1996). Competitive exclusion and coexistence for competitive systems on ordered danach spaces.

*Transactions of the American Mathematical Society*,*348*(10), 4083-4094.