Stable coexistence and bi-stability for competitive systems on ordered Banach spaces

Hal Smith; Horst Thieme

doi:10.1006/jdeq.2001.3981

Stable coexistence and bi-stability for competitive systems on ordered Banach spaces

Hal Smith, Horst Thieme

Mathematical and Statistical Sciences, School of (SoMSS)

Research output: Contribution to journal › Article › peer-review

40 Scopus citations

Abstract

Autonomous and asymptotically autonomous semiflows modeling two species competition are studied which are strongly order preserving on a convex subset of a Banach space with competitive order. Conditions are derived for stable coexistence, bi-stability, and competitive exclusion. A complete classification of all possible outcomes is obtained in case that there is at most one positive steady state representing coexistence of both species.

Original language	English (US)
Pages (from-to)	195-222
Number of pages	28
Journal	Journal of Differential Equations
Volume	176
Issue number	1
DOIs	https://doi.org/10.1006/jdeq.2001.3981
State	Published - Oct 10 2001

Keywords

Asymptotically autonomous semiflows
Competitive systems
Order-preserving semiflows
Positive fixed points

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1006/jdeq.2001.3981

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abstract = "Autonomous and asymptotically autonomous semiflows modeling two species competition are studied which are strongly order preserving on a convex subset of a Banach space with competitive order. Conditions are derived for stable coexistence, bi-stability, and competitive exclusion. A complete classification of all possible outcomes is obtained in case that there is at most one positive steady state representing coexistence of both species.",

keywords = "Asymptotically autonomous semiflows, Competitive systems, Order-preserving semiflows, Positive fixed points",

author = "Hal Smith and Horst Thieme",

note = "Funding Information: 1Research of the first author supported by NSF Grant DMS 9700910. 2Research of the second author supported by NSF Grant DMS 9706787.",

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AU - Thieme, Horst

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N2 - Autonomous and asymptotically autonomous semiflows modeling two species competition are studied which are strongly order preserving on a convex subset of a Banach space with competitive order. Conditions are derived for stable coexistence, bi-stability, and competitive exclusion. A complete classification of all possible outcomes is obtained in case that there is at most one positive steady state representing coexistence of both species.

AB - Autonomous and asymptotically autonomous semiflows modeling two species competition are studied which are strongly order preserving on a convex subset of a Banach space with competitive order. Conditions are derived for stable coexistence, bi-stability, and competitive exclusion. A complete classification of all possible outcomes is obtained in case that there is at most one positive steady state representing coexistence of both species.

KW - Asymptotically autonomous semiflows

KW - Competitive systems

KW - Order-preserving semiflows

KW - Positive fixed points

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Stable coexistence and bi-stability for competitive systems on ordered Banach spaces

Abstract

Keywords

ASJC Scopus subject areas

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