Stable Coexistence and Bi-stability for Competitive Systems on Ordered Banach Spaces

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 classifi...

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Bibliographic Details
Published in:Journal of Differential Equations 2001-10, Vol.176 (1), p.195-222
Main Authors: Smith, H.L., Thieme, H.R.
Format: Article
Language:English
Subjects:
asymptotically autonomous semiflows
competitive systems
order-preserving semiflows
positive fixed points
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Summary: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.
ISSN:0022-0396
1090-2732
DOI:10.1006/jdeq.2001.3981