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

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. © 2001 Academic Press.