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Competitive exclusion and coexistence for competitive systems on ordered Banach spaces |
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| Authors: | S B Hsu H L Smith Paul Waltman |
| Institution: | Institute of Applied Mathematics, National Tsing Hua University, Hsinchu, Taiwan ; Department of Mathematics, Arizona State University, Tempe, Arizona 85287--1804 ; Department of Mathematics, Emory University, Atlanta, Georgia 30322 |
| 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. |
| Keywords: | Discrete order-preserving semigroup order-preserving semiflow positive fixed points competitive systems ejective fixed points |
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