Competitive exclusion and coexistence for competitive systems on ordered Banach spaces

Hsu, S.; Smith, H.; Waltman, Paul

doi:10.1090/S0002-9947-96-01724-2

Competitive exclusion and coexistence for competitive systems on ordered Banach spaces
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by S. B. Hsu, H. L. Smith and Paul Waltman

Trans. Amer. Math. Soc. 348 (1996), 4083-4094

DOI: https://doi.org/10.1090/S0002-9947-96-01724-2

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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.

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