Transactions of the American Mathematical Society

Competitive exclusion and coexistence for competitive systems on ordered Banach spaces

Author(s): S. B. Hsu; H. L. Smith; Paul Waltman
Journal: Trans. Amer. Math. Soc. 348 (1996), 4083-4094.
MSC (1991): Primary 47H07, 47H20; Secondary 92A15
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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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Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 47H07, 47H20, 92A15

S. B. Hsu
Affiliation: Institute of Applied Mathematics, National Tsing Hua University, Hsinchu, Taiwan
Email: sbhsu@am.nthu.edu.tw

H. L. Smith
Affiliation: Department of Mathematics, Arizona State University, Tempe, Arizona 85287--1804
Email: halsmith@math.la.asu.edu

Paul Waltman
Affiliation: Department of Mathematics, Emory University, Atlanta, Georgia 30322
Email: waltman@mathcs.emory.edu

DOI: 10.1090/S0002-9947-96-01724-2
PII: S 0002-9947(96)01724-2
Keywords: Discrete order-preserving semigroup, order-preserving semiflow, positive fixed points, competitive systems, ejective fixed points
Received by editor(s): March 5, 1995
Additional Notes: Research of the first author was supported by the National Science Council, Republic of China.
Research of the second author was supported by NSF Grant DMS 9300974.
Research of the third author was supported by NSF Grants DMS 9204490 and 9424592.
The third author wishes to express his thanks to Professor Peter Takác for many stimulating discussions on ordered spaces and monotone operators.
Copyright of article: Copyright 1996, American Mathematical Society

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