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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Competitive exclusion and coexistence
for competitive systems
on ordered Banach spaces


Authors: S. B. Hsu, H. L. Smith and Paul Waltman
Journal: Trans. Amer. Math. Soc. 348 (1996), 4083-4094
MSC (1991): Primary 47H07, 47H20; Secondary 92A15
MathSciNet review: 1373638
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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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Additional Information

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: http://dx.doi.org/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.\endgraf Research of the second author was supported by NSF Grant DMS 9300974.\endgraf Research of the third author was supported by NSF Grants DMS 9204490 and 9424592.\endgraf The third author wishes to express his thanks to Professor Peter Takáĉ for many stimulating discussions on ordered spaces and monotone operators.
Article copyright: © Copyright 1996 American Mathematical Society