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 | References | Similar Articles | Additional Information

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

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