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 PDF
- Trans. Amer. Math. Soc. 348 (1996), 4083-4094 Request permission
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.References
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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
- 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 Takáĉ for many stimulating discussions on ordered spaces and monotone operators.
- © Copyright 1996 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 348 (1996), 4083-4094
- MSC (1991): Primary 47H07, 47H20; Secondary 92A15
- DOI: https://doi.org/10.1090/S0002-9947-96-01724-2
- MathSciNet review: 1373638