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The global stability of a system modeling a community with limited competition
Author(s):
J.
F.
Jiang
Journal:
Proc. Amer. Math. Soc.
125
(1997),
1381-1389.
MSC (1991):
Primary 34C11;
Secondary 92A15
MathSciNet review:
1376765
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Abstract:
In this paper the global behavior of solutions of a class of ordinary differential equations modelling a biological community of species is determined. The community consists of two competing subcommunities each of which has the property that each pair of species of the subcommunity interact in a mutually beneficial manner. Sufficient conditions are presented that the two subcommunities can coexist in a globally asymptotically stable steady state.
References:
- 1.
- H. L. Smith, Competing subcommunities of mutualists and a generalized Kamke theorem, SIAM J. Appl. Math., 46 (1986), 856-873. MR 87i:92047
- 2.
- H. L. Smith, On the asymptotic behavior of a class of deterministic models of cooperating speies, SIAM J. Appl. Anal., 46 (1986), 368-375. MR 87j:34066
- 3.
- M. W. Hirsch, Systems of differential equations which are competitive or cooperative I. Limit sets, SIAM J. Math. Anal., 13 (1982), 167-179. MR 83i:58081
- 4.
- M. W. Hirsch, Systems of differential equations which are competitive or cooperative II. Convergence almost everywhere, SIAM J. Math. Anal., 16 (1985), 423-439. MR 87a:58137
- 5.
- J. F. Selgrade, Asymptotic behavior of solutions to single loop positive feedback systems, J. Differential Equations, 38 (1980), 80-103. MR 82a:34038
- 6.
- W. A. Coppel, Stability and Asymptotic Behavior of Ordinary Differential Equations, D. C. Heath, Boston, 1965.
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Additional Information:
J.
F.
Jiang
Affiliation:
Department of Mathematics, University of Science and Technology of China, Hefei, China
DOI:
10.1090/S0002-9939-97-03805-7
PII:
S 0002-9939(97)03805-7
Keywords:
Competition,
mutualism,
coexistence,
global stability
Received by editor(s):
November 8, 1995
Additional Notes:
This research was supported by the National Science Foundation of China.
Communicated by:
Hal L. Smith
Copyright of article:
Copyright
1997,
American Mathematical Society
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