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The necessary and sufficient conditions for the global stability of type- Lotka-Volterra system
Author(s):
Tu
Caifeng;
Jiang
Jifa
Journal:
Proc. Amer. Math. Soc.
127
(1999),
3181-3186.
MSC (1991):
Primary 34C11, 92A15
Posted:
July 8, 1999
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Abstract:
This paper provides necessary and sufficient conditions for the type- Lotka-Volterra system to have a globally asymptotically stable positive steady state. The generalization of such a result is given.
References:
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- Y. Takeuchi, and N. Adachi, The existence of globally stable equilibria of ecosystems of the generalized Volterra type, J. Math. Biol. 10 (1980), 401-415. MR 82e:92048
- [2]
- H. L. Smith, Competing subcommunities of mutualists and a generalized Kamke Theorem, SIAM J. Appl. Math. 46 (1986), 856-873. MR 87i:92047
- [3]
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- 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]
- Tu Caifeng and Jiang Jifa, The coexistence of a community of species with limited competition, J. Math. Anal. Appl. 217 (1998), 233-245. MR 99c:92061
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- J. F. Selgrade, Asymptotic behavior of solutions to single loop positive feedlack systems, J. Differential Equations 38 (1980), 80-103. MR 82a:34038
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- Tu Caifeng and Jiang Jifa, Global stability and permanence for a class of Type K monotone system, submitted to SIAM J. Math. Anal..
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Additional Information:
Tu
Caifeng
Affiliation:
Department of Mathematics, The University of Science and Technology of China, Hefei, People's Republic of China
Email:
jiangjf@math.ustc.edu.cn
Jiang
Jifa
Affiliation:
Department of Mathematics, The University of Science and Technology of China, Hefei, People's Republic of China
DOI:
10.1090/S0002-9939-99-05077-7
PII:
S 0002-9939(99)05077-7
Keywords:
Lotka--Volterra system,
steady state,
global stability
Received by editor(s):
January 7, 1998
Posted:
July 8, 1999
Additional Notes:
This project was supported by the National Natural Science Foundation of China.
Communicated by:
Hal L. Smith
Copyright of article:
Copyright
1999,
American Mathematical Society
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