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On the finite-dimensional dynamical systems with limited competition


Authors: Xing Liang and Jifa Jiang
Journal: Trans. Amer. Math. Soc. 354 (2002), 3535-3554
MSC (2000): Primary 34D23, 47H07; Secondary 92B05
DOI: https://doi.org/10.1090/S0002-9947-02-03032-5
Published electronically: April 30, 2002
MathSciNet review: 1911510
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Abstract: The asymptotic behavior of dynamical systems with limited competition is investigated. We study index theory for fixed points, permanence, global stability, convergence everywhere and coexistence. It is shown that the system has a globally asymptotically stable fixed point if every fixed point is hyperbolic and locally asymptotically stable relative to the face it belongs to. A nice result is the necessary and sufficient conditions for the system to have a globally asymptotically stable positive fixed point. It can be used to establish the sufficient conditions for the system to persist uniformly and the convergence result for all orbits. Applications are made to time-periodic ordinary differential equations and reaction-diffusion equations.


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Additional Information

Xing Liang
Affiliation: Department of Mathematics University of Science and Technology of China Hefei, Anhui 230026, P. R. China
Email: xliang@mail.ustc.edu.cn

Jifa Jiang
Affiliation: Department of Mathematics University of Science and Technology of China Hefei, Anhui 230026, P. R. China
Email: jiangjf@ustc.edu.cn

DOI: https://doi.org/10.1090/S0002-9947-02-03032-5
Keywords: Map with limited competition, index of fixed points, global stability, permanence, coexistence
Received by editor(s): May 25, 2001
Published electronically: April 30, 2002
Additional Notes: Research supported by the National Natural Science Foundation of China
Article copyright: © Copyright 2002 American Mathematical Society

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