On the finite-dimensional dynamical systems with limited competition
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- by Xing Liang and Jifa Jiang PDF
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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.References
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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
- Received by editor(s): May 25, 2001
- Published electronically: April 30, 2002
- Additional Notes: Research supported by the National Natural Science Foundation of China
- © Copyright 2002 American Mathematical Society
- 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
- MathSciNet review: 1911510