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Dynamics of a non-autonomous ratio-dependent predator—prey system

Published online by Cambridge University Press:  12 July 2007

Meng Fan ,
Qian Wang  and
Xingfu Zou
Meng Fan
Affiliation:
Department of Mathematics, Northeast Normal University, Changchun, Jilin 130024, People's Republic of China (mfan@nenu.edu.cn)
Qian Wang
Affiliation:
Department of Mathematics, Northeast Normal University, Changchun, Jilin 130024, People's Republic of China (mfan@nenu.edu.cn)
Xingfu Zou
Affiliation:
Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NF A1C 5S7, Canada (xzou@math.mun.ca)
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Abstract

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We investigate a non-autonomous ratio-dependent predator–prey system, whose autonomous versions have been analysed by several authors. For the general non-autonomous case, we address such properties as positive invariance, permanence, non-persistence and the globally asymptotic stability for the system. For the periodic and almost-periodic cases, we obtain conditions for existence, uniqueness and stability of a positive periodic solution, and a positive almost-periodic solution, respectively.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 133 , Issue 1 , February 2003 , pp. 97 - 118
Copyright
Copyright © Royal Society of Edinburgh 2003