Limit cycles in a general Kolmogorov model |
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Authors: | Xun C Huang Lemin Zhu |
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Institution: | Department of Mathematics, Yangzhou Polytechnic University, 20 Mountain Tiger Road, 2-403, Yangzhou Jiangsu 225002, China |
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Abstract: | The problem of limit cycles is interesting and significant both in theory and applications. In mathematical ecology, finding models that display a stable limit cycle—an attracting stable self-sustained oscillation, is a primary work.In this paper, a general Kolmogorov system, which includes the Gause-type model (Math. Biosci. 88 (1988) 67), the general predator-prey model (J. Phys. A: Math. Gen. 21 (1988) L685; Math. Biosci. 96 (1989) 47), and many other models (J. Biomath. 15(3) (2001) 266; J. Biomath. 16(2) (2001) 156; J. Math. 21(22) (2001) 145), is studied. The conditions for the existence and uniqueness of limit cycles in this model are proved. Some known results are easily derived as an illustration of our work. |
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Keywords: | Limit cycle Predator– prey system Kolmogorov model |
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