| THE VOLTERRA MODEL FOR THREE SPACIES PREDATOR-PREY SYSTEMS IN LOOPS |
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| 引用本文： | 王远世,吴红,朱思铭. THE VOLTERRA MODEL FOR THREE SPACIES PREDATOR-PREY SYSTEMS IN LOOPS[J]. Annals of Differential Equations, 2003, 0(1) |
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| 作者姓名： | 王远世 吴红 朱思铭 |
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| 作者单位： | College of Math. & Scientific Computations，Zhongshan University，Guangzhou 510275，College of Math. & Scientific Computations，Zhongshan University，Guangzhou 510275，College of Math. & Scientific Computations，Zhongshan University，Guangzhou 510275 |
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| 摘 要： | We consider the three species predator-prey model with the same intrinsic growth rates, where species 3 feeds on species 2, species 2 feeds on species 1, species 1 feeds on species 3. An open question raised by Nishan Krikorian is answered: We obtain the necessary and sufficient conditions for all the orbits to be unbounded. We also obtain the necessary and sufficient conditions for the positive equilibrium to be globally stable. It is shown that there exists a family of neutrally stable periodic orbits, in which we extend Darboux method to three-species models for the first time.
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THE VOLTERRA MODEL FOR THREE SPACIES PREDATOR-PREY SYSTEMS IN LOOPS |
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| Wang Yuanshi Wu Hong Zhu Siming. THE VOLTERRA MODEL FOR THREE SPACIES PREDATOR-PREY SYSTEMS IN LOOPS[J]. 微分方程年刊(英文版), 2003, 0(1) |
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| Authors: | Wang Yuanshi Wu Hong Zhu Siming |
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| Abstract: | We consider the three species predator-prey model with the same intrinsic growth rates, where species 3 feeds on species 2, species 2 feeds on species 1, species 1 feeds on species 3. An open question raised by Nishan Krikorian is answered: We obtain the necessary and sufficient conditions for all the orbits to be unbounded. We also obtain the necessary and sufficient conditions for the positive equilibrium to be globally stable. It is shown that there exists a family of neutrally stable periodic orbits, in which we extend Darboux method to three-species models for the first time. |
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| Keywords: | Darboux method predator-prey model of three-species globally asymptotically stable Stocks theorem |
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