| Optimal Harvesting and Stability for a Predator-prey System with Stage Structure |
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| 作者姓名： | Xin-yu Song Lan-sun Chen |
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| 作者单位： | Xin-yu Song，Lan-sun ChenDepartment of Mathematics. Xinyang Teachers College，Henan 464000，ChinaInstitute of Mathematics，Academy of Mathematics and System Sciences，Chinese Academy of Sciences，Beijing100080，China |
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| 基金项目： | the National Natural Science Foundation of China (No.10171106)，the Natural Science Foundation of Henan Province (No.0211010400). |
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| 摘 要： | The dynamics of a predator-prey system, where prey population has two stages, an immature stage and a mature stage with harvesting, the growth of predator population is of Lotka-Volterra nature, are modelled by a system of retarded functional differential equations. We obtain conditions for global asymptotic stability of three nonnegative equilibria and a threshold of harvesting for the mature prey population. The effect of delay on the population at positive equilibrium and the optimal harvesting of the mature prey population are also considered.
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| 收稿时间： | 29 December 2000 |
Optimal Harvesting and Stability for a Predator-prey System with Stage Structure |
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| Xin-yu Song,Lan-sun Chen.Optimal Harvesting and Stability for a Predator-prey System with Stage Structure[J].Acta Mathematicae Applicatae Sinica,2002,18(3):423-430. |
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| Authors: | Email author" target="_blank">Xin-yu?SongEmail author Lan-sun?Chen |
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| Institution: | (1) Department of Mathematics, Xinyang Teachers College, Henan 464000, China (E-mail: xysong@xytc.edu.cn), CN;(2) Institute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China (E-mail: lschen@math08.math.edu.cn), CN |
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| Abstract: | The dynamics of a predator-prey system, where prey population has two stages, an immature stage and a mature stage with harvesting, the growth of predator population is of Lotka-Volterra nature, are modelled by a system of retarded functional differential equations. We obtain conditions for global asymptotic stability of three nonnegative equilibria and a threshold of harvesting for the mature prey population. The effect of delay on the population at positive equilibrium and the optimal harvesting of the mature prey population are also considered. |
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| Keywords: | Optimal harvesting stage structure predator-prey system global asymptotic stability |
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