| 一类Rosenzweing-MacArthur捕食模型的周期解 |
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| 引用本文： | 肖海滨. 一类Rosenzweing-MacArthur捕食模型的周期解[J]. 宁波大学学报(理工版), 2003, 16(1): 25-29 |
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| 作者姓名： | 肖海滨 |
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| 作者单位： | 宁波大学,理学院,浙江,宁波,315211 |
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| 摘 要： | 研究一类Rosenzweing-MacArthur捕食模型的周期解,首先以食饵的环境容纳量k为分支参数,从Hopf的角度得到该系统小振幅稳定极限环的存在性,然后用定性的方法得到系统在第一象限内非小振幅稳定极限环的存在惟一性,推广了陈均平等的相关结论。同时也讨论正平衡点的全局稳定性。
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| 关 键 词： | 捕食系统 极限环 存在惟一性 全局稳定 |
| 文章编号： | 1001-5132(2003)01-0025-05 |
| 修稿时间： | 2002-11-14 |
Periodic Solutions of a Class Rosenzweing-MacArthur Predator-Prey Biology Model |
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| XIAO Hai-bin. Periodic Solutions of a Class Rosenzweing-MacArthur Predator-Prey Biology Model[J]. Journal of Ningbo University(Natural Science and Engineering Edition), 2003, 16(1): 25-29 |
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| Authors: | XIAO Hai-bin |
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| Abstract: | The periodic solution of Rosenzweing-MacArthur Predator-Prey Biology Model is studied. At first, by take k, the environmental earring capacity of the prey, as the bifurcation parameter, the existence of the small amplitude stable limit cycle created by Hopf bifurcation is obtained. Then by using qualitative analysis methods, it follows that the existence and uniqueness of non-small amplitude stable limit cycle, and the relevant results obtained by CHEN Jun-ping etc. are generalized. The global stability of the positive equilibrium is also discussed. |
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| Keywords: | predator-prey biology model limit cycle existence and uniqueness global stability |
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