| 一类具功能性反应的食饵-捕食者两种群模型的定性分析 |
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| 引用本文： | 倪春霞,李学鹏. 一类具功能性反应的食饵-捕食者两种群模型的定性分析[J]. 淮阴师范学院学报(自然科学版), 2010, 9(1): 14-18 |
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| 作者姓名： | 倪春霞 李学鹏 |
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| 作者单位： | 福建师范大学,数学与计算机科学学院,福建,福州,350007 |
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| 基金项目： | 福建省教育厅自然科学基金资助项目(JA05204);;福建省科技厅基金资助项目(2005K027) |
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| 摘 要： | 研究了一类具功能性反应的食饵-捕食者两种群模型.利用微分方程定性理论,当给定参数满足一定条件下,讨论了该系统平衡点的稳定性态.运用Dulac函数法,得到了系统不存在闭轨的充分条件.运用Poincare-Bendixson环域定理,证明了极限环的存在性.运用张芷芬惟一性定理,证明了极限环的惟一性.
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| 关 键 词： | 平衡点 极限环 存在惟一性 |
A Qualitative Analysis of Two Species Predator-Prey Model with Functional Response |
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| NI Chun-xia,LI Xue-peng. A Qualitative Analysis of Two Species Predator-Prey Model with Functional Response[J]. Journal of Huaiyin Teachers College(Natrual Science Edition), 2010, 9(1): 14-18 |
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| Authors: | NI Chun-xia LI Xue-peng |
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| Affiliation: | School of Mathmatics and Computer Science;Fujian Normal University;Fuzhou Fujian 350007;China |
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| Abstract: | In this paper,a class of two species predator-prey model with functional response is studied.By using stability methods,when the given parameter meets certain conditions,the stability of equilibrium is discussed.The sufficient condition for nonexistence of the closed orbit is got by using the method of Dulac function.The existence and uniqueness of the limit cycle are proved by applying Poincare-Bendixson theorem and Zhang Zhifen's Uniqueness theorem. |
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| Keywords: | equilibrium limit cycle existence and uniqueness |
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