| 一类捕食-食饵模型的全局分歧研究 |
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| 引用本文： | 李善兵,李艳玲.一类捕食-食饵模型的全局分歧研究[J].纺织高校基础科学学报,2012,25(3):299-303. |
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| 作者姓名： | 李善兵 李艳玲 |
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| 作者单位： | 陕西师范大学 数学与信息科学学院,陕西 西安,710062 |
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| 基金项目： | 国家自然科学基金资助项目(10971124);教育部高等学校博士点专项基金资助(100807180004) |
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| 摘 要： | 研究了一类具有避难所的捕食-食饵模型平衡态正解的存在性,其功能函数为Holling Ⅱ型.利用线性稳定理论得到常数平衡解的稳定性,借助Crandall-Rabinowitz分歧理论,得到局部分歧正解的存在性;将局部分歧延拓为全局分歧,得到正解存在的充分条件,从而给出捕食者与食饵在一定条件下可以共存的结果.
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| 关 键 词： | 捕食-食饵模型 Holling Ⅱ型 稳定性 全局分歧 |
Research on global bifurcation of a predator-prey model |
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| LI Shan-bing
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LI Yan-ling.Research on global bifurcation of a predator-prey model[J].Basic Sciences Journal of Textile Universities,2012,25(3):299-303. |
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| Authors: | LI Shan-bing LI Yan-ling |
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| Affiliation: | (College of Mathematics and Information Science,Shaanxi Normal University,Xi′an 710062,China) |
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| Abstract: | In this paper,the existence of positive solution of the steady-state system for the predator-prey model with Holling type II functional response incorporating a prey refuge is studied.Firstly,by the linearized stability theory,the stability of positive constant steady-state solution is obtained.Secondly,by the Crandall-Rabinowitz local bifurcation theory,the existence of local bifurcation positive solution is obtained.Finally,resorting to the global bifurcation theory,the local bifurcation solution to the global one is extended.The results show that the predator and prey can co-exist under certain conditions. |
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| Keywords: | predator-prey model Holling Ⅱ type stability global bifurcation |
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