| 一类捕食——食饵模型正平衡解的整体分歧 |
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| 引用本文： | 张汉姜,李艳玲.一类捕食——食饵模型正平衡解的整体分歧[J].系统科学与数学,2007,27(5):791-800. |
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| 作者姓名： | 张汉姜 李艳玲 |
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| 作者单位： | 1. 陕西师范大学数学与信息科学学院,西安,710062;西安邮电学院应用数理系,西安,710061
2. 西安邮电学院应用数理系,西安,710061 |
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| 摘 要： | 讨论了一类改进的Leslie-Gower和Holling-Type Ⅱ型捕食-食饵模型对应的平衡态系统正解的结构.以捕食者的出生率b为分歧参数,利用局部分歧理论和整体分歧理论,得到了此平衡态系统正解的存在性与参数b的关系,即当b适当大时,该平衡态系统具有共存正解.
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| 关 键 词： | 捕食-食饵模型 主特征值 局部分歧 整体分歧. |
| 收稿时间： | 2006-6-28 |
| 修稿时间： | 2006年6月28日 |
Global Bifurcation of Positive Steady-State Solutions for a Classof Predator-Prey Model |
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| Zhang Hanjiang,Li Yanling.Global Bifurcation of Positive Steady-State Solutions for a Classof Predator-Prey Model[J].Journal of Systems Science and Mathematical Sciences,2007,27(5):791-800. |
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| Authors: | Zhang Hanjiang Li Yanling |
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| Institution: | (1) College of Mathematics and Information Science, Shannxi NormalUniversity, Xi'an 710062; (2) Department of Mathematics and Physics, Xi'an Institute of Post & Telecoms, Xi'an 710061 |
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| Abstract: | In this paper the structure of a predator-prey model with modified Leslie-Gower and Holling-Type II schemes is investigated. By use of the theorems of local bifurcation and global bifurcation theory, we get the ralationship between the existence of positive solutions for the system and bifurcation parameter $b$-the birth-rate of predator $v$, that is, the system has coexistence positive solutions when $b$ is in a proper range. |
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| Keywords: | Predator-prey model principal eigenvalue local bifurcation global bifurcation |
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