| 食饵带疾病的捕食模型的全局稳定性 |
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| 引用本文： | 刘细宪,李必文,陈伯山.食饵带疾病的捕食模型的全局稳定性[J].数学杂志,2015,35(1):85-94. |
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| 作者姓名： | 刘细宪 李必文 陈伯山 |
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| 作者单位： | 湖北师范学院数学与统计学院,湖北黄石,435002 |
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| 基金项目： | Supported by National Natural Science Foundation of China (10671182). |
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| 摘 要： | 本文研究了一类三维生态传染病模型的正解性和边界性，并分析了系统平衡点的局部稳定性。利用一种新的几何方法，获得了内平衡点的全稳定性，推广了Li和Muldowney1]提出的这种方法的应用，这种方法避免了寻找Lyapunov的困难。
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| 关 键 词： | 捕食者与被捕食者 疾病 Hopf分支 全局稳定 |
| 收稿时间： | 2013/10/14 0:00:00 |
| 修稿时间： | 2013/11/11 0:00:00 |
GLOBAL STABILITY FOR A PREDATOR-PREY MODEL WITH DISEASE IN THE PREY |
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| LIU Xi-xian,LI Bi-wen and CHEN Bo-shan.GLOBAL STABILITY FOR A PREDATOR-PREY MODEL WITH DISEASE IN THE PREY[J].Journal of Mathematics,2015,35(1):85-94. |
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| Authors: | LIU Xi-xian LI Bi-wen and CHEN Bo-shan |
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| Institution: | School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China,School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China and School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China |
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| Abstract: | This paper describes a three dimensional eco-epidemiological model consisting of susceptible prey, infected prey and predator. We consider the positivity and boundedness of the solution first and the local stability of the equilibrium is discussed. Obviously, the interior equilibrium A* is always locally asymptotically stable according to the Routh-Hurwitz criterion. At last, the geometric method of Li and Muldowney is used to investigate the global stability of the interior equilibrium. |
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| Keywords: | predator-prey disease geometric method global stability |
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