一个食饵有病的捕食与被捕食模型分析

J4 ›› 2011, Vol. 49 ›› Issue (02): 191-194.

一个食饵有病的捕食与被捕食模型分析

张永坡¹, 马明娟¹, 黄庆道²

1. 空军航空大学基础部, 长春 130022； 2. 吉林大学数学学院, 长春 130012

收稿日期:2010-05-19 出版日期:2011-03-26 发布日期:2011-06-14
通讯作者: 黄庆道 E-mail:hqdao@email.jlu.edu.cn

Analysis of PredatorPrey Model with Disease in the Prey

ZHANG Yongpo¹, MA Mingjuan¹, HUANG Qingdao^2

1. Department of Foundation, Aviation University of Air Force, Changchun 130022, China;2. College of Mathematics, Jilin University, Changchun 130012, China

Received:2010-05-19 Online:2011-03-26 Published:2011-06-14
Contact: HUANG Qingdao E-mail:hqdao@email.jlu.edu.cn

摘要/Abstract

摘要：

建立一个食饵具有疾病的生态流行病模型, 讨论了该模型平衡点的存在性, 并利用特征根法对边界平衡点进行局部渐近稳定性分析, 通过构造Liapunov函数得到了两个边界平衡点的全局渐近稳定性和正平衡点的局部渐近稳定性的充分条件.

关键词: 平衡点；局部渐近稳定；全局渐近稳定

Abstract:

A predatorprey model with disease in the prey was established and analysed. The existence of the equilibrium points and the boundedness of solution were studied. The sufficient condition of the local asymptotical stability of the boundary equilibrium was studied with the method of latent root, and furthermore, the global asymptotical stability of two boundary equilibrium points, and the local asymptotical stability of the positive equilibrium point were analyzed, with the sufficient condition of their stability obtained.

Key words: equilibrium, locally asymptotical stability, global asymptotical stability , 

中图分类号:

O175.13

张永坡, 马明娟, 黄庆道. 一个食饵有病的捕食与被捕食模型分析[J]. J4, 2011, 49(02): 191-194.

ZHANG Yong-Po, MA Meng-Juan, HUANG Qiang-Dao. Analysis of PredatorPrey Model with Disease in the Prey[J]. J4, 2011, 49(02): 191-194.

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