[1]李冬梅,张凤,宋颖伟,等.一类捕食者具有流行病的时滞捕食系统定性分析[J].哈尔滨理工大学学报,2009,(05):89-92.
 LI Dong-mei,ZHANG Feng,SONG Ying-wei.On the Qualitative Analysis of Delayed Predator-Prey Model with Epidemic in the Predator[J].哈尔滨理工大学学报,2009,(05):89-92.
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一类捕食者具有流行病的时滞捕食系统定性分析()
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《哈尔滨理工大学学报》[ISSN:1007-2683/CN:23-1404/N]

卷:
期数:
2009年05期
页码:
89-92
栏目:
数理科学
出版日期:
2009-10-25

文章信息/Info

Title:
On the Qualitative Analysis of Delayed Predator-Prey Model with Epidemic in the Predator
作者:
李冬梅; 张凤; 宋颖伟;
哈尔滨理工大学应用科学学院;
Author(s):
LI Dong-mei; ZHANG Feng; SONG Ying-wei
School of Applied Science; Harbin University of Science and Technology; Harbin 150080; China
关键词:
捕食-被捕食模型 渐近稳定 时滞 阈值 Hopf分支
Keywords:
predator-prey model asymptotical stability delay threshold hopf bifurcation
分类号:
O175.1
文献标志码:
A
摘要:
研究了一类捕食者具有流行病的时滞捕食-被捕食模型,分析了边界平衡点的性质和全局稳定性,给出疾病是否流行的阈值.证明了当时滞τ适当小时,正平衡点是局部渐近稳定的,随着时滞的增加正平衡点由稳定变为不稳定,系统在正平衡点附近发生Hopf分支.
Abstract:
A system of retarded functional differential equations is proposed as a predator-prey model with epidemic in the predator.The nature of boundary equilibria and global stability are analyzed.A threshold is identified which determines the outcome of the disease.This paper shows that positive equilibrium is locally asymptotically stable when time delay τ is suitable small,while a loss of stability by a Hopf bifurcation can occur as the delay increases.

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备注/Memo

备注/Memo:
黑龙江省自然基金资助项目(A200502);; 黑龙江省教育厅资助项目(10051061)
更新日期/Last Update: 2009-12-16