| 具有多时滞捕食-被捕食流行病模型的稳定性 |
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| 引用本文： | 朱道军,兰叶霞.具有多时滞捕食-被捕食流行病模型的稳定性[J].安徽大学学报(自然科学版),2007,31(4):5-8. |
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| 作者姓名： | 朱道军 兰叶霞 |
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| 作者单位： | 南昌大学,理学院数学系,江西,南昌,330047;南昌三中,江西,南昌,330006 |
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| 基金项目： | 南昌大学科研基金资助项目（2006Z03371） |
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| 摘 要： | 考虑传染病对捕食-被捕食者都具有致病作用的一类时滞捕食-被捕食模型,分析了系统的非负不变性、边界平衡点的性质和全局稳定性,证明了当时滞u=τ1+τ2适当小时,边界平衡点E3是局部渐近稳定的,随着时滞的增加, E3由稳定变为不稳定,系统在E3附近发生Hopf分支;当时滞τ1+2τ2充分小时,边界平衡点E2=(1,0,0)是全局稳定的.
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| 关 键 词： | 捕食模型 局部稳定性 Hopf分支 全局稳定性 |
| 文章编号： | 1000-2162（2007）04-0005-04 |
| 修稿时间： | 2006-09-21 |
The stability of a multi-delay predator-prey systems with epidemic disease |
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| ZHU Dao-jun,LAN Ye-xia.The stability of a multi-delay predator-prey systems with epidemic disease[J].Journal of Anhui University(Natural Sciences),2007,31(4):5-8. |
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| Authors: | ZHU Dao-jun LAN Ye-xia |
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| Institution: | 1. Department of Mathematics, Nanchang University,Nanchang 330047, China; 2. The Third Senior- middle School in Nanchang , Nanchang 330006, China |
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| Abstract: | A system of retarded functional differential equations is proposed as a predator-prey model with disease in the prey and predator.The invariance of none-negativity,nature of boundary equilibria and global stability are analyzed.The author shows that boundary equilibrium E3 is locally asymptotically stable when time delays u=τ1+τ2 is suitable small,while a loss of stability by a Hopf bifurcation can occur as the delays increase, and shows that boundary equilibrium E2=(1,0,0) is global stability when time delay τ1+2τ2 is suitable small. |
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| Keywords: | predator-prey model local stability Hopf bifurcation global stability |
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