ANALYSIS OF A PREDATOR-PREY MODEL WITH DISEASE IN THE PREY

被引：14
|
作者：
Ji, Chunyan y [1 ,2 ]
Jiang, Daqing [2 ]
机构：
[1] Changshu Inst Technol, Sch Math & Stat, Changshu 215500, Jiangsu, Peoples R China
[2] NE Normal Univ, Sch Math & Stat, Changchun 130024, Jilin, Peoples R China
来源：
INTERNATIONAL JOURNAL OF BIOMATHEMATICS | 2013年 / 6卷 / 03期
关键词：
Predator-prey model with disease; Ito formula; stable; stochastically unstable; stochastically stable in the large; PERSISTENCE; STABILITY;
D O I：
10.1142/S1793524513500125
中图分类号：
Q [生物科学];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
In this paper, we discuss the behavior of a predator-prey model with disease in the prey with and without stochastic perturbation, respectively. First, we briefly give the dynamic of the deterministic system, by analyzing stabilities of its four equilibria. Then, we consider the asymptotic behavior of the stochastic system. By Lyapunov analysis methods, we show the stochastic stability and its long time behavior around the equilibrium of the deterministic system. We obtain there are similar properties between the stochastic system and its corresponding deterministic system, when white noise is small. But large white noise can make a unstable deterministic system to be stable.
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页数：21
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