A Lyapunov functional for a stage-structured predator-prey model with nonlinear predation rate

被引：21

作者：

Georgescu, Paul ^{[3
]}

Hsieh, Ying-Hen ^{[1
,2
]}

Zhang, Hong ^{[4
,5
]}

机构：

[1] China Med Univ, Dept Publ Hlth, Taichung 40402, Taiwan

[2] China Med Univ, Ctr Infect Dis Epidemiol Res, Taichung 40402, Taiwan

[3] Tech Univ Iasi, Dept Math, Iasi 700506, Romania

[4] Jiangsu Univ, Dept Math, Zhenjiang 212013, Jiangsu, Peoples R China

[5] Umea Univ, Dept Math & Math Stat, SE-90187 Umea, Sweden

来源：

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2010年 / 11卷 / 05期

基金：

瑞典研究理事会;

关键词：

Lyapunov functional; Predator-prey model; Stage structure; Nonlinear predation rate; Stability; GLOBAL STABILITY; VIRUS DYNAMICS; PERSISTENCE; INFECTION;

D O I：

10.1016/j.nonrwa.2010.01.012

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the dynamics of a general stage-structured predator-prey model which generalizes several known predator-prey, SEIR, and virus dynamics models, assuming that the intrinsic growth rate of the prey, the predation rate, and the removal functions are given in an unspecified form. Using the Lyapunov method, we derive sufficient conditions for the local stability of the equilibria together with estimations of their respective domains of attraction, while observing that in several particular but important situations these conditions yield global stability results. The biological significance of these conditions is discussed and the existence of the positive steady state is also investigated. (C) 2010 Elsevier Ltd. All rights reserved.

引用

页码：3653 / 3665

页数：13

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