Necessary and sufficient conditions for the nonexistence of limit cycles of Leslie-Gower predator-prey models

被引：4
|
作者：
Zhang Daoxiang [1 ,3 ]
Ping Yan [2 ,3 ]
机构：
[1] Anhui Normal Univ, Sch Math & Comp Sci, Wuhu 241002, Anhui, Peoples R China
[2] Zhejiang A&F Univ, Sch Sci, Hangzhou 311300, Zhejiang, Peoples R China
[3] Univ Helsinki, Dept Math & Stat, POB 68, FIN-00014 Helsinki, Finland
来源：
APPLIED MATHEMATICS LETTERS | 2017年 / 71卷
基金：
芬兰科学院;
关键词：
Leslie-Gower; Limit cycle; Geometric criterion; Dulac theorem; Predator-prey system; STOCHASTIC MODEL; SYSTEMS;
D O I：
10.1016/j.aml.2017.03.008
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we consider a predator-prey model with Leslie Gower functional response. We present the necessary and sufficient conditions for the nonexistence of limit cycles by the application of the generalized Dulac theorem. As a result, we give the necessary and sufficient conditions for which the local asymptotic stability of the positive equilibrium implies the global stability for this model. Our results extend and improve the results presented by Aghajani and Moradifam (2006) and Hsu and Huang (1995). (C) 2017 Elsevier Ltd. All rights reserved.
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页码：1 / 5
页数：5
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