Bogdanov-Takens Bifurcation in a Leslie-Gower Predator-prey Model with Prey Harvesting

被引：39

作者：

Gong, Yi-jun ^{[1
]}

Huang, Ji-cai ^{[1
]}

机构：

[1] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China

来源：

ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES | 2014年 / 30卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Leslie-Gower predator-prey model; Bogdanov-Takens bifurcation; limit cycle; homoclinic loop; HETEROCLINIC BIFURCATION; HOPF BIFURCATIONS; SYSTEM;

D O I：

10.1007/s10255-014-0279-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper discuss the cusp bifurcation of codimension 2 (i.e. Bogdanov-Takens bifurcation) in a Leslie-Gower predator-prey model with prey harvesting, which was not revealed by Zhu and Lan [Phase portraits, Hopf bifurcation and limit cycles of Leslie-Gower predator-prey systems with harvesting rates, Discrete and Continuous Dynamical Systems Series B. 14(1) (2010), 289-306]. It is shown that there are different parameter values for which the model has a limit cycle or a homoclinic loop.

引用

页码：239 / 244

页数：6

共 17 条

[1]

Bogdanov R., 1988, SELECTA MATH SOVIET, V1, P389

[2]

Bogdanov R.I., 1981, Selecta Mathematica Sovietica, V1, P373

[3]

Broer HW, 2007, DISCRETE CONT DYN-A, V18, P221

[4] Bifurcation analysis of a generalized Gause model with prey harvesting and a generalized Holling response function of type III [J].

Etoua, Remy Magloire ;

Rousseau, Christiane .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2010, 249 (09) :2316-2356

[5]

Huang Jicai, 2004, [Acta Mathematicae Applicatae Sinica, Ying yung shu hseh hseh pao], V20, P167

[6] Bifurcation analysis of a predator-prey system with generalised Holling type III functional response [J].

Lamontagne, Yann ;

Coutu, Caroline ;

Rousseau, Christiane .

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2008, 20 (03) :535-571

[7] Heteroclinic bifurcation in the Michaelis-Menten-type ratio-dependent predator-prey system [J].

Li, Bingtuan ;

Kuang, Yang .

SIAM JOURNAL ON APPLIED MATHEMATICS, 2007, 67 (05) :1453-1464

[8]

Perko L., 1996, Differential Equations and Dynamical Systems, V7

[9]

Ruan SG, 2000, SIAM J APPL MATH, V61, P1445

[10]

Takens F., 1974, COMMUN MATH I RIJKSU, V3, P1, DOI DOI 10.1201/9781420034288

← 1 2 →