Hopf bifurcation of a predator-prey system with stage structure and harvesting

被引：11

作者：

Ge, Zhihao ^{[1
]}

Yan, Jingjing

机构：

[1] Henan Univ, Sch Math & Informat Sci, Kaifeng 475001, Peoples R China

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2011年 / 74卷 / 02期

关键词：

Predator-prey system; Stage structure; Delay; Hopf bifurcation; MODEL; STABILITY;

D O I：

10.1016/j.na.2010.09.019

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, a two-species predator-prey system with stage structure and harvesting is investigated. The existence of Hopf bifurcations of the system is given. And the stability and directions of Hopf bifurcations are determined by applying the normal form theory and the center manifold theorem. (C) 2010 Elsevier Ltd. All rights reserved.

引用

页码：652 / 660

页数：9

共 15 条

[1] ANALYSIS OF A MODEL REPRESENTING STAGE-STRUCTURED POPULATION-GROWTH WITH STATE-DEPENDENT TIME-DELAY [J].

AIELLO, WG ;

FREEDMAN, HI ;

WU, J .

SIAM JOURNAL ON APPLIED MATHEMATICS, 1992, 52 (03) :855-869

[2]

[Anonymous], 2013, Mathematical Biology

[3] SIMPLE MATHEMATICAL-MODELS FOR CANNIBALISM - A CRITIQUE AND A NEW APPROACH [J].

DIEKMANN, O ;

NISBET, RM ;

GURNEY, WSC ;

VANDENBOSCH, F .

MATHEMATICAL BIOSCIENCES, 1986, 78 (01) :21-46

[4] Stability and bifurcation for a delayed predator-prey model and the effect of diffusion [J].

Faria, T .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2001, 254 (02) :433-463

[5] PERSISTENCE AND GLOBAL ASYMPTOTIC STABILITY OF SINGLE SPECIES DISPERSAL MODELS WITH STAGE STRUCTURE [J].

FREEDMAN, HI ;

WU, JH .

QUARTERLY OF APPLIED MATHEMATICS, 1991, 49 (02) :351-371

[6]

Freedman HI., 1980, DETERMINISTIC MATH M

[7] A stage structured predator-prey model and its dependence on maturation delay and death rate [J].

Gourley, SA ;

Kuang, Y .

JOURNAL OF MATHEMATICAL BIOLOGY, 2004, 49 (02) :188-200

[8]

Hale J.K., 1977, THEORY FUNCTIONAL DI

[9]

Hassard B.D., 1981, Theory and Applications of Hopf Bifurcation

[10]

Kuang Y., 1993, Delay Differential Equations with Applications in Population Dynamics

← 1 2 →