Stability and Hopf bifurcation of a predator-prey model with stage structure and time delay for the prey

被引：29

作者：

Song, Yan ^{[1
]}

Xiao, Wen ^{[1
]}

Qi, Xiaoyu ^{[1
]}

机构：

[1] Bohai Univ, Sch Math & Phys, Jinzhou 121003, Peoples R China

来源：

NONLINEAR DYNAMICS | 2016年 / 83卷 / 03期

关键词：

Predator-prey model; Stage structure; Time delay; Local and global stability; Hopf bifurcation; SYSTEM; GROWTH;

D O I：

10.1007/s11071-015-2413-6

中图分类号：

TH [机械、仪表工业];

学科分类号：

0802 ;

摘要：

A predator-prey system with stage structure and time delay for the prey is investigated. By analyzing the corresponding characteristic equations, the local stability of a positive equilibrium and two boundary equilibria of the system is discussed, respectively. By using persistence theory on infinite dimensional systems and comparison argument, respectively, sufficient conditions are obtained for the global stability of the positive equilibrium and one of the boundary equilibria of the proposed system. Further, the existence of a Hopf bifurcation at the positive equilibrium is studied. Numerical simulations are carried out to illustrate the main results.

引用

页码：1409 / 1418

页数：10

共 17 条

[1] A TIME-DELAY MODEL OF SINGLE-SPECIES GROWTH WITH STAGE STRUCTURE [J].

AIELLO, WG ;

FREEDMAN, HI .

MATHEMATICAL BIOSCIENCES, 1990, 101 (02) :139-153

[2]

[Anonymous], 2013, Mathematical Biology

[3] Geometric stability switch criteria in delay differential systems with delay dependent parameters [J].

Beretta, E ;

Kuang, Y .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2002, 33 (05) :1144-1165

[4]

Chen L. S., 1988, MATH ECOLOGY MODELIN

[5] The effect of dispersal on population growth with stage-structure [J].

Cui, JA ;

Chen, LS ;

Wang, WD .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2000, 39 (1-2) :91-102

[6] Global dynamics of a predator-prey model with stage structure for the predator [J].

Georgescu, Paul ;

Hsieh, Ying-Hen .

SIAM JOURNAL ON APPLIED MATHEMATICS, 2007, 67 (05) :1379-1395

[7]

Hale J.K., 1976, Theory of Functional Differential Equations

[8] PERSISTENCE IN INFINITE-DIMENSIONAL SYSTEMS [J].

HALE, JK ;

WALTMAN, P .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1989, 20 (02) :388-395

[9]

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

[10] Optimal harvesting and stability for a two-species competitive system with stage structure [J].

Song, XY ;

Chen, LS .

MATHEMATICAL BIOSCIENCES, 2001, 170 (02) :173-186

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