Stability and Hopf bifurcation in a diffusive predator-prey system with delay effect

被引：87

作者：

Zuo, Wenjie ^{[1
,2
]}

Wei, Junjie ^{[1
]}

机构：

[1] Harbin Inst Technol, Dept Math, Harbin 150001, Heilongjiang, Peoples R China

[2] China Univ Petr E China, Sch Math & Computat Sci, Qingdao 266555, Peoples R China

来源：

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2011年 / 12卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Prey-predator system; Delay; Diffusion; Hopf bifurcation; Periodic solutions; GLOBAL PERIODIC-SOLUTIONS; MODEL;

D O I：

10.1016/j.nonrwa.2010.12.016

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with a delayed predator-prey system with diffusion effect. First, the stability of the positive equilibrium and the existence of spatially homogeneous and spatially inhomogeneous periodic solutions are investigated by analyzing the distribution of the eigenvalues. Next the direction and the stability of Hopf bifurcation are determined by the normal form theory and the center manifold reduction for partial functional differential equations. Finally, some numerical simulations are carried out for illustrating the theoretical results. (C) 2010 Elsevier Ltd. All rights reserved.

引用

页码：1998 / 2011

页数：14

共 20 条

[1] NORMAL FORMS FOR RETARDED FUNCTIONAL-DIFFERENTIAL EQUATIONS WITH PARAMETERS AND APPLICATIONS TO HOPF-BIFURCATION [J].

FARIA, T ;

MAGALHAES, LT .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1995, 122 (02) :181-200

[2] Normal forms and Hopf bifurcation for partial differential equations with delays [J].

Faria, T .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2000, 352 (05) :2217-2238

[3] 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

[4]

Hale J.K., 1977, THEORY FUNCTIONAL DI

[5]

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

[6] Stability and delays in a predator-prey system [J].

He, XZ .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1996, 198 (02) :355-370

[7] Hopf bifurcation analysis for a delayed predator-prey system with diffusion effects [J].

Hu, Guang-Ping ;

Li, Wan-Tong .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2010, 11 (02) :819-826

[8] Stability and Hopf bifurcation for a delayed cooperation diffusion system with Dirichlet boundary conditions [J].

Li, Wan-Tong ;

Yan, Xiang-Ping ;

Zhang, Cun-Hua .

CHAOS SOLITONS & FRACTALS, 2008, 38 (01) :227-237

[9] TIME-DELAY VERSUS STABILITY IN POPULATION MODELS WITH 2 AND 3 TROPHIC LEVELS [J].

MAY, RM .

ECOLOGY, 1973, 54 (02) :315-325

[10]

Ruan SG, 2001, IMA J MATH APPL MED, V18, P41

← 1 2 →