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

被引：86
|
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.
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页码：1998 / 2011
页数：14
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