Hopf bifurcation analysis of a food-limited population model with delay

被引：19

作者：

Wan, Aying ^{[1
,2
]}

Wei, Junjie ^{[1
]}

机构：

[1] Harbin Inst Technol, Dept Math, Harbin 150006, Peoples R China

[2] Hulunbeir Coll, Dept Math, Hailar, Peoples R China

来源：

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2010年 / 11卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Food-limited system; Delay; Hopf bifurcation; Periodic solutions; PERIODIC-SOLUTIONS; EXISTENCE; TOXICANTS;

D O I：

10.1016/j.nonrwa.2009.01.052

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The dynamics of a food-limited population model with delay are investigated. We prove that a sequence of Hopf bifurcations occur at the positive equilibrium as the delay increases. An explicit algorithm for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions is derived, using the theory of normal form and center manifold. Global existence of periodic solutions is established by using a global Hopf bifurcation result due to [J. Wu, Symmetric functional differential equations and neural networks with memory, Trails. Amer. Math. Soc. 350 (1998) 4799-4838]. (C) 2009 Elsevier Ltd. All rights reserved.

引用

页码：1087 / 1095

页数：9

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