Global Hopf Bifurcation Analysis of a Nicholson's Blowflies Equation of Neutral Type

被引：10

作者：

Li, Michael Y. ^{[1
]}

Wang, Chuncheng ^{[2
]}

Wei, Junjie ^{[2
]}

机构：

[1] Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada

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

来源：

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS | 2014年 / 26卷 / 01期

基金：

加拿大创新基金会; 加拿大自然科学与工程研究理事会; 中国国家自然科学基金;

关键词：

NFDEs; Nicholson's blowflies equation; Hopf bifurcations; FUNCTIONAL-DIFFERENTIAL EQUATIONS;

D O I：

10.1007/s10884-014-9349-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate Hopf bifurcations in a delayed Nicholson's blowflies equation of neutral type, derived from the Gurtin-MacCamy model. A key parameter that determines the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions is derived. Global extension of local Hopf branches is established by combining a global Hopf bifurcation theorem with a Bendixson criterion for higher dimensional ordinary differential equations. We show that a branch of slowly varying periodic solutions and a branch of fast oscillating periodic solutions coexist for all large delays.

引用

页码：165 / 179

页数：15

共 25 条

[1]

[Anonymous], 2012, Applications of centre manifold theory

[2] Structured population models, conservation laws, and delay equations [J].

Bocharov, G ;

Hadeler, KP .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2000, 168 (01) :212-237

[3] 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

[4]

Gourley S.A., J DIFFER EQ IN PRESS

[5] Equivariant Hopf bifurcation for neutral functional differential equations [J].

Guo, Shangjiang ;

Lamb, Jeroen S. W. .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2008, 136 (06) :2031-2041

[6] NICHOLSON BLOWFLIES REVISITED [J].

GURNEY, WSC ;

BLYTHE, SP ;

NISBET, RM .

NATURE, 1980, 287 (5777) :17-21

[7]

GURTIN ME, 1974, ARCH RATION MECH AN, V54, P280

[8]

Hale J.K., 1993, Introduction to Functional Differntial Equations

[9] On perturbations of delay-differential equations with periodic orbits [J].

Hale, JK ;

Weedermann, M .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2004, 197 (02) :219-246

[10]

Jun Jie Wei, 2002, Acta Mathematica Sinica, V45, P93

← 1 2 3 →