Hopf bifurcation of a five-dimensional delay differential system

被引：4

作者：

Li, Xiaofang ^{[1
,2
]}

Qu, Rongning ^{[2
]}

Feng, Enmin ^{[1
]}

机构：

[1] Dalian Univ Technol, Dept Math, Dalian 116024, Peoples R China

[2] Harbin Inst Technol, Dept Math, Weihai 264209, Peoples R China

来源：

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS | 2011年 / 88卷 / 01期

基金：

中国国家自然科学基金;

关键词：

delay; Hopf bifurcation; stability; periodic solution; oscillation; ANAEROBIC CONTINUOUS-CULTURE; KLEBSIELLA-PNEUMONIAE; CONTINUOUS FERMENTATION; OSCILLATORY BEHAVIOR; GLYCEROL METABOLISM; CHEMOSTAT SUBJECT; DYNAMIC-BEHAVIOR; KINETIC-MODEL; 1,3-PROPANEDIOL; SUBSTRATE;

D O I：

10.1080/00207160903197187

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A five-dimensional delay differential system is proposed to describe oscillatory behaviour in microbial continuous culture. Stability and Hopf bifurcation are discussed, including the changing regularity of the bifurcation value. An explicit algorithm for determining the direction of Hopf bifurcation and the stability of periodic solution is derived, using the theory of normal form and centre manifold. Finally, some numerical simulations are performed to illustrate the analytical results found.

引用

页码：79 / 96

页数：18

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