Hopf bifurcation of a chemostat model

Rongning Qu; Xiaofang Li

doi:10.1016/j.amc.2012.09.036

Hopf bifurcation of a chemostat model

Rongning Qu
, Xiaofang Li^*

^*Corresponding author for this work

Harbin Institute of Technology Weihai

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

A chemostat model with discrete time delay is proposed to describe oscillatory behavior in microbial continuous culture. Stability and Hopf bifurcation are discussed, including the changing regularity of bifurcation value. Explicit algorithm for determining the direction of Hopf bifurcation and the stability of periodic solution is derived, using the theory of normal form and center manifold. Finally, some numerical simulations are performed to illustrate the analytical results found.

Original language	English
Pages (from-to)	3541-3552
Number of pages	12
Journal	Applied Mathematics and Computation
Volume	219
Issue number	8
DOIs	https://doi.org/10.1016/j.amc.2012.09.036
State	Published - 15 Dec 2012
Externally published	Yes

Keywords

Delay
Hopf bifurcation
Oscillation
Periodic solution
Stability

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10.1016/j.amc.2012.09.036

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title = "Hopf bifurcation of a chemostat model",

abstract = "A chemostat model with discrete time delay is proposed to describe oscillatory behavior in microbial continuous culture. Stability and Hopf bifurcation are discussed, including the changing regularity of bifurcation value. Explicit algorithm for determining the direction of Hopf bifurcation and the stability of periodic solution is derived, using the theory of normal form and center manifold. Finally, some numerical simulations are performed to illustrate the analytical results found.",

keywords = "Delay, Hopf bifurcation, Oscillation, Periodic solution, Stability",

author = "Rongning Qu and Xiaofang Li",

year = "2012",

month = dec,

day = "15",

doi = "10.1016/j.amc.2012.09.036",

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T1 - Hopf bifurcation of a chemostat model

AU - Qu, Rongning

AU - Li, Xiaofang

PY - 2012/12/15

Y1 - 2012/12/15

N2 - A chemostat model with discrete time delay is proposed to describe oscillatory behavior in microbial continuous culture. Stability and Hopf bifurcation are discussed, including the changing regularity of bifurcation value. Explicit algorithm for determining the direction of Hopf bifurcation and the stability of periodic solution is derived, using the theory of normal form and center manifold. Finally, some numerical simulations are performed to illustrate the analytical results found.

AB - A chemostat model with discrete time delay is proposed to describe oscillatory behavior in microbial continuous culture. Stability and Hopf bifurcation are discussed, including the changing regularity of bifurcation value. Explicit algorithm for determining the direction of Hopf bifurcation and the stability of periodic solution is derived, using the theory of normal form and center manifold. Finally, some numerical simulations are performed to illustrate the analytical results found.

KW - Delay

KW - Hopf bifurcation

KW - Oscillation

KW - Periodic solution

KW - Stability

UR - https://www.scopus.com/pages/publications/84870062936

U2 - 10.1016/j.amc.2012.09.036

DO - 10.1016/j.amc.2012.09.036

M3 - 文章

AN - SCOPUS:84870062936

SN - 0096-3003

VL - 219

SP - 3541

EP - 3552

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

IS - 8

ER -

Hopf bifurcation of a chemostat model

Abstract

Keywords

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