Proceedings of the 2nd International Conference on Computer Science and Electronics Engineering (ICCSEE 2013)

Stability and bifurcation analysis in leukopoiesis models with two delays

Authors
Cuilian Zhang, Zhaozhuang Guo
Corresponding Author
Cuilian Zhang
Available Online March 2013.
DOI
https://doi.org/10.2991/iccsee.2013.705How to use a DOI?
Keywords
Leukopoiesis, Delay differential equations, Stability, Hopf bifurcation.
Abstract

We consider a nonlinear system of two equations, describing the evolution of a stem cell population and the resulting white blood cell population. Two delays appear in this model to describe the cell cycle duration of the stem cell population and the time required to produce white blood cells. We establish sufficient conditions for the asymptotic stability of the unique nontrivial positive steady state of the model by analyzing roots of a second degree exponential polynomial characteristic equation with delay-dependent coefficients. We also prove the existence of Hopf bifurcations which leads to periodic solutions.

Copyright
© 2013, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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Volume Title
Proceedings of the 2nd International Conference on Computer Science and Electronics Engineering (ICCSEE 2013)
Series
Advances in Intelligent Systems Research
Publication Date
March 2013
ISBN
978-90-78677-61-1
ISSN
1951-6851
DOI
https://doi.org/10.2991/iccsee.2013.705How to use a DOI?
Copyright
© 2013, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - CONF
AU  - Cuilian Zhang
AU  - Zhaozhuang Guo
PY  - 2013/03
DA  - 2013/03
TI  - Stability and bifurcation analysis in leukopoiesis models with two delays
BT  - Proceedings of the 2nd International Conference on Computer Science and Electronics Engineering (ICCSEE 2013)
PB  - Atlantis Press
SP  - 2824
EP  - 2828
SN  - 1951-6851
UR  - https://doi.org/10.2991/iccsee.2013.705
DO  - https://doi.org/10.2991/iccsee.2013.705
ID  - Zhang2013/03
ER  -