Qualitative Properties in a More General Delayed Hematopoietic Stem Cells Model*

Qualitative Properties in a More General Delayed Hematopoietic Stem Cells Model*

In this paper, we consider a more general model describing the dynamics of Hematopoietic Stem Cells (HSC) model with one delay. Its dynamics are studied in terms of local stability and Hopf bifurcation. We prove the existence of the possible steady state and their stability with respect to the ti...

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Main Authors: Aziz-Alaoui M. A., Yafia R.
Format: Article
Language:English
Published: EDP Sciences 2013-05-01
Series:ESAIM: Proceedings and Surveys
Online Access:http://dx.doi.org/10.1051/proc/201339009
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spelling doaj-d531878c004249de8da6e19d0dd050282021-08-02T09:29:59ZengEDP SciencesESAIM: Proceedings and Surveys1270-900X2013-05-0139667710.1051/proc/201339009Qualitative Properties in a More General Delayed Hematopoietic Stem Cells Model*Aziz-Alaoui M. A.Yafia R.In this paper, we consider a more general model describing the dynamics of Hematopoietic Stem Cells (HSC) model with one delay. Its dynamics are studied in terms of local stability and Hopf bifurcation. We prove the existence of the possible steady state and their stability with respect to the time delay and without delay. We show that a sequence of Hopf bifurcations occur at the positive steady state as the delay crosses some critical values. We illustrate our results by some numerical simulations. http://dx.doi.org/10.1051/proc/201339009
collection DOAJ
language English
format Article
sources DOAJ
author Aziz-Alaoui M. A.
Yafia R.
spellingShingle Aziz-Alaoui M. A.
Yafia R.
Qualitative Properties in a More General Delayed Hematopoietic Stem Cells Model*
ESAIM: Proceedings and Surveys
author_facet Aziz-Alaoui M. A.
Yafia R.
author_sort Aziz-Alaoui M. A.
title Qualitative Properties in a More General Delayed Hematopoietic Stem Cells Model*
title_short Qualitative Properties in a More General Delayed Hematopoietic Stem Cells Model*
title_full Qualitative Properties in a More General Delayed Hematopoietic Stem Cells Model*
title_fullStr Qualitative Properties in a More General Delayed Hematopoietic Stem Cells Model*
title_full_unstemmed Qualitative Properties in a More General Delayed Hematopoietic Stem Cells Model*
title_sort qualitative properties in a more general delayed hematopoietic stem cells model*
publisher EDP Sciences
series ESAIM: Proceedings and Surveys
issn 1270-900X
publishDate 2013-05-01
description In this paper, we consider a more general model describing the dynamics of Hematopoietic Stem Cells (HSC) model with one delay. Its dynamics are studied in terms of local stability and Hopf bifurcation. We prove the existence of the possible steady state and their stability with respect to the time delay and without delay. We show that a sequence of Hopf bifurcations occur at the positive steady state as the delay crosses some critical values. We illustrate our results by some numerical simulations.
url http://dx.doi.org/10.1051/proc/201339009
work_keys_str_mv AT azizalaouima qualitativepropertiesinamoregeneraldelayedhematopoieticstemcellsmodel
AT yafiar qualitativepropertiesinamoregeneraldelayedhematopoieticstemcellsmodel
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