Geodesic
Qualitative Properties in a More General Delayed Hematopoietic Stem Cells Model
R. Yafia1 ; M. A. Aziz-Alaoui2
1 Corresponding author: R. Yafia, yafia1@yahoo.fr, Ibnou Zohr University, Polydisciplinary Faculty of Ouarzazate, B.P : 638, Ouarzazate, Morocco
2 Laboratoire de Mathématiques Appliquées, 25 Rue Ph. Lebon, BP 540, 76058 Le Havre Cedex, France.
ESAIM. Proceedings, Tome 39 (2013), pp. 66-77.

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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.
DOI : 10.1051/proc/201339009

R. Yafia 1 ; M. A. Aziz-Alaoui 2

1 Corresponding author: R. Yafia, yafia1@yahoo.fr, Ibnou Zohr University, Polydisciplinary Faculty of Ouarzazate, B.P : 638, Ouarzazate, Morocco
2 Laboratoire de Mathématiques Appliquées, 25 Rue Ph. Lebon, BP 540, 76058 Le Havre Cedex, France. 
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R. Yafia; M. A. Aziz-Alaoui. Qualitative Properties in a More General Delayed Hematopoietic Stem Cells Model. ESAIM. Proceedings, Tome 39 (2013), pp. 66-77. doi : 10.1051/proc/201339009. http://geodesic.mathdoc.fr/articles/10.1051/proc/201339009/

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