| Issue |
ESAIM: Proc.
Volume 39, March 2013
Conference on Structural Nonlinear Dynamics and Diagnosis – CSNDD 2012
|
|
|---|---|---|
| Page(s) | 66 - 77 | |
| DOI | https://doi.org/10.1051/proc/201339009 | |
| Published online | 14 May 2013 | |
Qualitative Properties in a More General Delayed Hematopoietic Stem Cells Model*
1 Corresponding author: R. Yafia,
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, 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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Abstract
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.
Key words and phrases : Hematopoietic Stem Cells Model; delayed differential equations; Hopf bifurcation; periodic solutions.
© EDP Sciences, SMAI 2013
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