2004-Fez conference on Differential Equations and Mechanics. Electron. J. Diff. Eqns., Conference 11, 2004, pp. 167-173.

Stability and Hopf bifurcation in a haematopoietic stem cells model

Hamad Talibi Alaoui, Radouane Yafia

Abstract:
We consider the Haematopoietic Stem Cells (HSC) Model with one delay, studied by Mackey [4,5] and Andersen and Mackey [1]. There are two possible stationary states in the model. One of them is trivial, the second $E^{*}(\tau )$, depending on the delay, may be non-trivial . This paper investigates the stability of the non trivial state as well as the occurrence of the Hopf bifurcation depending on time delay. We prove the existence and uniqueness of a critical values $\tau_{0}$ and $\overline{\tau}$ of the delay such that $E^{*}(\tau )$ is asymptotically stable for $\tau$ less than $\tau _{0}$ and unstable for $\tau _{0}$ less than $\tau$ less than $\overline{\tau }$. We show that $E^{*}(\tau_{0})$ is a Hopf bifurcation critical point for an approachable model.

Published October 15, 2004
Math Subject Classifications: 34K18
Key Words: Haematopoietic stem cells model; delayed differential equations; Hopf bifurcation; periodic solutions.

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Hamad Talibi Alaoui
Université Chouaib Doukkali Faculté des Sciences
Département de Mathématiques et Informatique
B.P. 20, El Jadida, Morocco
email: talibi@math.net
Radouane Yafia
Université Chouaib Doukkali Faculté des Sciences
Département de Mathématiques et Informatique
B. P. 20, El Jadida, Morocco
email: yafia_radouane@hotmail.com

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