2004-Fez conference on Differential Equations and Mechanics.
Electronic Journal of Differential Equations,
Conference 11, 2004, pp. 167-173.
Title: Stability and Hopf bifurcation in
a haematopoietic stem cells model
Authors: Hamad Talibi Alaoui (Univ. Chouaib Doukkali, El Jadida, Morocco)
Radouane Yafia (Univ. Chouaib Doukkali, El Jadida, Morocco)
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 $\tau <\tau _{0}$
and unstable for $\tau _{0}<\tau <\overline{\tau }$.
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.