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
,
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
and
of the delay such that
is asymptotically stable for
and unstable for
.
We show that
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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