Stability and Hopf bifurcation in a mathematical model of pluripotent stem cell dynamics

We study a mathematical model describing the dynamics of a pluripotent stem cell population involved in the blood production process in the bone marrow. This model is a differential equation with a time delay. The delay describes the cell cycle duration and is uniformly distributed on an interval. W...

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Bibliographic Details
Published in:Nonlinear analysis: real world applications 2005-09, Vol.6 (4), p.651-670
Main Authors: Adimy, Mostafa, Crauste, Fabien, Ruan, Shigui
Format: Article
Language:English
Subjects:
Analysis of PDEs
Blood production system
Delay differential equations
Hopf bifurcation
Mathematics
Stability
Stem cells
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Summary:We study a mathematical model describing the dynamics of a pluripotent stem cell population involved in the blood production process in the bone marrow. This model is a differential equation with a time delay. The delay describes the cell cycle duration and is uniformly distributed on an interval. We obtain stability conditions independent of the delay and show that the distributed delay can destabilize the entire system. In particular, it is shown that a Hopf bifurcation can occur.
ISSN:1468-1218
1878-5719
DOI:10.1016/j.nonrwa.2004.12.010