April  2005, 12(3): 501-522. doi: 10.3934/dcds.2005.12.501

On the stability of a nonlinear maturity structured model of cellular proliferation

1. 

Laboratoire de Mathématiques Appliquées, FRE 2570, Université de Pau et des Pays de l'Adour, Avenue de l'université, 64000 Pau, France

2. 

Department of Physiology, McGill University, McIntyre Medical Sciences Building, 3655 Promenade Sir William Osler, Montreal, QC, Canada H3G 1Y6

Received  October 2003 Revised  September 2004 Published  December 2004

We analyze the asymptotic behavior of a nonlinear mathematical model of cellular proliferation which describes the production of blood cells in the bone marrow. This model takes the form of a system of two maturity structured partial differential equations, with a retardation of the maturation variable and a time delay depending on this maturity. We show that the stability of this system depends strongly on the behavior of the immature cell population. We obtain conditions for the global stability and the instability of the trivial solution.
Citation: Mostafa Adimy, Fabien Crauste, Laurent Pujo-Menjouet. On the stability of a nonlinear maturity structured model of cellular proliferation. Discrete & Continuous Dynamical Systems - A, 2005, 12 (3) : 501-522. doi: 10.3934/dcds.2005.12.501
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