Boundedness and Lyapunov function for a nonlinear system of hematopoietic stem cell dynamics |
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| Authors: | Mostafa Adimy Fabien Crauste Abderrahim El Abdllaoui |
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| Institution: | 1. INRIA Rhône-Alpes, institut Camille-Jordan UMR 5208, 43, boulevard du 11 novembre 1918, 69622 Villeurbanne cedex, France;2. Université de Lyon, Université Lyon 1, CNRS UMR 5208 Institut Camille Jordan, Bâtiment du doyen Jean Braconnier, 43 boulevard du 11 novembre 1918, 69622 Villeurbanne cedex, France;3. Laboratoire de mathématiques appliquées CNRS UMR 5142, université de Pau et des Pays de l''Adour, 64000 Pau, France |
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| Abstract: | We investigate a system of nonlinear differential equations with distributed delays, arising from a model of hematopoietic stem cell dynamics. We state uniqueness of a global solution under a classical Lipschitz condition. Sufficient conditions for the global stability of the population are obtained, through the analysis of the asymptotic behavior of the trivial steady state and using a Lyapunov function. Finally, we give sufficient conditions for the unbounded proliferation of a given cell generation. |
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