Boundedness and Lyapunov function for a nonlinear system of hematopoietic stem cell dynamics

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• 作者：Mostafa Adimy ; Fabien Crauste ; Abderrahim El Abdllaoui
• 刊名：Comptes Rendus Mathematique
• 出版年：2010
• 出版时间：April 2010
• 年：2010
• 卷：348
• 期：7-8
• 页码：373-377
• 全文大小：145 K

文摘

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.