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.
Nous considérons un système d'équations différentielles non-linéaires avec retards distribués. L'existence d'une unique solution globale sous une condition classique de Lipschitz est tout d'abord mentionnée. Ensuite, des conditions suffisantes pour la stabilité globale de la population de cellules sont établies, par l'analyse du comportement asymptotique de l'état d'équilibre trivial et en utilisant une fonction de Lyapunov. Finalement, des conditions suffisantes pour une proliferation non-bornée d'une génération de cellules sont données.
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Mostafa Adimy 1; Fabien Crauste 2; Abderrahim El Abdllaoui 3
@article{CRMATH_2010__348_7-8_373_0, author = {Mostafa Adimy and Fabien Crauste and Abderrahim El Abdllaoui}, title = {Boundedness and {Lyapunov} function for a nonlinear system of hematopoietic stem cell dynamics}, journal = {Comptes Rendus. Math\'ematique}, pages = {373--377}, publisher = {Elsevier}, volume = {348}, number = {7-8}, year = {2010}, doi = {10.1016/j.crma.2010.02.018}, language = {en}, }
TY - JOUR AU - Mostafa Adimy AU - Fabien Crauste AU - Abderrahim El Abdllaoui TI - Boundedness and Lyapunov function for a nonlinear system of hematopoietic stem cell dynamics JO - Comptes Rendus. Mathématique PY - 2010 SP - 373 EP - 377 VL - 348 IS - 7-8 PB - Elsevier DO - 10.1016/j.crma.2010.02.018 LA - en ID - CRMATH_2010__348_7-8_373_0 ER -
%0 Journal Article %A Mostafa Adimy %A Fabien Crauste %A Abderrahim El Abdllaoui %T Boundedness and Lyapunov function for a nonlinear system of hematopoietic stem cell dynamics %J Comptes Rendus. Mathématique %D 2010 %P 373-377 %V 348 %N 7-8 %I Elsevier %R 10.1016/j.crma.2010.02.018 %G en %F CRMATH_2010__348_7-8_373_0
Mostafa Adimy; Fabien Crauste; Abderrahim El Abdllaoui. Boundedness and Lyapunov function for a nonlinear system of hematopoietic stem cell dynamics. Comptes Rendus. Mathématique, Volume 348 (2010) no. 7-8, pp. 373-377. doi : 10.1016/j.crma.2010.02.018. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.02.018/
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