Delay Differential Equations and Autonomous Oscillations in Hematopoietic Stem Cell Dynamics Modeling

M. Adimy; F. Crauste

doi:10.1051/mmnp/20127601

M. Adimy ^1,² ; F. Crauste ^1,²

¹ INRIA Team Dracula, INRIA Grenoble Rhône-Alpes Center, France
² Université de Lyon, Université Lyon 1, CNRS UMR 5208, Institut Camille Jordan, 43 blvd du 11 novembre 1918, F-69622 Villeurbanne-Cedex, France

Mathematical modelling of natural phenomena, Tome 7 (2012) no. 6, pp. 1-22

Voir la notice de l'article provenant de la source EDP Sciences

Résumé

We illustrate the appearance of oscillating solutions in delay differential equations modeling hematopoietic stem cell dynamics. We focus on autonomous oscillations, arising as consequences of a destabilization of the system, for instance through a Hopf bifurcation. Models of hematopoietic stem cell dynamics are considered for their abilities to describe periodic hematological diseases, such as chronic myelogenous leukemia and cyclical neutropenia. After a review of delay models exhibiting oscillations, we focus on three examples, describing different delays: a discrete delay, a continuous distributed delay, and a state-dependent delay. In each case, we show how the system can have oscillating solutions, and we characterize these solutions in terms of periods and amplitudes.

DOI : 10.1051/mmnp/20127601

Affiliations des auteurs :

M. Adimy ^{1, 2} ; F. Crauste ^{1, 2}

¹ INRIA Team Dracula, INRIA Grenoble Rhône-Alpes Center, France
² Université de Lyon, Université Lyon 1, CNRS UMR 5208, Institut Camille Jordan, 43 blvd du 11 novembre 1918, F-69622 Villeurbanne-Cedex, France

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M. Adimy; F. Crauste. Delay Differential Equations and Autonomous Oscillations in Hematopoietic Stem Cell Dynamics Modeling. Mathematical modelling of natural phenomena, Tome 7 (2012) no. 6, pp. 1-22. doi: 10.1051/mmnp/20127601

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