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

Mostafa Adimy 1, * Fabien Crauste 1, 2, *
* Auteur correspondant
1 DRACULA - Multi-scale modelling of cell dynamics : application to hematopoiesis
CGMC - Centre de génétique moléculaire et cellulaire, Inria Grenoble - Rhône-Alpes, ICJ - Institut Camille Jordan [Villeurbanne], UCBL - Université Claude Bernard Lyon 1 : EA
Abstract : 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.
Type de document :
Article dans une revue
Mathematical Modelling of Natural Phenomena, EDP Sciences, 2012, 7 (6), pp.1-22. <10.1051/mmnp/20127601>
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https://hal.inria.fr/hal-00766339
Contributeur : Fabien Crauste <>
Soumis le : mardi 18 décembre 2012 - 10:44:08
Dernière modification le : lundi 5 octobre 2015 - 16:59:16

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Mostafa Adimy, Fabien Crauste. Delay Differential Equations and Autonomous Oscillations in Hematopoietic Stem Cell Dynamics Modeling. Mathematical Modelling of Natural Phenomena, EDP Sciences, 2012, 7 (6), pp.1-22. <10.1051/mmnp/20127601>. <hal-00766339>

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