Delay Differential Equations and Autonomous Oscillations in Hematopoietic Stem Cell Dynamics Modeling
Delay Differential Equations and Autonomous Oscillations in Hematopoietic Stem Cell Dynamics Modeling
复制标题
造血干细胞动力学建模中的时滞微分方程和自主振荡
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
F. Crauste
中科院分区：
文献类型：
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作者：
M. Adimy;F. Crauste
我们说明的外观振荡解决方案的延迟微分方程建模造血干细胞动力学。我们专注于自主振荡，所产生的后果，系统的不稳定，例如通过一个霍普夫分岔。造血干细胞动力学模型被认为能够描述周期性血液病，如慢性粒细胞白血病和周期性中性粒细胞减少症。在回顾了表现出振荡的延迟模型之后，我们重点讨论了三个例子，描述了不同的延迟：离散延迟，连续分布延迟和状态依赖延迟。在每种情况下，我们展示了系统如何可以有振荡的解决方案，我们这些解决方案的周期和振幅的特点。
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.