一类血细胞生成模型的全局渐近稳定性与Hopf分支
Global Asymptotic Stability and Hopf Bifurcation for a Blood Cell Production Model
摘要：
我们分析了一个描述血细胞生产动态的两个具有时滞的微分方程的非线性系统的渐近稳定性。这一过程发生在骨髓中，干细胞在血细胞的整个分裂过程中分化。考虑到造血干细胞的总人口在周期中引入细胞的明确作用，我们导致研究的延迟依赖系数的特征方程。我们确定了模型第一个定态（描述种群灭绝）的全局稳定性的一个充要条件，并且得到了唯一的非平凡正定态的Hopf分支的存在性，从而得到了周期解的存在性.后者与影响以其循环性质而闻名的血细胞的动力学疾病有关。
英文摘要：
We analyze the asymptotic stability of a nonlinear system of two differential equations with delay describing the dynamics of blood cell production. This process takes place in the bone marrow where stem cells differentiate throughout divisions in blood cells. Taking into account an explicit role of the total population of hematopoietic stem cells on the introduction of cells in cycle, we are lead to study a characteristic equation with delay-dependent coefficients. We determine a necessary and sufficient condition for the global stability of the first steady state of our model, which describes the population's dying out, and we obtain the existence of a Hopf bifurcation for the only nontrivial positive steady state, leading to the existence of periodic solutions. These latter are related to dynamical diseases affecting blood cells known for their cyclic nature.
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