Existence regions of positive periodic solutions for a discrete hematopoiesis model with unimodal production functions
Existence regions of positive periodic solutions for a discrete hematopoiesis model with unimodal production functions
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DOI：
10.1016/j.apm.2018.11.003
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发表时间：
2019-04
影响因子：
5
通讯作者：
Yan Yan-Yan;J. Sugie
中科院分区：
文献类型：
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作者：
Yan Yan-Yan;J. Sugie
本文考虑了一个描述血细胞增减的离散模型。该造血模型是一个具有单峰生产函数的时滞微分方程的离散化，其系数和时滞是具有ω周期的周期离散函数。本文研究了正ω-周期解的存在性.利用重合度理论中著名的延拓定理证明了我们的结果。同时也阐明了正ω-周期解的存在范围。最后给出了一个具体的例子和模拟结果.最后，我们研究了构成我们模型的正数和系数如何影响血细胞计数的上限和下限。
A discrete model describing the increase and decrease of blood cells is considered in this paper. This hematopoiesis model is a discretization of a delay differential equation with unimodal production function whose coefficients and delays are periodic discrete functions withω-period. This paper is concerned with the existence of positiveω-periodic solutions. Our results are proved by using the well-known continuation theorem of coincidence degree theory. The existence range of the positiveω-periodic solutions is also clarified. A concrete example and its simulation are also given to illustrate our result. Finally, we examine how positive numbers and coefficients making up our model influence the upper and lower limits of blood cell counts.