The main purpose of this paper is to study the existence of periodic solutions for a nonautonomous differential–difference system describing the dynamics of hematopoietic stem cell (HSC) population under some external periodic regulatory factors at the cellular cycle level. The starting model is a nonautonomous system of two age-structured partial differential equations describing the HSC population in quiescent ($G_0$) and proliferating ($G_1$, $S$, $G_2$ and $M$) phase. We are interested in the effects of periodically time varying coefficients due for example to circadian rhythms or to the periodic use of certain drugs, on the dynamics of HSC population. The method of characteristics reduces the age-structured model to a nonautonomous differential–difference system. We prove under appropriate conditions on the parameters of the system, using topological degree techniques and fixed point methods, the existence of periodic solutions of our model.

本文的主要目的是研究一个非自治的差分系统的周期解的存在，该系统描述了在细胞周期水平上某些外部周期性调节因子作用下造血干细胞（HSC）群体的动力学。初始模型是一个由两个年龄结构的偏微分方程组成的非自治系统，该方程描述了HSC处于静止状态的总体（$G_0$）并激增（$G_{\mathrm{1个}}$， $\mathrm{小号}$， $G_{\mathrm{2个}}$ 和 $\mathrm{中号}$） 阶段。我们对由于例如昼夜节律或某些药物的周期性使用而导致的周期性时变系数对HSC种群动态的影响感兴趣。特征方法将年龄结构模型简化为非自治的差分系统。我们使用拓扑度技术和不动点方法，在适当的条件下证明了系统的参数是否存在周期解。