An analysis approach to permanence of a delay differential equations model of microorganism flocculation
An analysis approach to permanence of a delay differential equations model of microorganism flocculation
复制标题
微生物絮凝延迟微分方程模型的持久性分析方法
DOI：
10.3934/dcdsb.2021208
复制
发表时间：
2022
影响因子：
1.2
通讯作者：
Wanbiao Ma
中科院分区：
文献类型：
--
作者：
Songbai Guo;Jing-An Cui;Wanbiao Ma
本文建立了具有一般单调功能响应的微生物絮凝时滞微分方程模型，并研究了该模型的持久性，以保证微生物絮凝的可持续性。对于一般微分系统，利用持续理论得到了正平衡的存在性，而利用隐函数定理给出了正平衡的存在性条件。然后，为了得到微生物浓度的最终下界的显式公式，我们提出了一种通用的分析方法，它既不同于持久性理论的传统方法，也扩展了现有相关工作的分析技术。
In this paper, we develop a delay differential equations model of microorganism flocculation with general monotonic functional responses, and then study the permanence of this model, which can ensure the sustainability of the collection of microorganisms. For a general differential system, the existence of a positive equilibrium can be obtained with the help of the persistence theory, whereas we give the existence conditions of a positive equilibrium by using the implicit function theorem. Then to obtain an explicit formula for the ultimate lower bound of microorganism concentration, we propose a general analysis method, which is different from the traditional approaches in persistence theory and also extends the analysis techniques of existing related works.