微生物培养模型的一致持续生存与周期解

Uniform persistence and periodic solution of chemostat model

讨论了一类单种群利用两种营养的微生物培养模型．该模型假设营养以周期方式输入并引入了从种群吸收营养到营养被转化为生物量的时滞．以Ｒａｚｕｍｉｋｈｉｎ方法为基础，得到了系统一致持续生存的充分条件．对一般的周期泛函数微分方程，导出了周期解存在的充分条件，并由此获得了微生物培养模型正周期的存在性．

A chemostat model which includes delay and admits periodic nutrient inputs, is considered.Based on the technique of Razumikhin,the sufficient conditions for uniform persistence are obtained.For general periodic functional differential equations,the suffcient conditions for the existence of periodic solution are obtained,therefore,the existence of positive periodic solution to the chemostat model is verified.