一类具有互补型营养基的时滞恒化器模型Hopf分支的存在性  

Existence of Hopf Bifurcation for a Delay Chemostat Model with Complementary Nutrients

作　　者：孙树林[1] 郭翠花 张宁 SUN SHULIN;GUO CUIHUA;ZHANG NING(School of Mathematics and Computer Science,Shanxi Normal University,Linfen 041000,China;School of Mathematics Science,Shanxi University,Taiyuan 030006,China)

机构地区：[1]山西师范大学数学与计算机科学学院,临汾041000 [2]山西大学数学科学学院,太原030006

出　　处：《应用数学学报》2019年第5期629-646,共18页Acta Mathematicae Applicatae Sinica

基　　金：山西省自然科学基金(201801D121011)资助项目

摘　　要：该文研究了一类具有互补型营养基和两个不同时滞的微生物培养恒化器模型.首先利用Lyapunov函数和极限集理论使系统降维,然后对时滞分情况讨论其对系统动力学行为的影响,得到系统平衡点稳定和Hopf分支存在的充分条件.最后,通过数值模拟验证了主要结论的正确性.This paper studies the existence of Hopf bifurcation for a chemostat model with complementary nutrients and two different delays.Firstly,a four dimension system is reduced to a two dimension system by Lyapunov function and limit set theory.Afterwards,according to the different cases of the delays,respectively,the influence of delays on the dynamic behaviors of the system is discussed,the sufficient conditions are obtained for the stability of the positive equilibrium and the existence of Hopf bifurcation in this system.Finally,some numerical simulations are carried out to verify the theoretical results in this paper.

关 键 词：恒化器 时滞 HOPF分支 稳定 

分 类 号：O175.14[理学—数学]