一类时滞造血模型周期解的指数稳定性  

Exponential stability of periodic solutions for a hematopoiesis model with a time-varying delay

作　　者：李华 龙志文 LI Hua;LONG Zhiwen(School of Mathematics and Big Data,Anhui University of Science and Technology,Huainan 232001,China;School of Mathematics and Finance,Hunan University of Humanities,Science and Technology,Loudi 417000,China)

机构地区：[1]安徽理工大学数学与大数据学院,安徽淮南232001 [2]湖南人文科技学院数学与金融学院,湖南娄底417000

出　　处：《哈尔滨商业大学学报（自然科学版）》2023年第4期426-430,共5页Journal of Harbin University of Commerce：Natural Sciences Edition

基　　金：安徽省自然科学基金(No.2208085MA04);安徽省教育厅高校自然科学研究项目重大项目(No.KJ2020ZD32);安徽省教育厅高校优秀人才支持计划重点项目(No.gxyqZD2022035);湖南省教育厅优秀青年项目(No.18B456).

摘　　要：研究了一类具有时变时滞的造血模型,利用Brouwer不动点定理,证明了所研究模型周期解的存在性,通过构造合适的Lyapunov函数,运用微分不等式技巧、连续性理论以及一种新的分析方法,获得了该模型正周期解指数稳定性的充分判据.给出了一个数值例子,证明了理论结果的有效性,并运用Matlab绘制了造血模型数值解的拟合图像.结论改进和推广了已有文献的相关结果.A class of hematopoietic model with time-varying delay was studied,using Brouwer fixed point theorem,the existence of periodic solution of the model was proved.By constructing suitable Lyapunov function,using differential inequality technique,continuity theory and a new analytical method,some sufficient criteria of exponential stability of the positive periodic solution of the model was obtained.Finally,a numerical example was given to prove the effectiveness of the theoretical results,and Matlab was used to draw the fitting image of the numerical solution of the hematopoietic model.Conclusion had improved and generalized the corresponding results of existing literatures.

关 键 词：造血模型 周期解 指数稳定性 非自治 时滞 不动点定理 

分 类 号：O193[理学—数学]