具有非单调反馈的随机Mackey-Glass造血模型  

Stochastic Mackey-Glass Model of Hematopoiesis with Non-monotone Feedback

作　　者：王文涛 刘福窑 陈娓 WANG WENTAO;LIU FUYAO;CHEN WEI(School of Mathematics,Physics and Statistics,Shanghai University of Engineering Science,Shanghai 201620,China;School of Statistics and Mathematics,Shanghai Lixin University of Accounting and Finance,Shanghai 201209,China)

机构地区：[1]上海工程技术大学数理与统计学院,上海201620 [2]上海立信会计金融学院统计与数学学院,上海201209

出　　处：《应用数学学报》2020年第5期865-874,共10页Acta Mathematicae Applicatae Sinica

基　　金：浙江省自然科学基金(LY18A010019)资助。

摘　　要：考虑到损坏率受到白噪声的干扰,本文介绍了一类具有非单调反馈的随机Mackey-Glass造血模型,用于描述其在随机环境中的动力学行为.首先,研究了在非负初值条件下全局正解的存在性和唯一性.接着,估计了解的平均最终有界性和Lyapunov指数.最后,给出了一个实例以及数值模拟以验证理论分析结果.Considering that the destruction rate is perturbed by white noises,we introduce a stochastic Mackey-Glass model of hematopoiesis with non-monotone feedback to describe its dynamics behaviors in random environments.Firstly,we study the existence and uniqueness of the global positive solution with the nonnegative initial condition.Next,we estimate its ultimate boundedness in mean and Lyapunov exponent.Finally,an example with its numerical simulations is carried out to validate the analytical results.

关 键 词：布朗运动 Mackey-Glass模型 非单调反馈 最终有界性 

分 类 号：O193[理学—数学]