摘要
研究了人工胰岛素泵实现血糖水平稳定性问题.首先证明了该生理系统解的正有界性.由于构造合适的Lyapunov泛函比较困难,采用了新的方法,把该非线性时滞系统转化为系数时变线性时滞系统,构造Lyapunov泛函并利用Razumikhin定理得到了其唯一平衡点的全局指数渐近稳定性条件.结果表明,当技术时滞τ1充分小时,全局指数渐近稳定,血糖水平稳定,易于达到疗效.
The stability problem of glucose level was considered by artificial pancreas.At first,the positivity and boundness of this physiological system were proven.Due to the difficulty of the appropriate Lyapunov functional construction,the new approach was employed.The nonlinear DDEs were transformed into the linear DDEs with the time-dependent coefficients.Then the Lyapunov functional was constructed and the global exponential asymptotic stability conditions of the unique equilibrium were obtained by the Razumikhin Theorem.The result showed that if the technolgical delay τ1 was sufficiently small,the global exponential asymptotic stability and the glucose stability were obtained.Its clinical efficiency could be easily obtained.
出处
《郑州大学学报（理学版）》
CAS
北大核心
2012年第4期50-54,共5页
Journal of Zhengzhou University:Natural Science Edition
基金
国家自然科学基金资助项目
编号10702065
关键词
人工胰岛素泵
糖尿病
生理模型
全局稳定性
血糖稳定
artificial pancreas
diabetes
physiological model
global stability
glucose stability
