中文摘要：

针对2型糖尿病建立了一个三时滞微分方程模型来描述糖尿病患者体内血糖-胰岛素调节系统的动力学行为.通过定性分析,得到了系统解的正性及有界性;通过构造Lyapunov函数的方法证明了在2型糖尿病患者体内胰脏仍保留部分胰岛素分泌功能的情况下,系统的正周期解是全局渐近稳定的,并给出了相应的稳定性判据.

英文摘要：

For type-2 diabetes, an delay differential equation （DDE） model of the glucose-insulin regulation sys- tem with three time delays was proposed to describe the dynamic behavior inside the diabetes patient＇ s body. The posi- tivity and boundness of solutions were analyzed. Furthermore, the globally asymptotical stability of the positive periodic solution was derived by a Lyapunov function in the situation of the type-2 diabetes. The relevant stability criterions were given.