单时滞葡萄糖-胰岛素调节模型的全局稳定性和周期性
Global Stability and Periodicity in a Glucose-Insulin Regulation Model with a Single Delay
摘要：
考虑了人体内葡萄糖-胰岛素相互作用过程的具有时滞的二维微分方程系统。得到了系统唯一正平衡点全局渐近稳定的充分条件。它们是根据极限区间映射中不动点的全局吸引性给出的。当平衡点不稳定时，证明了慢振荡周期解的存在性。数学结果得到了广泛的数值模拟的支持。它表明，在系统中的典型行为是收敛到一个稳定的周期解或唯一的稳定平衡。几个周期解的共存与稳定平衡被证明是一种可能性。
英文摘要：
A two-dimensional system of differential equations with delay modelling the glucose-insulin interaction processes in the human body is considered. Sufficient conditions are derived for the unique positive equilibrium in the system to be globally asymptotically stable. They are given in terms of the global attractivity of the fixed point in a limiting interval map. The existence of slowly oscillating periodic solutions is shown in the case when the equilibrium is unstable. The mathematical results are supported by extensive numerical simulations. It is shown that typical behaviour in the system is the convergence to either a stable periodic solution or to the unique stable equilibrium. The coexistence of several periodic solutions together with the stable equilibrium is demonstrated as a possibility.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
