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 deduced 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.

考虑了具有延迟模型的人体内葡萄糖-胰岛素相互作用过程的二维微分方程系统。得出了足以使系统中的唯一正平衡成为全局渐近稳定的充分条件。它们是根据限制区间图中固定点的整体吸引性给出的。在平衡不稳定的情况下，表明存在缓慢振荡的周期解。数学结果得到大量数值模拟的支持。可以推断，系统中的典型行为是收敛到稳定的周期解或唯一的稳定平衡。几个周期解和稳定平衡的共存被证明是可能的。