论文标题
单个延迟的葡萄糖胰岛素调节模型中的全球稳定性和周期性
Global Stability and Periodicity in a Glucose-Insulin Regulation Model with a Single Delay
论文作者
论文摘要
考虑了人体中葡萄糖 - 胰岛素相互作用过程的延迟建模的微分方程的二维系统。为系统中唯一的正均衡得出了足够的条件，以使全球渐近稳定。它们是根据限制间隔图以固定点的全球诱之间吸引力给出的。在平衡不稳定的情况下显示了缓慢振荡的周期性解决方案的存在。数学结果由广泛的数值模拟支持。结果表明，系统中的典型行为是稳定的周期性解决方案或唯一稳定平衡的收敛性。几种周期溶液与稳定平衡的共存被证明是一种可能性。
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.
