Mathematical modeling is very helpful for noninvasive investigation of glucose-insulin interaction. In this paper, a new time-delay mathematical model is proposed for glucose-insulin endocrine metabolic regulatory feedback system incorporating the [Formula: see text]-cell dynamic and function for regulating and maintaining bloodstream insulin level. The model includes the insulin degradation due to glucose interaction. The dynamical behavior of the model is analyzed and two-dimensional bifurcation diagrams with respect to two essential parameters of the model are obtained. The results show that the time-delay in insulin secretion in response to blood glucose level, and the delay in glucose drop due to increased insulin concentration, can give rise to complex dynamics, such as periodic oscillation. These dynamics are consistent with the biological findings and period doubling cascade and chaotic state which represent metabolic disorder that may lead to diabetes mellitus.

中文翻译：

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一种新的混沌葡萄糖-胰岛素调节系统的延时模型

数学建模对于葡萄糖-胰岛素相互作用的无创研究非常有帮助。本文提出了一种新的葡萄糖-胰岛素内分泌代谢调节反馈系统的时延数学模型，该模型结合了[公式：见正文]-细胞动力学和调节和维持血流胰岛素水平的功能。该模型包括由于葡萄糖相互作用引起的胰岛素降解。分析了模型的动力学行为，得到了模型两个基本参数的二维分岔图。结果表明，胰岛素分泌响应血糖水平的时间延迟，以及由于胰岛素浓度增加而导致的葡萄糖下降延迟，可以引起复杂的动力学，例如周期性振荡。