一类典型葡萄糖-胰岛素模型的时滞不确定性
Delay-Induced Uncertainty for a Paradigmatic Glucose-Insulin Model
摘要：
重症监护病房的医疗实践是基于这样的假设，即生理系统如人葡萄糖-胰岛素系统是可预测的。我们证明了葡萄糖-胰岛素系统内的延迟可以引起持续的时间混沌，使系统不可预测。具体来说，我们表现出这样的超dian葡萄糖胰岛素模型的混乱。这个经过验证的有限维模型将反馈延迟表示为三级滤波器。利用光滑动力系统的秩一映射理论，我们精确地解释了由此产生的延迟诱导不确定性（DIU）的性质。我们开发了一个配方，可以用来诊断DIU在一般的振荡动力系统。对于无限维时滞系统，不存在类似的秩一映射理论。然而，我们表明，编码在我们的DIU配方的几何原理适用于这样的系统表现出持续的时间混沌的线性剪切流。我们的结果是潜在的广泛适用，因为延迟是无处不在的整个数学生理学。
英文摘要：
Medical practice in the intensive care unit is based on the supposition that physiological systems such as the human glucose-insulin system are predictable. We demonstrate that delay within the glucose-insulin system can induce sustained temporal chaos, rendering the system unpredictable. Specifically, we exhibit such chaos for the Ultradian glucose-insulin model. This well-validated, finite-dimensional model represents feedback delay as a three-stage filter. Using the theory of rank one maps from smooth dynamical systems, we precisely explain the nature of the resulting delay-induced uncertainty (DIU). We develop a recipe one may use to diagnose DIU in a general oscillatory dynamical system. For infinite-dimensional delay systems, no analog of the theory of rank one maps exists. Nevertheless, we show that the geometric principles encoded in our DIU recipe apply to such systems by exhibiting sustained temporal chaos for a linear shear flow. Our results are potentially broadly applicable because delay is ubiquitous throughout mathematical physiology.
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