Department of Mathematics and Institute of Molecular Biophysics, Florida State University, Tallahassee, Florida 32306, USA.
Department of Biomedical Informatics, Columbia University, New York, New York 10032, USA.
Chaos. 2021 Feb;31(2):023142. doi: 10.1063/5.0027682.
Medical practice in the intensive care unit is based on the assumption 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 framework 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 framework 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.
重症监护病房的医疗实践基于这样一种假设，即人体葡萄糖-胰岛素系统等生理系统是可预测的。我们证明，葡萄糖-胰岛素系统中的延迟会导致持续的时间混沌，从而使系统变得不可预测。具体来说，我们展示了超短周期葡萄糖-胰岛素模型中的这种混沌。这个经过良好验证的有限维模型将反馈延迟表示为三阶滤波器。我们使用来自光滑动力系统的一阶映射理论，精确地解释了由此产生的延迟诱导不确定性（DIU）的性质。我们提出了一个框架，人们可以用它来诊断一般振荡动力系统中的 DIU。对于无限维延迟系统，不存在一阶映射理论的类似物。然而，我们通过展示线性剪切流中的持续时间混沌，表明我们的 DIU 框架中编码的几何原理适用于此类系统。我们的结果具有广泛的潜在适用性，因为延迟在整个数学生理学中无处不在。
