Delay-Induced Uncertainty for a Paradigmatic Glucose-Insulin Model
arXiv:2007.09309 · doi:10.1063/5.0027682
Abstract
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.
arXiv comment19 pages; 9 figures
References in corpus (9)
- Transcriptional delay stabilizes bistable gene networks
- Shear-Induced Chaos
- Population physiology: leveraging population scale (EHR) data to understand human endocrine dynamics
- From limit cycles to strange attractors
- Enhancing noise-induced switching times in systems with distributed delays
- Strange attractors in periodically-kicked degenerate Hopf bifurcations
- A Simple Modeling Framework For Prediction In The Human Glucose-Insulin System
- Multi-Task Gaussian Processes and Dilated Convolutional Networks for Reconstruction of Reproductive Hormonal Dynamics
- Reduced model for female endocrine dynamics: Validation and functional variations