Delay-induced uncertainty for a paradigmatic glucose–insulin model
Open accessAbstract
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.
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Time delays may induce uncertainty and make machine learning challenging to capture chaotic phenomena.
“Time delays, which are common in modeling the metabolic system (82–85), may induce uncertainty and make machine learning challenging to capture chaotic phenomena (86, 87).”
From The progression of secondary diabetes: A review of modeling studies (2022) · cites this paper as [86]
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- Authors
- Karamched, B., Hripcsak, G., Albers, D., & Ott, W.
- Affiliations
- Florida State University (US)
- Columbia University (US)
- University of Colorado Anschutz (US)
- University of Houston (US)
- Corresponding author
- Ott, William
- Venue
- Chaos: An Interdisciplinary Journal of Nonlinear Science
- Publisher
- AIP Publishing
- Published
- 2021-02-01
- Volume
- 31
- Issue
- 2
- Pages
- 023142-023142
- ISSN
- 1054-1500 (ISSN-L)
- 1089-7682
- PMC
- PMC7910007
- OpenAlex
- W3113053863
- Cited by
- 12
- References
- 47
- Citations by year
- 2026: 3 · 2025: 1 · 2024: 1 · 2023: 2 · 2022: 4 · 2021: 1
- FWCI
- 0.79
- Type
- journal article
- Language
- en
- Open access
- green
- www.ncbi.nlm.nih.gov
- Locations
- Chaos An Interdisciplinary Journal of Nonlinear Science (publishedVersion)
- PubMed Central (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Science Foundation (DMS 1816315)
- National Institutes of Health (R01 LM006910, R01 LM012734, R01 GM117138)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Chaos control and synchronization
- Physical Sciences › Mathematics › Mathematical Physics › Mathematical Dynamics and Fractals
- Physical Sciences › Computer Science › Computer Networks and Communications › Nonlinear Dynamics and Pattern Formation
- Keywords
- glucose-insulin model, feedback delay, temporal chaos, linear shear flow, predictability, intensive care
- MeSH terms
- Feedback, Glucose, Humans, Insulin, Uncertainty
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