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Investigation of stability in a two-delay model of the ultradian oscillations in glucose-insulin regulation
journal contribution
posted on 2015-09-01, 00:00 authored by B Huard, J F Easton, Maia Angelova TurkedjievaMaia Angelova TurkedjievaIn this paper, a two-delay model for the ultradian oscillatory behaviour of the glucose-insulin regulation system is studied. Hill functions are introduced to model nonlinear physiological interactions within this system and ranges on parameters reproducing biological oscillations are determined on the basis of analytical and numerical considerations. Local and global stability are investigated and delay-dependent conditions are obtained through the construction of Lyapunov-Krasovskii functionals. The effect of Hill parameters on these conditions, as well as the boundary of the stability region in the delay domain, are established for the first time. Numerical simulations demonstrate that the model with Hill functions represents well the oscillatory behaviour of the system with the advantage of incorporating new meaningful parameters. The influence of the time delays on the period of oscillations and the sensitivity of the latter to model parameters, in particular glucose infusion, are investigated. The model can contribute to the better understanding and treatment of diabetes.
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Journal
Communications in nonlinear science and numerical simulationVolume
26Issue
1-3Pagination
211 - 222Publisher
ElsevierLocation
Amsterdam, The NetherlandsPublisher DOI
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ISSN
1007-5704Language
engPublication classification
C Journal article; C1.1 Refereed article in a scholarly journalCopyright notice
2015, The AuthorsUsage metrics
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No categories selectedKeywords
Glucose–insulin regulationDifferential delay equationsStability analysisHill functionsScience & TechnologyPhysical SciencesTechnologyMathematics, AppliedMathematics, Interdisciplinary ApplicationsMechanicsPhysics, Fluids & PlasmasPhysics, MathematicalMathematicsPhysicsGlucose-insulin regulationTIME DELAYSSYSTEMSECRETION
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