@article{f67ccfdb567f4a81a90cde3b6dea04b9,
title = "Global stability and periodicity in a glucose-insulin regulation model with a single delay",
abstract = "A two-dimensional system of differential equations with delay modelling the glucose-insulin interaction processes in the human body is considered. Sufficient conditions are derived for the unique positive equilibrium in the system to be globally asymptotically stable. They are given in terms of the global attractivity of the fixed point in a limiting interval map. The existence of slowly oscillating periodic solutions is shown in the case when the equilibrium is unstable. The mathematical results are supported by extensive numerical simulations. It is deduced that typical behaviour in the system is the convergence to either a stable periodic solution or to the unique stable equilibrium. The coexistence of several periodic solutions together with the stable equilibrium is demonstrated as a possibility.",
author = "Maia Angelova and Gleb Beliakov and Anatoli Ivanov and Sergiy Shelyag",
note = "Funding Information: This work was initiated during AI{\textquoteright}s visit to Deakin University, Burwood Campus, in December 2017. He would like to express his appreciation of the accommodation and support from the School of Information Technology, Faculty of Science, and of the hospitality and collegiality from staff and his coauthors. This research was undertaken with the assistance of resources and services from the National Computational Infrastructure (NCI), which is supported by the Australian Government. MA thanks Newton Advanced Fellowship (UK Royal Society) / Academy of Medical Sciences UK for partial funding to develop this research. Funding Information: This work was initiated during AI's visit to Deakin University, Burwood Campus, in December 2017. He would like to express his appreciation of the accommodation and support from the School of Information Technology, Faculty of Science, and of the hospitality and collegiality from staff and his coauthors. This research was undertaken with the assistance of resources and services from the National Computational Infrastructure (NCI), which is supported by the Australian Government. MA thanks Newton Advanced Fellowship (UK Royal Society) / Academy of Medical Sciences UK for partial funding to develop this research. Publisher Copyright: {\textcopyright} 2020",
year = "2021",
month = apr,
doi = "10.1016/j.cnsns.2020.105659",
language = "English (US)",
volume = "95",
journal = "Communications in Nonlinear Science and Numerical Simulation",
issn = "1007-5704",
publisher = "Elsevier",
}