Global stability and periodicity in a glucose-insulin regulation model with a single delay

Maia Angelova, Gleb Beliakov, Anatoli Ivanov, Sergiy Shelyag

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Article number105659
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume95
DOIs
StatePublished - Apr 2021

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modeling and Simulation
  • Applied Mathematics

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