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

2 Citations (Scopus)


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
Article number105659
Number of pages18
JournalCommunications in Nonlinear Science and Numerical Simulation
Early online date7 Dec 2020
Publication statusPublished - Apr 2021
Externally publishedYes


  • Delay differential equations
  • Diabetes
  • Existence of periodic solutions
  • Global asymptotic stability
  • Limiting interval maps
  • Linearization
  • Stability analysis


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