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Hopf bifurcation and chaos in time-delay model of glucose-insulin regulatory system

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  • Al-Hussein, Abdul-Basset A.
  • Rahma, Fadihl
  • Jafari, Sajad

Abstract

Mathematical modeling is very helpful for non-invasive investigation of glucose-insulin interaction. In this paper a new time delay mathematical model for glucose-insulin endocrine metabolic regulatory feedback system incorporating the β-cell dynamic and function for regulating and maintaining bloodstream insulin level, has been proposed. The proposed model includes the mathematical representation of an important biological fact that the moderate hyperglycemia leads to the growth of the β-cell number (negative feedback) while extreme hyperglycemia leads to the reduction of the β-cell number (positive feedback). The dynamical behavior of the model is analyzed analytically using Hopf bifurcation theorem and numerically such as two dimensional bifurcation diagrams with respect to two essential parameters of the model are obtained. The results show that the time delay in insulin secretion in response to blood glucose level, and the delay in glucose drop due to increased insulin concentration can give rise to complex dynamics, such as periodic oscillation consistent with the biological findings and periodic doubling cascade and chaotic state which represent metabolic disorder that may lead to diabetes mellitus.

Suggested Citation

  • Al-Hussein, Abdul-Basset A. & Rahma, Fadihl & Jafari, Sajad, 2020. "Hopf bifurcation and chaos in time-delay model of glucose-insulin regulatory system," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    • Handle: RePEc:eee:chsofr:v:137:y:2020:i:c:s0960077920302459
    DOI: 10.1016/j.chaos.2020.109845
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    References listed on IDEAS

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    1. Boutayeb, A. & Derouich, M., 2002. "Age structured models for diabetes in East Morocco," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 58(3), pages 215-229.
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    Cited by:

    1. Sardar, Mrinmoy & Khajanchi, Subhas & Biswas, Santosh & Ghosh, Sumana, 2024. "A mathematical model for tumor-immune competitive system with multiple time delays," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    2. Dai, Hao & Han, Zikun & Wang, Qiubao, 2022. "Effects of noise on bursting phenomenon and bifurcation in glucose-insulin regulation system," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    3. Ying, Jiajie & Liang, Yan & Wang, Junlan & Dong, Yujiao & Wang, Guangyi & Gu, Meiyuan, 2021. "A tristable locally-active memristor and its complex dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).

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