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Fractional dynamical behavior of electrical activity in a model of pancreatic β-cells

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  • Bodo, Bertrand
  • Mvogo, Alain
  • Morfu, Saverio

Abstract

The electrical activity of a three dimensional fractional-order model of pancreatic β-cells is numerically studied. The dynamics of the model is understood through the Adams–Bashforth–Moulton predictor corrector scheme, which is a time-domain approach. By considering both integer-order and fractional-order models, we highlight some differences in their dynamics characteristics. It is shown that the fractional model can give rise to chaotic dynamics due to the existence of a Smale horseshoe. Some behaviors related with diabetes mellitus are also reported. The fractional model gets closer to the real biological behavior, thus provides motivation in modeling biological systems with fractional order derivatives.

Suggested Citation

  • Bodo, Bertrand & Mvogo, Alain & Morfu, Saverio, 2017. "Fractional dynamical behavior of electrical activity in a model of pancreatic β-cells," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 426-432.
    • Handle: RePEc:eee:chsofr:v:102:y:2017:i:c:p:426-432
    DOI: 10.1016/j.chaos.2017.04.036
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    References listed on IDEAS

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    1. Bordet, M. & Morfu, S., 2013. "Experimental and numerical study of noise effects in a FitzHugh–Nagumo system driven by a biharmonic signal," Chaos, Solitons & Fractals, Elsevier, vol. 54(C), pages 82-89.
    2. L. J. Ontañón-García & E. Campos-Cantón, 2013. "Discrete Coupling and Synchronization in the Insulin Release in the Mathematical Model of the Cells," Discrete Dynamics in Nature and Society, Hindawi, vol. 2013, pages 1-7, February.
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    Cited by:

    1. Fendzi Donfack, Emmanuel & Nguenang, Jean Pierre & Nana, Laurent, 2020. "On the traveling waves in nonlinear electrical transmission lines with intrinsic fractional-order using discrete tanh method," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    2. Yousefpour, Amin & Jahanshahi, Hadi & Munoz-Pacheco, Jesus M. & Bekiros, Stelios & Wei, Zhouchao, 2020. "A fractional-order hyper-chaotic economic system with transient chaos," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).

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