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Elimination of spiral waves in a one-layer and two-layer network of pancreatic beta cells using a periodic stimuli

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  • Rajagopal, Karthikeyan
  • Wei, Zhouchao
  • Moroz, Irene
  • Karthikeyan, Anitha
  • Duraisamy, Prakash

Abstract

Regulating the glucose level in human body is achieved through the Pancreaticβcells and the glucose release is mainly governed by the bursting activity of the βcells. The Pernarowski model is one of the well known Pancreatic model and is analogous to some of the well known neuron models. The Pernarowski model exhibits chaotic spiking and periodic bursting. In this paper we investigate the dynamical properties of the model through various tools like stability of equilibrium, Hopf's bifurcation, Lyapunov exponents and bifurcation diagrams. As was discussed in literatures the neuron models exhibit spiral waves and so we are interested in understanding such spiral wave generation in the Pernarowski model. For this we construct One-layer and Two-layer network of βcells and study the impact of the plane waves on the spiral wave existence. We show that by a selection of the amplitude and frequency of the stimuli, we can eliminate the spiral waves in the both One-layer and Two-layer network of βcells.

Suggested Citation

  • Rajagopal, Karthikeyan & Wei, Zhouchao & Moroz, Irene & Karthikeyan, Anitha & Duraisamy, Prakash, 2020. "Elimination of spiral waves in a one-layer and two-layer network of pancreatic beta cells using a periodic stimuli," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    • Handle: RePEc:eee:chsofr:v:139:y:2020:i:c:s0960077920304902
    DOI: 10.1016/j.chaos.2020.110093
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    References listed on IDEAS

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    1. Baleanu, Dumitru & Jajarmi, Amin & Mohammadi, Hakimeh & Rezapour, Shahram, 2020. "A new study on the mathematical modelling of human liver with Caputo–Fabrizio fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    2. Jajarmi, Amin & Yusuf, Abdullahi & Baleanu, Dumitru & Inc, Mustafa, 2020. "A new fractional HRSV model and its optimal control: A non-singular operator approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).
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    Cited by:

    1. Rajgopal, Karthikeyan & Karthikeyan, Anitha & V.R., Varun Raj, 2022. "Dynamical behavior of pancreatic β cells with memductance flux coupling: Considering nodal properties and wave propagation in the excitable media," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    2. Smidtaite, Rasa & Ragulskis, Minvydas, 2022. "Spiral waves of divergence in the Barkley model of nilpotent matrices," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    3. El-Nabulsi, Rami Ahmad & Anukool, Waranont, 2024. "Spiral waves in fractal dimensions and their elimination in λ − ω systems with less damaging intervention," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    4. Hu, Yipeng & Ding, Qianming & Wu, Yong & Jia, Ya, 2023. "Polarized electric field-induced drift of spiral waves in discontinuous cardiac media," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).

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