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Synchronization patterns with strong memory adaptive control in networks of coupled neurons with chimera states dynamics

Author

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  • Vázquez-Guerrero, P.
  • Gómez-Aguilar, J.F.
  • Santamaria, F.
  • Escobar-Jiménez, R.F.

Abstract

This work presents the Hindmarsh–Rose fractional model of three-state using the Atangana–Baleanu–Caputo fractional derivative with strong memory. The model allows simulating the chimera states in a neural network. To achieve the synchronization was developed a fractional adaptive controller which is based on the uncertainty of the coupling parameters. The synchronization was studied using different fractional-orders and for 15, 40, 65 and 90 neurons. We consider fractional derivatives with nonlocal and non-singular Mittag-Leffler law. The simulations results show that the neurons synchronization is reached using the proposed method. We believe that the application of fractional operators to synchronization of chimera states open a new direction of research in the near future.

Suggested Citation

  • Vázquez-Guerrero, P. & Gómez-Aguilar, J.F. & Santamaria, F. & Escobar-Jiménez, R.F., 2019. "Synchronization patterns with strong memory adaptive control in networks of coupled neurons with chimera states dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 167-175.
    • Handle: RePEc:eee:chsofr:v:128:y:2019:i:c:p:167-175
    DOI: 10.1016/j.chaos.2019.07.057
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    References listed on IDEAS

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    Cited by:

    1. Gao, Wei & Baskonus, Haci Mehmet, 2022. "Deeper investigation of modified epidemiological computer virus model containing the Caputo operator," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    2. Fateev, I. & Polezhaev, A., 2024. "Chimera states in a lattice of superdiffusively coupled neurons," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).

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