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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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    1. Altaf Khan, Muhammad & Ullah, Saif & Farooq, Muhammad, 2018. "A new fractional model for tuberculosis with relapse via Atangana–Baleanu derivative," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 227-238.
    2. Atangana, Abdon & Khan, Muhammad Altaf, 2019. "Validity of fractal derivative to capturing chaotic attractors," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 50-59.
    3. Atangana, Abdon, 2018. "Blind in a commutative world: Simple illustrations with functions and chaotic attractors," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 347-363.
    4. Fatmawati, & Khan, Muhammad Altaf & Azizah, Muftiyatul & Windarto, & Ullah, Saif, 2019. "A fractional model for the dynamics of competition between commercial and rural banks in Indonesia," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 32-46.
    5. Atangana, Abdon, 2018. "Non validity of index law in fractional calculus: A fractional differential operator with Markovian and non-Markovian properties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 688-706.
    6. Ullah, Saif & Altaf Khan, Muhammad & Farooq, Muhammad, 2018. "A fractional model for the dynamics of TB virus," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 63-71.
    7. Bin, Deng & Jiang, Wang & Xiangyang, Fei, 2006. "Synchronizing two coupled chaotic neurons in external electrical stimulation using backstepping control," Chaos, Solitons & Fractals, Elsevier, vol. 29(1), pages 182-189.
    8. Bin, Deng & Jiang, Wang & Xiangyang, Fei, 2005. "Chaotic synchronization with gap junction of multi-neurons in external electrical stimulation," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 1185-1192.
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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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