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Design of a high-gain observer for the synchronization of chimera states in neurons coupled with fractional dynamics

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

Abstract

In this paper, we propose a high-gain observer to synchronize chimera states in coupled neurons with fractional dynamics. The observer allows the synchronization with a master–slave topology. The master describes a dynamical system in state-space representation, whereas the slave is described by a high-gain state observer. The fractional differential equations are described by the Riemann–Liouville fractional derivative, also for non-local conformable derivatives and Atangana–Baleanu operators both in Caputo sense. We present numerical simulations involving the synchronization of Hindmarsh–Rose and Hodgking–Huxley models. The numerical simulations showed that the chimera states can be synchronized using fractional derivatives. 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., 2020. "Design of a high-gain observer for the synchronization of chimera states in neurons coupled with fractional dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 539(C).
    • Handle: RePEc:eee:phsmap:v:539:y:2020:i:c:s0378437119316449
    DOI: 10.1016/j.physa.2019.122896
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    References listed on IDEAS

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    1. Coronel-Escamilla, A. & Gómez-Aguilar, J.F. & Torres, L. & Escobar-Jiménez, R.F. & Valtierra-Rodríguez, M., 2017. "Synchronization of chaotic systems involving fractional operators of Liouville–Caputo type with variable-order," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 487(C), pages 1-21.
    2. Abdon Atangana & Aydin Secer, 2013. "A Note on Fractional Order Derivatives and Table of Fractional Derivatives of Some Special Functions," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, April.
    3. 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.
    4. Atangana, Abdon & Jain, Sonal, 2018. "The role of power decay, exponential decay and Mittag-Leffler function’s waiting time distribution: Application of cancer spread," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 330-351.
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    1. Ngueuteu Mbouna, S.G. & Banerjee, Tanmoy & Yamapi, René & Woafo, Paul, 2022. "Diverse chimera and symmetry-breaking patterns induced by fractional derivation effect in a network of Stuart-Landau oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).

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