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Interlayer And Intralayer Synchronization In Multiplex Fractional-Order Neuronal Networks

Author

Listed:
  • BO YAN

    (School of Information Engineering, Shaoyang University, Shaoyang 422000, P. R. China)

  • FATEMEH PARASTESH

    (Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran)

  • SHAOBO HE

    (School of Physics and Electronics, Central South University, Changsha 410083, P. R. China)

  • KARTHIKEYAN RAJAGOPAL

    (Centre for Nonlinear Systems, Chennai Institute of Technology, Chennai 600069, India)

  • SAJAD JAFARI

    (Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran5Health Technology Research Institute, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran)

  • MATJAŽ PERC

    (Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, 2000 Maribor, Slovenia7Complexity Science Hub Vienna, Josefstädterstraße 39, 1080 Vienna, Austria8Department of Medical Research, China Medical University Hospital, China Medical University, 404332, Taichung, Taiwan9Alma Mater Europaea, Slovenska ulica 17, 2000 Maribor, Slovenia)

Abstract

Fractional-order models describing neuronal dynamics often exhibit better compatibility with diverse neuronal firing patterns that can be observed experimentally. Due to the overarching significance of synchronization in neuronal dynamics, we here study synchronization in multiplex neuronal networks that are composed of fractional-order Hindmarsh–Rose neurons. We compute the average synchronization error numerically for different derivative orders in dependence on the strength of the links within and between network layers. We find that, in general, fractional-order models synchronize better than integer-order models. In particular, we show that the required interlayer and intralayer coupling strengths for interlayer or intralayer synchronization can be weaker if we reduce the derivative order of the model describing the neuronal dynamics. Furthermore, the dependence of the interlayer or intralayer synchronization on the intralayer or interlayer coupling strength vanishes with decreasing derivative order. To support these results analytically, we use the master stability function approach for the considered multiplex fractional-order neuronal networks, by means of which we obtain sufficient conditions for the interlayer and intralayer synchronizations that are in agreement with numerical results.

Suggested Citation

  • Bo Yan & Fatemeh Parastesh & Shaobo He & Karthikeyan Rajagopal & Sajad Jafari & Matjaå½ Perc, 2022. "Interlayer And Intralayer Synchronization In Multiplex Fractional-Order Neuronal Networks," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(10), pages 1-11, December.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:10:n:s0218348x22401946
    DOI: 10.1142/S0218348X22401946
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