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The Impact of Higher-Order Interactions on the Synchronization of Hindmarsh–Rose Neuron Maps under Different Coupling Functions

Author

Listed:
  • Mahtab Mehrabbeik

    (Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran P.O. Box 15875-4413, Iran)

  • Atefeh Ahmadi

    (Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran P.O. Box 15875-4413, Iran)

  • Fatemeh Bakouie

    (Institute for Cognitive and Brain Sciences, Shahid Beheshti University, Tehran P.O. Box 14155-6354, Iran)

  • Amir Homayoun Jafari

    (Biomedical Engineering and Medical Physics Department, Faculty of Medicine, Tehran University of Medical Sciences (TUMS), Tehran P.O. Box 14155-6559, Iran
    Research Center for Biomedical Technologies and Robotics (RCBTR), Tehran P.O. Box 14185-615, Iran)

  • Sajad Jafari

    (Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran P.O. Box 15875-4413, Iran
    Health Technology Research Institute, Amirkabir University of Technology (Tehran Polytechnic), Tehran P.O. Box 15875-4413, Iran)

  • Dibakar Ghosh

    (Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108, India)

Abstract

In network analysis, links depict the connections between each pair of network nodes. However, such pairwise connections fail to consider the interactions among more agents, which may be indirectly connected. Such non-pairwise or higher-order connections can be signified by involving simplicial complexes. The higher-order connections become even more noteworthy when it comes to neuronal network synchronization, an emerging phenomenon responsible for the many biological processes in real-world phenomena. However, involving higher-order interactions may considerably increase the computational costs. To confound this issue, map-based models are more suitable since they are faster, simpler, more flexible, and computationally more optimal. Therefore, this paper addresses the impact of pairwise and non-pairwise neuronal interactions on the synchronization state of 10 coupled memristive Hindmarsh–Rose neuron maps. To this aim, electrical, inner linking, and chemical synaptic functions are considered as two- and three-body interactions in three homogeneous and two heterogeneous cases. The results show that through chemical pairwise and non-pairwise synapses, the neurons achieve synchrony with the weakest coupling strengths.

Suggested Citation

  • Mahtab Mehrabbeik & Atefeh Ahmadi & Fatemeh Bakouie & Amir Homayoun Jafari & Sajad Jafari & Dibakar Ghosh, 2023. "The Impact of Higher-Order Interactions on the Synchronization of Hindmarsh–Rose Neuron Maps under Different Coupling Functions," Mathematics, MDPI, vol. 11(13), pages 1-18, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:13:p:2811-:d:1177088
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    References listed on IDEAS

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    1. Xu, Ying & Jia, Ya & Ma, Jun & Alsaedi, Ahmed & Ahmad, Bashir, 2017. "Synchronization between neurons coupled by memristor," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 435-442.
    2. Ruofeng Rao & Zhi Lin & Xiaoquan Ai & Jiarui Wu, 2022. "Synchronization of Epidemic Systems with Neumann Boundary Value under Delayed Impulse," Mathematics, MDPI, vol. 10(12), pages 1-10, June.
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    Cited by:

    1. Ma, Jun & Guo, Yitong, 2024. "Model approach of electromechanical arm interacted with neural circuit, a minireview," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).

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