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



Mehrabbeik M1 ; Ahmadi A1 ; Bakouie F2 ; Jafari AH3, 4 ; Jafari S1, 5 ; Ghosh D6
Authors
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Authors Affiliations
  1. 1. Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), P.O. Box 15875-4413, Tehran, Iran
  2. 2. Institute for Cognitive and Brain Sciences, Shahid Beheshti University, P.O. Box 14155-6354, Tehran, Iran
  3. 3. Biomedical Engineering and Medical Physics Department, Faculty of Medicine, Tehran University of Medical Sciences (TUMS), P.O. Box 14155-6559, Tehran, Iran
  4. 4. Research Center for Biomedical Technologies and Robotics (RCBTR), P.O. Box 14185-615, Tehran, Iran
  5. 5. Health Technology Research Institute, Amirkabir University of Technology (Tehran Polytechnic), P.O. Box 15875-4413, Tehran, Iran
  6. 6. Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata, 700108, India

Source: Mathematics Published:2023


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. © 2023 by the authors.