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

Mahtab Mehrabbeik, Atefeh Ahmadi, Fatemeh Bakouie, Amir Homayoun Jafari, Sajad Jafari and Dibakar Ghosh ()
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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
Sajad Jafari: Department of Biomedical Engineering, 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

Mathematics, 2023, vol. 11, issue 13, 1-18

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.

Keywords: higher-order network; simplicial complex; synchronization; neuron; map-based model (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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