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Impact of network structure on synchronization of Hindmarsh–Rose neurons coupled in structured network

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  • Bandyopadhyay, Abhirup
  • Kar, Samarjit

Abstract

Emergence of synchronization is a remarkable collective phenomena between apparently independent agents in numerous multilevel and complex systems. The evidence of synchronization ranges from the elementary biological organisms to the most sophisticated human societies. In this paper, the problem of synchronization of nonlinearly coupled dynamical networks of Hindmarsh–Rose neurons with a sigmoidal coupling function is addressed. Sufficient condition for synchrony in terms of network structure is developed. A study on the basis of attraction of the complete synchronization is carried out for different structured networks. Also the phase synchronization of dynamical network of Hindmarsh–Rose neurons are studied. The impact of different structural properties of complex network on the phase synchronization are analyzed. The synchronization of Hindmarsh–Rose neurons are evaluated and compared on different structured network like random, regular, small-world, scale-free and modular networks. Interestingly, it was found that networks with high clustering coefficient and neutral degree mixing pattern promote better synchronization. Some chimera like state are also found in different structural networks. Further the effect of time delay dynamics on the synchronization of nonlinearly coupled network of Hindmarsh–Rose neurons are illustrated.

Suggested Citation

  • Bandyopadhyay, Abhirup & Kar, Samarjit, 2018. "Impact of network structure on synchronization of Hindmarsh–Rose neurons coupled in structured network," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 194-212.
    • Handle: RePEc:eee:apmaco:v:333:y:2018:i:c:p:194-212
    DOI: 10.1016/j.amc.2018.03.084
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    References listed on IDEAS

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    1. Liu, Xiwei & Chen, Tianping, 2008. "Synchronization analysis for nonlinearly-coupled complex networks with an asymmetrical coupling matrix," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(16), pages 4429-4439.
    2. Jalili, Mahdi, 2017. "Spike phase synchronization in multiplex cortical neural networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 466(C), pages 325-333.
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    Cited by:

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    2. Branislav Rehák & Volodymyr Lynnyk, 2021. "Synchronization of a Network Composed of Stochastic Hindmarsh–Rose Neurons," Mathematics, MDPI, vol. 9(20), pages 1-16, October.
    3. Li, Yingying & Wei, Zhouchao & Zhang, Wei & Perc, Matjaž & Repnik, Robert, 2019. "Bogdanov–Takens singularity in the Hindmarsh–Rose neuron with time delay," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 180-188.
    4. Akhmet, Marat & Başkan, Kağan & Yeşil, Cihan, 2024. "Markovian noise-induced delta synchronization approach for Hindmarsh–Rose model," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
    5. Zhao, Yiran & Gao, Xiangyun & An, Haizhong & Xi, Xian & Sun, Qingru & Jiang, Meihui, 2020. "The effect of the mined cobalt trade dependence Network's structure on trade price," Resources Policy, Elsevier, vol. 65(C).
    6. Lu, Lulu & Ge, Mengyan & Xu, Ying & Jia, Ya, 2019. "Phase synchronization and mode transition induced by multiple time delays and noises in coupled FitzHugh–Nagumo model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    7. Ramasamy, Mohanasubha & Devarajan, Subhasri & Kumarasamy, Suresh & Rajagopal, Karthikeyan, 2022. "Effect of higher-order interactions on synchronization of neuron models with electromagnetic induction," Applied Mathematics and Computation, Elsevier, vol. 434(C).
    8. Li, Y.L. & Chen, B. & Chen, G.Q., 2020. "Carbon network embodied in international trade: Global structural evolution and its policy implications," Energy Policy, Elsevier, vol. 139(C).
    9. Andreev, Andrey V. & Ivanchenko, Mikhail V. & Pisarchik, Alexander N. & Hramov, Alexander E., 2020. "Stimulus classification using chimera-like states in a spiking neural network," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    10. Aghababaei, Sajedeh & Balaraman, Sundarambal & Rajagopal, Karthikeyan & Parastesh, Fatemeh & Panahi, Shirin & Jafari, Sajad, 2021. "Effects of autapse on the chimera state in a Hindmarsh-Rose neuronal network," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).

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