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Adaptive synchronization in the complex heterogeneous networks of Hindmarsh–Rose neurons

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  • Semenov, Danila M.
  • Fradkov, Alexander L.

Abstract

This paper is devoted to the adaptive synchronization problem in the heterogeneous Hindmarsh–Rose neuronal networks. Heterogeneity is a natural property of biological neuronal networks, as each neuron has its own physiological characteristics, which may differ from other neurons within the population. Therefore, the study of the effect of heterogeneity on the synchronization in the biological neuronal network is an important problem. In order to solve this problem, the ultimate boundedness of the network trajectories is established, and also the limit set is defined for these trajectories. Based on the boundedness analysis and the Speed Gradient method, the adaptive algorithm for adjusting the coupling strength is developed. It is proved mathematically that the developed algorithm provides synchronization in the network under study. The obtained theoretical results are confirmed by the simulations.

Suggested Citation

  • Semenov, Danila M. & Fradkov, Alexander L., 2021. "Adaptive synchronization in the complex heterogeneous networks of Hindmarsh–Rose neurons," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    • Handle: RePEc:eee:chsofr:v:150:y:2021:i:c:s0960077921005245
    DOI: 10.1016/j.chaos.2021.111170
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    References listed on IDEAS

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    1. Nian, Fuzhong & Liu, Weilong, 2016. "Hybrid synchronization of heterogeneous chaotic systems on dynamic network," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 554-561.
    2. Plotnikov, Sergei A. & Fradkov, Alexander L., 2019. "On synchronization in heterogeneous FitzHugh–Nagumo networks," Chaos, Solitons & Fractals, Elsevier, vol. 121(C), pages 85-91.
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    Cited by:

    1. Bao, Han & Rong, Kang & Chen, Mo & Zhang, Xi & Bao, Bocheng, 2023. "Multistability and synchronization of discrete maps via memristive coupling," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    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, Kexin & Bao, Bocheng & Ma, Jun & Chen, Mo & Bao, Han, 2022. "Synchronization transitions in a discrete memristor-coupled bi-neuron model," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).

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