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Synchronization of a Network Composed of Stochastic Hindmarsh–Rose Neurons

Author

Listed:
  • Branislav Rehák

    (The Czech Academy of Sciences, Institute of Information Theory and Automation, Pod Vodarenskou vezi 4, 182 00 Praha 8, Czech Republic
    These authors contributed equally to this work.)

  • Volodymyr Lynnyk

    (The Czech Academy of Sciences, Institute of Information Theory and Automation, Pod Vodarenskou vezi 4, 182 00 Praha 8, Czech Republic
    These authors contributed equally to this work.)

Abstract

An algorithm for synchronization of a network composed of interconnected Hindmarsh–Rose neurons is presented. Delays are present in the interconnections of the neurons. Noise is added to the controlled input of the neurons. The synchronization algorithm is designed using convex optimization and is formulated by means of linear matrix inequalities via the stochastic version of the Razumikhin functional. The recovery and the adaptation variables are also synchronized; this is demonstrated with the help of the minimum-phase property of the Hindmarsh–Rose neuron. The results are illustrated by an example.

Suggested Citation

  • Branislav Rehák & Volodymyr Lynnyk, 2021. "Synchronization of a Network Composed of Stochastic Hindmarsh–Rose Neurons," Mathematics, MDPI, vol. 9(20), pages 1-16, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:20:p:2625-:d:659091
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    References listed on IDEAS

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    1. 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.
    2. 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).
    3. 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.
    4. Yu, Hongjie & Peng, Jianhua, 2006. "Chaotic synchronization and control in nonlinear-coupled Hindmarsh–Rose neural systems," Chaos, Solitons & Fractals, Elsevier, vol. 29(2), pages 342-348.
    5. Ma, Jun & Mi, Lv & Zhou, Ping & Xu, Ying & Hayat, Tasawar, 2017. "Phase synchronization between two neurons induced by coupling of electromagnetic field," Applied Mathematics and Computation, Elsevier, vol. 307(C), pages 321-328.
    6. Djeundam, S.R. Dtchetgnia & Filatrella, G. & Yamapi, R., 2018. "Desynchronization effects of a current-driven noisy Hindmarsh–Rose neural network," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 204-211.
    7. 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. Natalya O. Sedova & Olga V. Druzhinina, 2023. "Exponential Stability of Nonlinear Time-Varying Delay Differential Equations via Lyapunov–Razumikhin Technique," Mathematics, MDPI, vol. 11(4), pages 1-15, February.

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