IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v150y2021ics0960077921005245.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921005245
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.111170?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wang, L.X. & Zheng, J.H. & Li, M.S. & Lin, X. & Jing, Z.X. & Wu, P.Z. & Wu, Q.H. & Zhou, X.X., 2019. "Multi-time scale dynamic analysis of integrated energy systems: An individual-based model," Applied Energy, Elsevier, vol. 237(C), pages 848-861.
    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. Egorov, Nikita M. & Sysoev, Ilya V. & Ponomarenko, Vladimir I. & Sysoeva, Marina V., 2022. "Complex regimes in electronic neuron-like oscillators with sigmoid coupling," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    4. Feifei Yang & Xikui Hu & Guodong Ren & Jun Ma, 2023. "Synchronization and patterns in a memristive network in noisy electric field," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(6), pages 1-14, June.
    5. Ge, Mengyan & Lu, Lulu & Xu, Ying & Mamatimin, Rozihajim & Pei, Qiming & Jia, Ya, 2020. "Vibrational mono-/bi-resonance and wave propagation in FitzHugh–Nagumo neural systems under electromagnetic induction," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    6. Plotnikov, Sergei A. & Fradkov, Alexander L., 2019. "On synchronization in heterogeneous FitzHugh–Nagumo networks," Chaos, Solitons & Fractals, Elsevier, vol. 121(C), pages 85-91.
    7. Nian, Fuzhong & Liu, Xinmeng & Zhang, Yaqiong, 2018. "Sliding mode synchronization of fractional-order complex chaotic system with parametric and external disturbances," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 22-28.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:150:y:2021:i:c:s0960077921005245. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.