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On synchronization in heterogeneous FitzHugh–Nagumo networks

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  • Plotnikov, Sergei A.
  • Fradkov, Alexander L.

Abstract

Biological systems are often composed of various heterogeneous units. It is an important problem to investigate how this heterogeneity affects the network dynamics, namely synchronization phenomenon. We study the heterogeneous networks of FitzHugh–Nagumo oscillators with diffusive coupling and present sufficient conditions for synchronization in these networks using the Lyapunov functions and Linear Matrix Inequalities (LMIs). Starting consideration with the case of two coupled systems further we extend the results to the networks with greater number of nodes. Numerical examples are presented to illustrate the obtained results.

Suggested Citation

  • Plotnikov, Sergei A. & Fradkov, Alexander L., 2019. "On synchronization in heterogeneous FitzHugh–Nagumo networks," Chaos, Solitons & Fractals, Elsevier, vol. 121(C), pages 85-91.
    • Handle: RePEc:eee:chsofr:v:121:y:2019:i:c:p:85-91
    DOI: 10.1016/j.chaos.2019.02.006
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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.
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    Cited by:

    1. 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).
    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. 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).
    5. 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.

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