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Dynamics and synchronization of boundary coupled FitzHugh-Nagumo neural networks

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  • Skrzypek, Leslaw
  • You, Yuncheng

Abstract

In this work a new mathematical model for complex neural networks is presented by the partly diffusive FitzHugh-Nagumo equations with ensemble boundary coupling. The dissipative dynamics and boundary coupling dynamics of solutions are proved with sharp uniform estimates. The synchronization of this kind complex neural networks is proved under the condition that boundary synaptic stimulation signal strength exceeds the threshold quantitatively expressed.

Suggested Citation

  • Skrzypek, Leslaw & You, Yuncheng, 2021. "Dynamics and synchronization of boundary coupled FitzHugh-Nagumo neural networks," Applied Mathematics and Computation, Elsevier, vol. 388(C).
    • Handle: RePEc:eee:apmaco:v:388:y:2021:i:c:s0096300320305014
    DOI: 10.1016/j.amc.2020.125545
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    References listed on IDEAS

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    1. D. Q. Wei & X. S. Luo & Y. L. Zou, 2008. "Firing activity of complex space-clamped FitzHugh-Nagumo neural networks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 63(2), pages 279-282, May.
    2. Wang, Jiang & Zhang, Ting & Deng, Bin, 2007. "Synchronization of FitzHugh–Nagumo neurons in external electrical stimulation via nonlinear control," Chaos, Solitons & Fractals, Elsevier, vol. 31(1), pages 30-38.
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    Cited by:

    1. Min, Fuhong & Zhang, Wen & Ji, Ziyi & Zhang, Lei, 2021. "Switching dynamics of a non-autonomous FitzHugh-Nagumo circuit with piecewise-linear flux-controlled memristor," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    2. Chen, Wei & Yu, Yongguang & Hai, Xudong & Ren, Guojian, 2022. "Adaptive quasi-synchronization control of heterogeneous fractional-order coupled neural networks with reaction-diffusion," Applied Mathematics and Computation, Elsevier, vol. 427(C).

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