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Synchronization of coupled FitzHugh–Nagumo systems via MIMO feedback linearization control

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  • Zhang, Ting
  • Wang, Jiang
  • Fei, Xiangyang
  • Deng, Bin

Abstract

In this paper, synchronization dynamics of two FitzHugh–Nagumo neurons electrically coupled with gap junction in external electrical stimulation is studied. In order to synchronize all state variables in the neuron system, we regard the nonlinear feedback system as a multi-input multi-output (MIMO) system. Then, a MIMO decoupling feedback linearization algorithm and an adaptive strategy are introduced respectively to design the synchronization controllers for the two coupled neurons. Numerical simulations demonstrate the effectiveness of the developed methods.

Suggested Citation

  • Zhang, Ting & Wang, Jiang & Fei, Xiangyang & Deng, Bin, 2007. "Synchronization of coupled FitzHugh–Nagumo systems via MIMO feedback linearization control," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 194-202.
    • Handle: RePEc:eee:chsofr:v:33:y:2007:i:1:p:194-202
    DOI: 10.1016/j.chaos.2006.01.037
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    References listed on IDEAS

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    1. Jiang, Guo-Ping & Zheng, Wei Xing, 2005. "An LMI criterion for linear-state-feedback based chaos synchronization of a class of chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 437-443.
    2. Yassen, M.T., 2005. "Feedback and adaptive synchronization of chaotic Lü system," Chaos, Solitons & Fractals, Elsevier, vol. 25(2), pages 379-386.
    3. Fotsin, Hilaire & Bowong, Samuel, 2006. "Adaptive control and synchronization of chaotic systems consisting of Van der Pol oscillators coupled to linear oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 822-835.
    4. Yassen, M.T., 2005. "Controlling chaos and synchronization for new chaotic system using linear feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 913-920.
    5. Zhang, Guang-Jun & Xu, Jian-Xue, 2005. "Stochastic resonance induced by novel random transitions of motion of FitzHugh–Nagumo neuron model," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1439-1449.
    6. Lu, Jun Guo, 2005. "Generating chaos via decentralized linear state feedback and a class of nonlinear functions," Chaos, Solitons & Fractals, Elsevier, vol. 25(2), pages 403-413.
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    Cited by:

    1. Deng, Bin & Zhu, Zechen & Yang, Shuangming & Wei, Xile & Wang, Jiang & Yu, Haitao, 2016. "FPGA implementation of motifs-based neuronal network and synchronization analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 451(C), pages 388-402.
    2. Yu, Dong & Lu, Lulu & Wang, Guowei & Yang, Lijian & Jia, Ya, 2021. "Synchronization mode transition induced by bounded noise in multiple time-delays coupled FitzHugh–Nagumo model," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    3. Che, Yan-Qiu & Wang, Jiang & Zhou, Si-Si & Deng, Bin, 2009. "Robust synchronization control of coupled chaotic neurons under external electrical stimulation," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1333-1342.
    4. Che, Yan-Qiu & Wang, Jiang & Zhou, Si-Si & Deng, Bin, 2009. "Synchronization control of Hodgkin–Huxley neurons exposed to ELF electric field," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1588-1598.

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