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Synchronization of coupled chaotic FitzHugh–Nagumo neurons via Lyapunov functions

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  • Nguyen, Le Hoa
  • Hong, Keum-Shik

Abstract

After investigating the effect of the frequency of an external electrical stimulation on the chaotic dynamics of a single FitzHugh–Nagumo (FHN) neuron, this paper derives both a sufficient and a necessary condition of the coupling coefficient for self-synchronization of two interacting FHN neurons by using the Lyapunov function method and the largest transverse Lyapunov exponent, respectively. Also, for the cases that self-synchronization is not achieved through the coupling coefficient, a feedback control law for synchronization using the Lyapunov method is investigated. The performance of the proposed control law is compared with that of an existing one in the literature. Simulation results are provided.

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  • Nguyen, Le Hoa & Hong, Keum-Shik, 2011. "Synchronization of coupled chaotic FitzHugh–Nagumo neurons via Lyapunov functions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(4), pages 590-603.
    • Handle: RePEc:eee:matcom:v:82:y:2011:i:4:p:590-603
    DOI: 10.1016/j.matcom.2011.10.005
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    References listed on IDEAS

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    1. Wan, Xiaojun & Sun, Jitao, 2011. "Adaptive–impulsive synchronization of chaotic systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(8), pages 1609-1617.
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    5. Mahmoud, Gamal M. & Mahmoud, Emad E., 2010. "Synchronization and control of hyperchaotic complex Lorenz system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(12), pages 2286-2296.
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    Cited by:

    1. Sabouri, Amir & Ghasemi, Mahdieh & Mehrabbeik, Mahtab, 2023. "The dynamical analysis of non-uniform neocortical network model in up-down state oscillations," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    2. Zhang, Qunjiao, 2014. "Robust synchronization of FitzHugh–Nagumo network with parameter disturbances by sliding mode control," Chaos, Solitons & Fractals, Elsevier, vol. 58(C), pages 22-26.
    3. Mbeunga, N.K. & Nana, B. & Woafo, P., 2021. "Dynamics of array mechanical arms coupled each to a Fitzhugh-Nagumo neuron," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    4. Das, Saureesh, 2022. "Recurrence quantification and bifurcation analysis of electrical activity in resistive/memristive synapse coupled Fitzhugh–Nagumo type neurons," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    5. Wang, Jing & Ye, Weijie & Liu, Shenquan & Lu, Bo & Jiang, Xiaofang, 2016. "Qualitative and quantitative aspects of synchronization in coupled CA1 pyramidal neurons," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 32-38.
    6. Wei Wei & Yanjie Shao & Min Zuo, 2018. "Active Disturbance Rejection Synchronization of Morris-Lecar Neurons," Complexity, Hindawi, vol. 2018, pages 1-10, June.

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