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Synchronizing two coupled chaotic neurons in external electrical stimulation using backstepping control

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

Abstract

Backstepping design is a recursive procedure that combines the choice of a Lyapunov function with the design of a controller. In this paper, the backstepping control is used to synchronize two coupled chaotic neurons in external electrical stimulation. The coupled model is based on the nonlinear cable model and only one state variable can be controlled in practice. The backstepping design needs only one controller to synchronize two chaotic systems and it can be applied to a variety of chaotic systems whether they contain external excitation or not, so the two coupled chaotic neurons in external electrical stimulation can be synchronized perfectly by backstepping control. Numerical simulations demonstrate the effectiveness of this design.

Suggested Citation

  • Bin, Deng & Jiang, Wang & Xiangyang, Fei, 2006. "Synchronizing two coupled chaotic neurons in external electrical stimulation using backstepping control," Chaos, Solitons & Fractals, Elsevier, vol. 29(1), pages 182-189.
    • Handle: RePEc:eee:chsofr:v:29:y:2006:i:1:p:182-189
    DOI: 10.1016/j.chaos.2005.08.027
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    Cited by:

    1. Usha, K. & Subha, P. A. & Nayak, Chitra R., 2018. "The route to synchrony via drum head mode and mixed oscillatory state in star coupled Hindmarsh–Rose neural network," Chaos, Solitons & Fractals, Elsevier, vol. 108(C), pages 25-31.
    2. Polynikis, A. & di Bernardo, M. & Hogan, S.J., 2009. "Synchronizability of coupled PWL maps," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1353-1367.
    3. Vázquez-Guerrero, P. & Gómez-Aguilar, J.F. & Santamaria, F. & Escobar-Jiménez, R.F., 2019. "Synchronization patterns with strong memory adaptive control in networks of coupled neurons with chimera states dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 167-175.
    4. Stan, Cristina & Cristescu, C.P. & Agop, M., 2007. "Golden mean relevance for chaos inhibition in a system of two coupled modified van der Pol oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 31(4), pages 1035-1040.

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