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Generalized synchronization of the extended Hindmarsh–Rose neuronal model with fractional order derivative

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  • Giresse, Tene Alain
  • Crepin, Kofane Timoleon
  • Martin, Tchoffo

Abstract

In the present paper, the synchronization of the extended Hindmarsh–Rose neuronal model with fractional order derivative is presented in detail taking into consideration the effects of the very slow intracellular exchange of calcium ion (Ca2+) occurring between cytoplasm and its store. That is, we approach the synchronization by the Ge–Yao–Chen partial region stability theory. The method of resolution used is the powerful Adam–Bashforth–Moulton method which converges quickly to the exact solution. Numerical simulations of the error dynamics proved the effectiveness of the control method. The synchronization time is evaluated for different orders of the derivative and its analysis shows that, it is closely related to the order of the derivative and that fractional order induces quick synchronization compared to integer order.

Suggested Citation

  • Giresse, Tene Alain & Crepin, Kofane Timoleon & Martin, Tchoffo, 2019. "Generalized synchronization of the extended Hindmarsh–Rose neuronal model with fractional order derivative," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 311-319.
    • Handle: RePEc:eee:chsofr:v:118:y:2019:i:c:p:311-319
    DOI: 10.1016/j.chaos.2018.11.028
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    References listed on IDEAS

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    1. Shichang Ma & Yufeng Xu & Wei Yue, 2012. "Numerical Solutions of a Variable-Order Fractional Financial System," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-14, September.
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    Cited by:

    1. Liu, Dan & Zhao, Song & Luo, Xiaoyuan & Yuan, Yi, 2021. "Synchronization for fractional-order extended Hindmarsh-Rose neuronal models with magneto-acoustical stimulation input," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).

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