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Analytical Study of Fractional-Order Multiple Chaotic FitzHugh-Nagumo Neurons Model Using Multistep Generalized Differential Transform Method

Author

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  • Shaher Momani
  • Asad Freihat
  • Mohammed AL-Smadi

Abstract

The multistep generalized differential transform method is applied to solve the fractional-order multiple chaotic FitzHugh-Nagumo (FHN) neurons model. The algorithm is illustrated by studying the dynamics of three coupled chaotic FHN neurons equations with different gap junctions under external electrical stimulation. The fractional derivatives are described in the Caputo sense. Furthermore, we present figurative comparisons between the proposed scheme and the classical fourth-order Runge-Kutta method to demonstrate the accuracy and applicability of this method. The graphical results reveal that only few terms are required to deduce the approximate solutions which are found to be accurate and efficient.

Suggested Citation

  • Shaher Momani & Asad Freihat & Mohammed AL-Smadi, 2014. "Analytical Study of Fractional-Order Multiple Chaotic FitzHugh-Nagumo Neurons Model Using Multistep Generalized Differential Transform Method," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-10, June.
    • Handle: RePEc:hin:jnlaaa:276279
    DOI: 10.1155/2014/276279
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    Cited by:

    1. Partohaghighi, Mohammad & Akgül, Ali, 2021. "Modelling and simulations of the SEIR and Blood Coagulation systems using Atangana-Baleanu-Caputo derivative," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    2. Mohammad Alaroud & Abedel-Karrem Alomari & Nedal Tahat & Shrideh Al-Omari & Anuar Ishak, 2023. "A Novel Solution Approach for Time-Fractional Hyperbolic Telegraph Differential Equation with Caputo Time Differentiation," Mathematics, MDPI, vol. 11(9), pages 1-19, May.
    3. Erum Saba & Imtiaz Hussain Kalwar & Mukhtiar Ali Unar & Abdul Latif Memon & Nasrullah Pirzada, 2021. "Fuzzy Logic-Based Identification of Railway Wheelset Conicity Using Multiple Model Approach," Sustainability, MDPI, vol. 13(18), pages 1-21, September.

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