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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, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:276279
    DOI: 10.1155/2014/276279
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    References listed on IDEAS

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    1. A. A. Soliman, 2012. "Numerical Simulation of the FitzHugh‐Nagumo Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    2. Li, Chunguang & Chen, Guanrong, 2004. "Chaos and hyperchaos in the fractional-order Rössler equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 341(C), pages 55-61.
    3. Asad Freihat & Shaher Momani, 2012. "Adaptation of Differential Transform Method for the Numeric‐Analytic Solution of Fractional‐Order Rössler Chaotic and Hyperchaotic Systems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    4. A. A. Soliman, 2012. "Numerical Simulation of the FitzHugh-Nagumo Equations," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-13, August.
    5. Deng, W.H. & Li, C.P., 2005. "Chaos synchronization of the fractional Lü system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 353(C), pages 61-72.
    6. Asad Freihat & Shaher Momani, 2012. "Adaptation of Differential Transform Method for the Numeric-Analytic Solution of Fractional-Order Rössler Chaotic and Hyperchaotic Systems," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-13, April.
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    Cited by:

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    2. Jiangang Zhang & Juan Nan & Wenju Du & Yandong Chu & Hongwei Luo, 2016. "Dynamic Analysis for a Fractional‐Order Autonomous Chaotic System," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2016(1).

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