Abstract and Applied Analysis

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

Shaher Momani, Asad Freihat, and Mohammed AL-Smadi

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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.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 276279, 10 pages.

Dates
First available in Project Euclid: 6 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412607125

Digital Object Identifier
doi:10.1155/2014/276279

Mathematical Reviews number (MathSciNet)
MR3224305

Zentralblatt MATH identifier
07022071

Citation

Momani, Shaher; Freihat, Asad; AL-Smadi, Mohammed. Analytical Study of Fractional-Order Multiple Chaotic FitzHugh-Nagumo Neurons Model Using Multistep Generalized Differential Transform Method. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 276279, 10 pages. doi:10.1155/2014/276279. https://projecteuclid.org/euclid.aaa/1412607125


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