Chaotic Behavior Analysis of a New Incommensurate Fractional-Order Hopfield Neural Network System

This study intends to examine different dynamics of the chaotic incommensurate fractional-order Hopfield neural network model. The stability of the proposed incommensurate-order model is analyzed numerically by continuously varying the values of the fractional-order derivative and the values of the...

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Autores principales:	Nadjette Debbouche, Adel Ouannas, Iqbal M. Batiha, Giuseppe Grassi, Mohammed K. A. Kaabar, Hadi Jahanshahi, Ayman A. Aly, Awad M. Aljuaid
Formato:	article
Lenguaje:	EN
Publicado:	Hindawi-Wiley 2021
Materias:	Electronic computers. Computer science QA75.5-76.95
Acceso en línea:	https://doaj.org/article/b39aeec8d5304a1d814a016fe35b2c0d
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spelling	oai:doaj.org-article:b39aeec8d5304a1d814a016fe35b2c0d2021-11-22T01:09:57ZChaotic Behavior Analysis of a New Incommensurate Fractional-Order Hopfield Neural Network System1099-052610.1155/2021/3394666https://doaj.org/article/b39aeec8d5304a1d814a016fe35b2c0d2021-01-01T00:00:00Zhttp://dx.doi.org/10.1155/2021/3394666https://doaj.org/toc/1099-0526This study intends to examine different dynamics of the chaotic incommensurate fractional-order Hopfield neural network model. The stability of the proposed incommensurate-order model is analyzed numerically by continuously varying the values of the fractional-order derivative and the values of the system parameters. It turned out that the formulated system using the Caputo differential operator exhibits many rich complex dynamics, including symmetry, bistability, and coexisting chaotic attractors. On the other hand, it has been detected that by adapting the corresponding controlled constants, such systems possess the so-called offset boosting of three variables. Besides, the resultant periodic and chaotic attractors can be scattered in several forms, including 1D line, 2D lattice, and 3D grid, and even in an arbitrary location of the phase space. Several numerical simulations are implemented, and the obtained findings are illustrated through constructing bifurcation diagrams, computing Lyapunov exponents, calculating Lyapunov dimensions, and sketching the phase portraits in 2D and 3D projections.Nadjette DebboucheAdel OuannasIqbal M. BatihaGiuseppe GrassiMohammed K. A. KaabarHadi JahanshahiAyman A. AlyAwad M. AljuaidHindawi-WileyarticleElectronic computers. Computer scienceQA75.5-76.95ENComplexity, Vol 2021 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Electronic computers. Computer science QA75.5-76.95
spellingShingle	Electronic computers. Computer science QA75.5-76.95 Nadjette Debbouche Adel Ouannas Iqbal M. Batiha Giuseppe Grassi Mohammed K. A. Kaabar Hadi Jahanshahi Ayman A. Aly Awad M. Aljuaid Chaotic Behavior Analysis of a New Incommensurate Fractional-Order Hopfield Neural Network System
description	This study intends to examine different dynamics of the chaotic incommensurate fractional-order Hopfield neural network model. The stability of the proposed incommensurate-order model is analyzed numerically by continuously varying the values of the fractional-order derivative and the values of the system parameters. It turned out that the formulated system using the Caputo differential operator exhibits many rich complex dynamics, including symmetry, bistability, and coexisting chaotic attractors. On the other hand, it has been detected that by adapting the corresponding controlled constants, such systems possess the so-called offset boosting of three variables. Besides, the resultant periodic and chaotic attractors can be scattered in several forms, including 1D line, 2D lattice, and 3D grid, and even in an arbitrary location of the phase space. Several numerical simulations are implemented, and the obtained findings are illustrated through constructing bifurcation diagrams, computing Lyapunov exponents, calculating Lyapunov dimensions, and sketching the phase portraits in 2D and 3D projections.
format	article
author	Nadjette Debbouche Adel Ouannas Iqbal M. Batiha Giuseppe Grassi Mohammed K. A. Kaabar Hadi Jahanshahi Ayman A. Aly Awad M. Aljuaid
author_facet	Nadjette Debbouche Adel Ouannas Iqbal M. Batiha Giuseppe Grassi Mohammed K. A. Kaabar Hadi Jahanshahi Ayman A. Aly Awad M. Aljuaid
author_sort	Nadjette Debbouche
title	Chaotic Behavior Analysis of a New Incommensurate Fractional-Order Hopfield Neural Network System
title_short	Chaotic Behavior Analysis of a New Incommensurate Fractional-Order Hopfield Neural Network System
title_full	Chaotic Behavior Analysis of a New Incommensurate Fractional-Order Hopfield Neural Network System
title_fullStr	Chaotic Behavior Analysis of a New Incommensurate Fractional-Order Hopfield Neural Network System
title_full_unstemmed	Chaotic Behavior Analysis of a New Incommensurate Fractional-Order Hopfield Neural Network System
title_sort	chaotic behavior analysis of a new incommensurate fractional-order hopfield neural network system
publisher	Hindawi-Wiley
publishDate	2021
url	https://doaj.org/article/b39aeec8d5304a1d814a016fe35b2c0d
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Chaotic Behavior Analysis of a New Incommensurate Fractional-Order Hopfield Neural Network System

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