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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| Main Authors: | , , , , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2021/3394666 |
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| 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 |
| collection | DOAJ |
| 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 |
| id | doaj-art-b39aeec8d5304a1d814a016fe35b2c0d |
| institution | Kabale University |
| issn | 1099-0526 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-b39aeec8d5304a1d814a016fe35b2c0d2025-02-03T01:03:41ZengWileyComplexity1099-05262021-01-01202110.1155/2021/3394666Chaotic Behavior Analysis of a New Incommensurate Fractional-Order Hopfield Neural Network SystemNadjette Debbouche0Adel Ouannas1Iqbal M. Batiha2Giuseppe Grassi3Mohammed K. A. Kaabar4Hadi Jahanshahi5Ayman A. Aly6Awad M. Aljuaid7Department of Mathematics and Computer ScienceLaboratory of Dynamical Systems and ControlDepartment of MathematicsDipartimento Ingegneria InnovazioneGofa CampDepartment of Mechanical EngineeringDepartment of Mechanical EngineeringDepartment of Industrial EngineeringThis 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.http://dx.doi.org/10.1155/2021/3394666 |
| spellingShingle | 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 Complexity |
| title | 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_short | 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 |
| url | http://dx.doi.org/10.1155/2021/3394666 |
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