The global attractive sets and synchronization of a fractional-order complex dynamical system
This paper presents a chaotic complex system with a fractional-order derivative. The dynamical behaviors of the proposed system such as phase portraits, bifurcation diagrams, and the Lyapunov exponents are investigated. The main contribution of this effort is an implementation of Mittag-Leffler boun...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2023179?viewType=HTML |
| _version_ | 1797953883105918976 |
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| author | Minghung Lin Yiyou Hou Maryam A. Al-Towailb Hassan Saberi-Nik |
| author_facet | Minghung Lin Yiyou Hou Maryam A. Al-Towailb Hassan Saberi-Nik |
| author_sort | Minghung Lin |
| collection | DOAJ |
| description | This paper presents a chaotic complex system with a fractional-order derivative. The dynamical behaviors of the proposed system such as phase portraits, bifurcation diagrams, and the Lyapunov exponents are investigated. The main contribution of this effort is an implementation of Mittag-Leffler boundedness. The global attractive sets (GASs) and positive invariant sets (PISs) for the fractional chaotic complex system are derived based on the Lyapunov stability theory and the Mittag-Leffler function. Furthermore, an effective control strategy is also designed to achieve the global synchronization of two fractional chaotic systems. The corresponding boundedness is numerically verified to show the effectiveness of the theoretical analysis. |
| first_indexed | 2024-04-10T23:10:10Z |
| format | Article |
| id | doaj.art-7dee1359dd434bb6aae46e9d47099b59 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-10T23:10:10Z |
| publishDate | 2023-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-7dee1359dd434bb6aae46e9d47099b592023-01-13T06:18:17ZengAIMS PressAIMS Mathematics2473-69882023-01-01823523354110.3934/math.2023179The global attractive sets and synchronization of a fractional-order complex dynamical systemMinghung Lin 0Yiyou Hou1Maryam A. Al-Towailb2Hassan Saberi-Nik31. Department of Electrical Engineering, Cheng Shiu University, Kaohsiung 83301, Taiwan2. Department of Intelligent Commerce, National Kaohsiung University of Science and Technology, Kaohsiung 824004, Taiwan3. Department of Computer Science and Engineering, College of Applied Studies and Community Service, King Saud University, Riyadh, KSA4. Department of Mathematics and Statistics, University of Neyshabur, Neyshabur, IranThis paper presents a chaotic complex system with a fractional-order derivative. The dynamical behaviors of the proposed system such as phase portraits, bifurcation diagrams, and the Lyapunov exponents are investigated. The main contribution of this effort is an implementation of Mittag-Leffler boundedness. The global attractive sets (GASs) and positive invariant sets (PISs) for the fractional chaotic complex system are derived based on the Lyapunov stability theory and the Mittag-Leffler function. Furthermore, an effective control strategy is also designed to achieve the global synchronization of two fractional chaotic systems. The corresponding boundedness is numerically verified to show the effectiveness of the theoretical analysis.https://www.aimspress.com/article/doi/10.3934/math.2023179?viewType=HTMLmittag-leffler gasfractional-order complex systemlyapunov stability theoryglobally synchronization |
| spellingShingle | Minghung Lin Yiyou Hou Maryam A. Al-Towailb Hassan Saberi-Nik The global attractive sets and synchronization of a fractional-order complex dynamical system AIMS Mathematics mittag-leffler gas fractional-order complex system lyapunov stability theory globally synchronization |
| title | The global attractive sets and synchronization of a fractional-order complex dynamical system |
| title_full | The global attractive sets and synchronization of a fractional-order complex dynamical system |
| title_fullStr | The global attractive sets and synchronization of a fractional-order complex dynamical system |
| title_full_unstemmed | The global attractive sets and synchronization of a fractional-order complex dynamical system |
| title_short | The global attractive sets and synchronization of a fractional-order complex dynamical system |
| title_sort | global attractive sets and synchronization of a fractional order complex dynamical system |
| topic | mittag-leffler gas fractional-order complex system lyapunov stability theory globally synchronization |
| url | https://www.aimspress.com/article/doi/10.3934/math.2023179?viewType=HTML |
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