The characteristics study of a bounded fractional-order chaotic system: Complexity, and energy control
The dynamics of a four-dimensional fractional-order (FO) dynamical system from the viewpoint of spectral entropy (SE), C0 complexity, and algorithm 0–1 are presented in detail in this article. The efficiency of these algorithms in the existence of chaos for FO systems has been investigated as well a...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-01-01
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| Series: | Alexandria Engineering Journal |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110016824011931 |
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| author | Qingzhe Wu Juling Zhang Miao Li Hassan Saberi-Nik Jan Awrejcewicz |
| author_facet | Qingzhe Wu Juling Zhang Miao Li Hassan Saberi-Nik Jan Awrejcewicz |
| author_sort | Qingzhe Wu |
| collection | DOAJ |
| description | The dynamics of a four-dimensional fractional-order (FO) dynamical system from the viewpoint of spectral entropy (SE), C0 complexity, and algorithm 0–1 are presented in detail in this article. The efficiency of these algorithms in the existence of chaos for FO systems has been investigated as well as other methods such as Lyapunov exponents, Lyapunov dimension, and bifurcation diagrams. With Hamilton’s energy analysis for the 4D FO system, it is found that chaotic behavior is more dependent on energy consumption. Therefore, it is necessary to design a negative feedback control to reduce energy consumption and suppress chaotic behavior. Finally, we obtain the global Mittag-Leffler positive invariant sets (GMLPISs) and global Mittag-Leffler attractive sets (GMLASs) of the introduced system. Numerical results indicate the effectiveness of complexity and chaos detection methods as well as bound calculation. |
| format | Article |
| id | doaj-art-d4057fcb87574ffe8269ac9b6933a195 |
| institution | Kabale University |
| issn | 1110-0168 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj-art-d4057fcb87574ffe8269ac9b6933a1952025-01-18T05:03:36ZengElsevierAlexandria Engineering Journal1110-01682025-01-01111588600The characteristics study of a bounded fractional-order chaotic system: Complexity, and energy controlQingzhe Wu0Juling Zhang1Miao Li2Hassan Saberi-Nik3Jan Awrejcewicz4Normal School, Shenyang University, Shenyang, Liaoning 110044, ChinaNormal School, Shenyang University, Shenyang, Liaoning 110044, ChinaNormal School, Shenyang University, Shenyang, Liaoning 110044, ChinaDepartment of Mathematics and Statistics, University of Neyshabur, Neyshabur, Iran; Corresponding author.Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, Stefanowskiego Str. 1/15, 90-924, Lodz, PolandThe dynamics of a four-dimensional fractional-order (FO) dynamical system from the viewpoint of spectral entropy (SE), C0 complexity, and algorithm 0–1 are presented in detail in this article. The efficiency of these algorithms in the existence of chaos for FO systems has been investigated as well as other methods such as Lyapunov exponents, Lyapunov dimension, and bifurcation diagrams. With Hamilton’s energy analysis for the 4D FO system, it is found that chaotic behavior is more dependent on energy consumption. Therefore, it is necessary to design a negative feedback control to reduce energy consumption and suppress chaotic behavior. Finally, we obtain the global Mittag-Leffler positive invariant sets (GMLPISs) and global Mittag-Leffler attractive sets (GMLASs) of the introduced system. Numerical results indicate the effectiveness of complexity and chaos detection methods as well as bound calculation.http://www.sciencedirect.com/science/article/pii/S1110016824011931ComplexitiesHamilton energy function (HEF)Fractional-orderEnergy control |
| spellingShingle | Qingzhe Wu Juling Zhang Miao Li Hassan Saberi-Nik Jan Awrejcewicz The characteristics study of a bounded fractional-order chaotic system: Complexity, and energy control Alexandria Engineering Journal Complexities Hamilton energy function (HEF) Fractional-order Energy control |
| title | The characteristics study of a bounded fractional-order chaotic system: Complexity, and energy control |
| title_full | The characteristics study of a bounded fractional-order chaotic system: Complexity, and energy control |
| title_fullStr | The characteristics study of a bounded fractional-order chaotic system: Complexity, and energy control |
| title_full_unstemmed | The characteristics study of a bounded fractional-order chaotic system: Complexity, and energy control |
| title_short | The characteristics study of a bounded fractional-order chaotic system: Complexity, and energy control |
| title_sort | characteristics study of a bounded fractional order chaotic system complexity and energy control |
| topic | Complexities Hamilton energy function (HEF) Fractional-order Energy control |
| url | http://www.sciencedirect.com/science/article/pii/S1110016824011931 |
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