Qingzhe Wu , Juling Zhang , Miao Li , Hassan Saberi-Nik , Jan Awrejcewicz
{"title":"有界分数阶混沌系统的特性研究：复杂性与能量控制","authors":"Qingzhe Wu , Juling Zhang , Miao Li , Hassan Saberi-Nik , Jan Awrejcewicz","doi":"10.1016/j.aej.2024.10.038","DOIUrl":null,"url":null,"abstract":"<div><div>The dynamics of a four-dimensional fractional-order (FO) dynamical system from the viewpoint of spectral entropy (SE), C<span><math><msub><mrow></mrow><mrow><mn>0</mn></mrow></msub></math></span> 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.</div></div>","PeriodicalId":7484,"journal":{"name":"alexandria engineering journal","volume":"111 ","pages":"Pages 588-600"},"PeriodicalIF":6.2000,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The characteristics study of a bounded fractional-order chaotic system: Complexity, and energy control\",\"authors\":\"Qingzhe Wu , Juling Zhang , Miao Li , Hassan Saberi-Nik , Jan Awrejcewicz\",\"doi\":\"10.1016/j.aej.2024.10.038\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>The dynamics of a four-dimensional fractional-order (FO) dynamical system from the viewpoint of spectral entropy (SE), C<span><math><msub><mrow></mrow><mrow><mn>0</mn></mrow></msub></math></span> 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.</div></div>\",\"PeriodicalId\":7484,\"journal\":{\"name\":\"alexandria engineering journal\",\"volume\":\"111 \",\"pages\":\"Pages 588-600\"},\"PeriodicalIF\":6.2000,\"publicationDate\":\"2024-10-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"alexandria engineering journal\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1110016824011931\",\"RegionNum\":2,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"ENGINEERING, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"alexandria engineering journal","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1110016824011931","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}
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), C 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.
期刊介绍：
Alexandria Engineering Journal is an international journal devoted to publishing high quality papers in the field of engineering and applied science. Alexandria Engineering Journal is cited in the Engineering Information Services (EIS) and the Chemical Abstracts (CA). The papers published in Alexandria Engineering Journal are grouped into five sections, according to the following classification:
• Mechanical, Production, Marine and Textile Engineering
• Electrical Engineering, Computer Science and Nuclear Engineering
• Civil and Architecture Engineering
• Chemical Engineering and Applied Sciences
• Environmental Engineering
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