{"title":"一种新型4D分数阶混沌振荡器的分析与反演控制","authors":"Amin Jajarmi, Majid Akbarian, Dumitru Baleanu","doi":"10.1002/mma.11211","DOIUrl":null,"url":null,"abstract":"<div>\n \n <p>In this study, we introduce a new 4D fractional model to extract the chaotic attractors of a biological oscillator. The proposed description includes a recently developed \n<span></span><math>\n <semantics>\n <mrow>\n <mi>ψ</mi>\n </mrow>\n <annotation>$$ \\psi $$</annotation>\n </semantics></math>-Caputo fractional derivative. To explore the model, we employ the time domain analysis and the phase plane method, both of which exhibit the chaotic attractors for some fractional orders. Furthermore, we implement a robust approximation scheme based on a sequential substitution rule and investigate its convergence. The last step is to design a stabilizing backstepping controller to eliminate undesired chaotic behaviors. We then show that the closed-loop system is globally asymptotically stable, as stated in Theorem 5.1, and use experiments to confirm that it works.</p>\n </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 16","pages":"14750-14762"},"PeriodicalIF":1.8000,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Analysis and Backstepping Control of a Novel 4D Fractional Chaotic Oscillator\",\"authors\":\"Amin Jajarmi, Majid Akbarian, Dumitru Baleanu\",\"doi\":\"10.1002/mma.11211\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>\\n \\n <p>In this study, we introduce a new 4D fractional model to extract the chaotic attractors of a biological oscillator. The proposed description includes a recently developed \\n<span></span><math>\\n <semantics>\\n <mrow>\\n <mi>ψ</mi>\\n </mrow>\\n <annotation>$$ \\\\psi $$</annotation>\\n </semantics></math>-Caputo fractional derivative. To explore the model, we employ the time domain analysis and the phase plane method, both of which exhibit the chaotic attractors for some fractional orders. Furthermore, we implement a robust approximation scheme based on a sequential substitution rule and investigate its convergence. The last step is to design a stabilizing backstepping controller to eliminate undesired chaotic behaviors. We then show that the closed-loop system is globally asymptotically stable, as stated in Theorem 5.1, and use experiments to confirm that it works.</p>\\n </div>\",\"PeriodicalId\":49865,\"journal\":{\"name\":\"Mathematical Methods in the Applied Sciences\",\"volume\":\"48 16\",\"pages\":\"14750-14762\"},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2025-07-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Methods in the Applied Sciences\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1002/mma.11211\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Methods in the Applied Sciences","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/mma.11211","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Analysis and Backstepping Control of a Novel 4D Fractional Chaotic Oscillator
In this study, we introduce a new 4D fractional model to extract the chaotic attractors of a biological oscillator. The proposed description includes a recently developed
-Caputo fractional derivative. To explore the model, we employ the time domain analysis and the phase plane method, both of which exhibit the chaotic attractors for some fractional orders. Furthermore, we implement a robust approximation scheme based on a sequential substitution rule and investigate its convergence. The last step is to design a stabilizing backstepping controller to eliminate undesired chaotic behaviors. We then show that the closed-loop system is globally asymptotically stable, as stated in Theorem 5.1, and use experiments to confirm that it works.
期刊介绍：
Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome.
Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted.
Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.
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