Exponential Quasi-Synchronization of Nonautonomous Complex Dynamical Networks With Conformable Fractional-Order Derivatives

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2024-12-23 DOI:10.1002/mma.10645

Baizeng Bao, Liguang Xu

{"title":"Exponential Quasi-Synchronization of Nonautonomous Complex Dynamical Networks With Conformable Fractional-Order Derivatives","authors":"Baizeng Bao, Liguang Xu","doi":"10.1002/mma.10645","DOIUrl":null,"url":null,"abstract":"<div>\n \n <p>This paper studies the exponential quasi-synchronization of nonautonomous conformable fractional-order complex dynamical networks (NCFCDNs) via means of the periodically intermittent pinning control (PIPC). First, a nonautonomous conformable fractional-order error systems are established, which include stable and unstable subsystems. Second, for the cases where the existing results are invalid to handle switched nonautonomous terms, a new conformable fractional-order Halanay inequality is obtained, which serves as a powerful tool in the analysis of quasi-synchronization of NCFCDNs. Then, by virtue of the obtained Halanay inequality, Lyapunov method, and periodically intermittent controller, sufficient conditions of exponential quasi-synchronization of NCFCDNs are derived. Our results allow nonautonomous terms to be switched during work time and rest time, which is more relaxing than the previous results. Finally, a simulation example is included to show the feasibility of the derived results.</p>\n </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 5","pages":"5906-5919"},"PeriodicalIF":2.1000,"publicationDate":"2024-12-23","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.10645","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

Abstract

This paper studies the exponential quasi-synchronization of nonautonomous conformable fractional-order complex dynamical networks (NCFCDNs) via means of the periodically intermittent pinning control (PIPC). First, a nonautonomous conformable fractional-order error systems are established, which include stable and unstable subsystems. Second, for the cases where the existing results are invalid to handle switched nonautonomous terms, a new conformable fractional-order Halanay inequality is obtained, which serves as a powerful tool in the analysis of quasi-synchronization of NCFCDNs. Then, by virtue of the obtained Halanay inequality, Lyapunov method, and periodically intermittent controller, sufficient conditions of exponential quasi-synchronization of NCFCDNs are derived. Our results allow nonautonomous terms to be switched during work time and rest time, which is more relaxing than the previous results. Finally, a simulation example is included to show the feasibility of the derived results.

查看原文本刊更多论文

具有合乎分数阶导数的非自治复杂动力网络的指数拟同步

本文利用周期性间歇钉住控制（PIPC）研究了非自治符合分数阶复杂动态网络的指数拟同步问题。首先，建立了包含稳定子系统和不稳定子系统的非自治的符合分数阶误差系统。其次，针对现有结果无法处理切换非自治项的情况，得到了一个新的符合分数阶Halanay不等式，为分析ncfcdn的准同步提供了有力的工具。然后，利用得到的Halanay不等式、Lyapunov方法和周期间歇控制器，导出了ncfcdn的指数拟同步的充分条件。我们的结果允许在工作时间和休息时间切换非自治项，这比以前的结果更轻松。最后通过仿真实例验证了所得结果的可行性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

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.