{"title":"Global Stability and Synchronization of Complex-Valued Differential-Algebraic Neural Networks With Delay: A Differential-Algebraic Inequality Approach","authors":"Weiqiang Gong, Yao Xiao, Kai Wang, Qiang Li","doi":"10.1002/mma.10677","DOIUrl":null,"url":null,"abstract":"<div>\n \n <p>This article proposes a novel complex-valued differential-algebraic neural network model with time delay (DDANN). Firstly, based on the differential-algebraic inequality technique, the global stability criteria of the considered system are obtained to ensure the complex-valued DDANN achieves global exponential stability. Next, by designing an appropriate feedback controller, to get the desired results, we present some constraint conditions, which make the drive system and the response system achieve the global exponential synchronization. Furthermore, as an application, a complex-valued neutral-type neural network (NDNN) can be transformed into a simple complex-valued DDANN and the global exponential stability results of NDNN are also proposed. In the end of paper, two examples are given to verify the superiority/feasibility of the presented theoretical results.</p>\n </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 6","pages":"6361-6374"},"PeriodicalIF":2.1000,"publicationDate":"2025-01-05","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.10677","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 article proposes a novel complex-valued differential-algebraic neural network model with time delay (DDANN). Firstly, based on the differential-algebraic inequality technique, the global stability criteria of the considered system are obtained to ensure the complex-valued DDANN achieves global exponential stability. Next, by designing an appropriate feedback controller, to get the desired results, we present some constraint conditions, which make the drive system and the response system achieve the global exponential synchronization. Furthermore, as an application, a complex-valued neutral-type neural network (NDNN) can be transformed into a simple complex-valued DDANN and the global exponential stability results of NDNN are also proposed. In the end of paper, two examples are given to verify the superiority/feasibility of the presented theoretical results.
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.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
