{"title":"Exponential stability of a class of quaternion-valued memristor-based neural network with time-varying delay via M-matrix","authors":"Shengye Wang, Yanchao Shi, Jun Guo","doi":"10.1002/mma.10486","DOIUrl":null,"url":null,"abstract":"<p>This paper investigates the problems of exponential stability for a class of quaternion-valued memristor-based neural networks. By using M-matrix theory and fixed point theorem, the existence and uniqueness of the equilibrium point of quaternion-valued neural network are proved, respectively. Then, by combining M-matrix with exponential stability theory, a non-factorization method is obtained by using some inequality techniques to give the effective conditions of global exponential stability of quaternion-valued memristor-based neural network with time-varying delay. Finally, numerical examples are given to demonstrate the validity of the derived results.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 3","pages":"3304-3315"},"PeriodicalIF":1.8000,"publicationDate":"2024-09-11","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.10486","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 investigates the problems of exponential stability for a class of quaternion-valued memristor-based neural networks. By using M-matrix theory and fixed point theorem, the existence and uniqueness of the equilibrium point of quaternion-valued neural network are proved, respectively. Then, by combining M-matrix with exponential stability theory, a non-factorization method is obtained by using some inequality techniques to give the effective conditions of global exponential stability of quaternion-valued memristor-based neural network with time-varying delay. Finally, numerical examples are given to demonstrate the validity of the derived results.
本文研究了一类基于四元数值忆阻器的神经网络的指数稳定性问题。利用 M 矩阵理论和定点定理，分别证明了四元数值神经网络平衡点的存在性和唯一性。然后，将 M 矩阵与指数稳定性理论相结合，利用一些不等式技术获得了一种非因子化方法，给出了具有时变延迟的基于四元数值忆阻器的神经网络的全局指数稳定性的有效条件。最后，给出了数值示例来证明推导结果的正确性。
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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