四元数值记忆神经网络的动态分析：一个新的广义不等式

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2025-07-25 DOI:10.1002/mma.70013

Chenyu Sun, Ruoxia Li, Zhengwen Tu

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引用次数: 0

摘要

本文考虑了QMNN的指数稳定性和同步性。首先，提出了一个新的指数稳定定义，它有效地估计了神经网络的收敛速度，并且通过修改控制器可以使神经网络以任意速率收敛到平衡点。然后，利用Halanay不等式推广出的一个新的引理，提出了一种简单的控制器来实现同步目标，并给出了一组实现同步控制的改进条件。最后通过仿真验证了这些定理。本文的结论不仅避免了对四元数“大小”的考虑，而且给出了更为灵活的判据。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Dynamic Analysis of Quaternion-Valued Memristive Neural Networks: A New Generalized Inequality

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Dynamic Analysis of Quaternion-Valued Memristive Neural Networks: A New Generalized Inequality

The exponential stability and the synchronization of QMNN are considered in this article. First, a new exponentially stable definition is proposed, it effectively estimates the rate of convergence, and the neural networks can converge to the equilibrium point at any rate by modifying the controller. Then, a simple controller is proposed to achieve the synchronization goal by a new lemma generalized from Halanay inequality, and a set of improved conditions are presented to achieve the synchronization control. The theorems are verified by some simulations in the end. The conclusions obtained in this paper not only avoid considering the “magnitude” of quaternion but also give a more flexible criteria.

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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.