具有混合时滞的离散分数阶Halanay不等式及其在离散分数阶神经网络系统中的应用

IF 2.5 2区数学 Q1 MATHEMATICS

Fractional Calculus and Applied Analysis Pub Date : 2025-03-31 DOI:10.1007/s13540-025-00395-4

Xiang Liu, Yongguang Yu

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引用次数: 0

摘要

在本文中，我们分析了具有混合时滞的离散分数阶神经网络系统的稳定性和同步性，这可以看作是我们之前在同一期刊上发表的文章（Liu and Yu In Fract Calc Appl Anal 25:40 -2061, 2022）的扩展。利用新技术，给出了包含离散时滞和分布时滞的混合时滞离散分数阶Halanay不等式的证明。然后，利用该分数阶Halanay不等式，构造适当的Lyapunov函数，给出了具有混合时滞的离散分数阶神经网络系统的Mittag-Leffler稳定性和同步性的充分判据。最后，给出了一个算例来说明其中一个结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Discrete fractional-order Halanay inequality with mixed time delays and applications in discrete fractional-order neural network systems

In this paper, which can be considered as an extension of our previous publication (Liu and Yu in Fract Calc Appl Anal 25:2040-2061, 2022) in same journal, we analyze the stability and synchronization for the discrete fractional-order neural network systems with mixed time delays. By new techniques, we give the proof of the discrete fractional-order Halanay inequality with mixed time delays, which contains both discrete and distributed time delays. Then, using this fractional-order Halanay inequality and constructing an appropriate Lyapunov function, we give the sufficient criteria of Mittag-Leffler stability and synchronization for the discrete fractional-order neural network systems with mixed time delays. Finally, an example is provided to illustrated one of the results.

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来源期刊

Fractional Calculus and Applied Analysis MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

4.70

自引率

16.70%

发文量

101

期刊介绍： Fractional Calculus and Applied Analysis (FCAA, abbreviated in the World databases as Fract. Calc. Appl. Anal. or FRACT CALC APPL ANAL) is a specialized international journal for theory and applications of an important branch of Mathematical Analysis (Calculus) where differentiations and integrations can be of arbitrary non-integer order. The high standards of its contents are guaranteed by the prominent members of Editorial Board and the expertise of invited external reviewers, and proven by the recently achieved high values of impact factor (JIF) and impact rang (SJR), launching the journal to top places of the ranking lists of Thomson Reuters and Scopus.