{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:25:59Z","timestamp":1760059559703,"version":"build-2065373602"},"reference-count":43,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2025,6,20]],"date-time":"2025-06-20T00:00:00Z","timestamp":1750377600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Science Foundation Project of Chongqing, China","award":["CSTB2022NSCQ-MSX0393","KJZD-M202301202","KJZD-K202201202","CSTB2023T-IADZXX0017"],"award-info":[{"award-number":["CSTB2022NSCQ-MSX0393","KJZD-M202301202","KJZD-K202201202","CSTB2023T-IADZXX0017"]}]},{"name":"Science and Technology Research Program of Chongqing Municipal Education Commission, China","award":["CSTB2022NSCQ-MSX0393","KJZD-M202301202","KJZD-K202201202","CSTB2023T-IADZXX0017"],"award-info":[{"award-number":["CSTB2022NSCQ-MSX0393","KJZD-M202301202","KJZD-K202201202","CSTB2023T-IADZXX0017"]}]},{"name":"Rural Revitalization Special Project of Chongqing Science and Technology Bureau, China","award":["CSTB2022NSCQ-MSX0393","KJZD-M202301202","KJZD-K202201202","CSTB2023T-IADZXX0017"],"award-info":[{"award-number":["CSTB2022NSCQ-MSX0393","KJZD-M202301202","KJZD-K202201202","CSTB2023T-IADZXX0017"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The stability of a class of quaternion-valued switching neural networks (QVSNNs) with time-varying delays is investigated in this paper. Limited prior research exists on the stability analysis of quaternion-valued neural networks (QVNNs). This paper addresses the stability analysis of quaternion-valued neural networks (QVNNs). With the help of some symmetric matrices with excellent properties, the stability analysis method in this paper is undecomposed. The QVSNN discussed herein evolves with average dwell time. Based on the Lyapunov theoretical framework and Wirtinger-based inequality, QVSNNs under any switching law have global asymptotic stability (GAS) and global exponential stability (GES). The state decay estimation of the system is also given and proved. Finally, the effective and practical applicability of the proposed method is demonstrated by two comprehensive numerical calculations.<\/jats:p>","DOI":"10.3390\/sym17070979","type":"journal-article","created":{"date-parts":[[2025,6,20]],"date-time":"2025-06-20T11:23:24Z","timestamp":1750418604000},"page":"979","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Analysis of Stability of Delayed Quaternion-Valued Switching Neural Networks via Symmetric Matrices"],"prefix":"10.3390","volume":"17","author":[{"given":"Yuan","family":"Dong","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing 404100, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tao","family":"Peng","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing 404100, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhengwen","family":"Tu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing 404100, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huiling","family":"Duan","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing 404100, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wei","family":"Tan","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing 404100, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1457","DOI":"10.1109\/TNN.2010.2050333","article-title":"Quaternion-based adaptive output feedback attitude control of spacecraft using Chebyshev neural networks","volume":"21","author":"Zou","year":"2010","journal-title":"IEEE Trans. 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