{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T03:03:49Z","timestamp":1774580629944,"version":"3.50.1"},"reference-count":44,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2020,4,25]],"date-time":"2020-04-25T00:00:00Z","timestamp":1587772800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"King Mongkut\u2019s University of Technology Thonburi","award":["King Mongkut\u2019s University of Technology Thonburi"],"award-info":[{"award-number":["King Mongkut\u2019s University of Technology Thonburi"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In scientific disciplines and other engineering applications, most of the systems refer to uncertainties, because when modeling physical systems the uncertain parameters are unavoidable. In view of this, it is important to investigate dynamical systems with uncertain parameters. In the present study, a delay-dividing approach is devised to study the robust stability issue of uncertain neural networks. Specifically, the uncertain stochastic complex-valued Hopfield neural network (USCVHNN) with time delay is investigated. Here, the uncertainties of the system parameters are norm-bounded. Based on the Lyapunov mathematical approach and homeomorphism principle, the sufficient conditions for the global asymptotic stability of USCVHNN are derived. To perform this derivation, we divide a complex-valued neural network (CVNN) into two parts, namely real and imaginary, using the delay-dividing approach. All the criteria are expressed by exploiting the linear matrix inequalities (LMIs). Based on two examples, we obtain good theoretical results that ascertain the usefulness of the proposed delay-dividing approach for the USCVHNN model.<\/jats:p>","DOI":"10.3390\/sym12050683","type":"journal-article","created":{"date-parts":[[2020,4,29]],"date-time":"2020-04-29T01:29:15Z","timestamp":1588123755000},"page":"683","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":52,"title":["A Delay-Dividing Approach to Robust Stability of Uncertain Stochastic Complex-Valued Hopfield Delayed Neural Networks"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0130-9304","authenticated-orcid":false,"given":"Pharunyou","family":"Chanthorn","sequence":"first","affiliation":[{"name":"Research Center in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6053-6219","authenticated-orcid":false,"given":"Grienggrai","family":"Rajchakit","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Maejo University, Chiang Mai 50290, Thailand"}]},{"given":"Usa","family":"Humphries","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, King Mongkut\u2019s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang mod, Thung Khru 10140, Thailand"}]},{"given":"Pramet","family":"Kaewmesri","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, King Mongkut\u2019s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang mod, Thung Khru 10140, Thailand"}]},{"given":"Ramalingam","family":"Sriraman","sequence":"additional","affiliation":[{"name":"Department of Science and Humanities, Vel Tech High Tech Dr. Rangarajan Dr. Sakunthala Engineering College, Avadi, Tamil Nadu 600062, India"}]},{"given":"Chee Peng","family":"Lim","sequence":"additional","affiliation":[{"name":"Institute for Intelligent Systems Research and Innovation, Deakin University, Waurn Ponds, VIC 3216, Australia"}]}],"member":"1968","published-online":{"date-parts":[[2020,4,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1239","DOI":"10.1109\/TNN.2002.1031957","article-title":"An analysis of global asymptotic stability of delayed cellular neural networks","volume":"13","author":"Arik","year":"2002","journal-title":"IEEE Trans. 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