{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T08:36:58Z","timestamp":1773131818783,"version":"3.50.1"},"reference-count":13,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2023,12,7]],"date-time":"2023-12-07T00:00:00Z","timestamp":1701907200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"funder":[{"name":"Vietnam National University Ho Chi Minh City","award":["A2023-28-01"],"award-info":[{"award-number":["A2023-28-01"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,3,21]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>This paper addresses the exponential stability of nonlinear delay differential equations with Markovian switching. Drawing upon the comparison principle, we introduce the explicit criteria for achieving the exponential stability in mean square (sense). These criteria are formulated in terms of the equation coefficients and the generator of the Markovian switching process. As a result, these criteria can be verified without needing to construct the Lyapunov functions, a departure from the conventional approach found in the Razumikhin-type theorems. The paper includes an illustrative example and also demonstrates an application to the switched neural networks.<\/jats:p>","DOI":"10.1093\/imamci\/dnad031","type":"journal-article","created":{"date-parts":[[2023,12,9]],"date-time":"2023-12-09T05:59:23Z","timestamp":1702101563000},"page":"18-29","source":"Crossref","is-referenced-by-count":2,"title":["On exponential stability in mean square of nonlinear delay differential equations with Markovian switching"],"prefix":"10.1093","volume":"41","author":[{"given":"Ky","family":"Quan Tran","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics and Statistics , State University of New York - Korea Campus, Songdo Moonhwa-ro 119-2, Yeonsu-Gu, Incheon, 21985, South Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pham","family":"Huu Anh Ngoc","sequence":"additional","affiliation":[{"name":"Vietnam National University, Ho Chi Minh City, International University , Department of Mathematics, Ho Chi Minh city, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Thai","family":"Bao Tran","sequence":"additional","affiliation":[{"name":"Faculty of Information Systems, University of Information Technology, Vietnam National University , Ho Chi Minh City, Quarter 6, Linh Trung Ward, Thu Duc City 71308, Saigon, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nguyen","family":"Dinh Huy","sequence":"additional","affiliation":[{"name":"Vietnam National University, Ho Chi Minh City, University of Technology , Ho Chi Minh City, 268, Ly Thuong Kiet, Ward 14, District 10, Ho Chi Minh City 72506, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2023,12,7]]},"reference":[{"key":"2024032115215467000_ref1","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-3038-0","volume-title":"Continuous-Time Markov Chains","author":"Anderson","year":"1991"},{"key":"2024032115215467000_ref2","volume-title":"Nonnegative Matrices in Mathematical Sciences","author":"Berman","year":"1979"},{"key":"2024032115215467000_ref3","doi-asserted-by":"crossref","DOI":"10.1002\/9781118033029","volume-title":"Positive Linear Systems: Theory and Applications","author":"Farina","year":"2000"},{"key":"2024032115215467000_ref4","doi-asserted-by":"crossref","first-page":"1201","DOI":"10.1002\/rnc.4402","article-title":"Generalized criteria on delay-dependent stability of highly nonlinear hybrid stochastic systems","volume":"29","author":"Fei","year":"2019","journal-title":"Int. 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