{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T11:20:22Z","timestamp":1760008822745,"version":"3.41.2"},"reference-count":27,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2011,11,22]],"date-time":"2011-11-22T00:00:00Z","timestamp":1321920000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["60904028"],"award-info":[{"award-number":["60904028"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2012,1]]},"abstract":"<jats:p>This work addresses the asymptotic stability for a class of impulsive cellular neural networks with time\u2010varying delays and reaction\u2010diffusion. By using the impulsive integral inequality of Gronwall\u2010Bellman type and Hardy\u2010Sobolev inequality as well as piecewise continuous Lyapunov functions, we summarize some new and concise sufficient conditions ensuring the global exponential asymptotic stability of the equilibrium point. The provided stability criteria are applicable to Dirichlet boundary condition and showed to be dependent on all of the reaction\u2010diffusion coefficients, the dimension of the space, the delay, and the boundary of the spatial variables. Two examples are finally illustrated to demonstrate the effectiveness of our obtained results.<\/jats:p>","DOI":"10.1155\/2012\/501891","type":"journal-article","created":{"date-parts":[[2011,11,22]],"date-time":"2011-11-22T21:18:15Z","timestamp":1321996695000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Asymptotic Stability of Impulsive Reaction\u2010Diffusion Cellular Neural Networks with Time\u2010Varying Delays"],"prefix":"10.1155","volume":"2012","author":[{"given":"Yutian","family":"Zhang","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2011,11,22]]},"reference":[{"key":"e_1_2_6_1_2","doi-asserted-by":"publisher","DOI":"10.1109\/31.7600"},{"key":"e_1_2_6_2_2","doi-asserted-by":"publisher","DOI":"10.1109\/31.7601"},{"key":"e_1_2_6_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0375-9601(02)01720-6"},{"key":"e_1_2_6_4_2","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1109\/81.222796","article-title":"On stability of cellular neural networks with delay","volume":"40","author":"Cao J.","year":"1993","journal-title":"IEEE Transactions on Circuits and Systems"},{"key":"e_1_2_6_5_2","doi-asserted-by":"publisher","DOI":"10.1109\/81.917987"},{"key":"e_1_2_6_6_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.81.10.3088"},{"key":"e_1_2_6_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0362-546X(98)00045-5"},{"key":"e_1_2_6_8_2","doi-asserted-by":"publisher","DOI":"10.1109\/TNN.2007.902725"},{"key":"e_1_2_6_9_2","doi-asserted-by":"publisher","DOI":"10.1080\/02681119408806175"},{"key":"e_1_2_6_10_2","doi-asserted-by":"publisher","DOI":"10.1109\/81.841859"},{"key":"e_1_2_6_11_2","doi-asserted-by":"publisher","DOI":"10.1109\/31.101272"},{"key":"e_1_2_6_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0893-6080(98)00133-6"},{"key":"e_1_2_6_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2004.01.004"},{"volume-title":"Systems with Impulse Effect","year":"1989","author":"Bainov D. 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