{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,8]],"date-time":"2026-05-08T17:43:42Z","timestamp":1778262222299,"version":"3.51.4"},"reference-count":48,"publisher":"Springer Science and Business Media LLC","issue":"21","license":[{"start":{"date-parts":[[2022,6,19]],"date-time":"2022-06-19T00:00:00Z","timestamp":1655596800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,6,19]],"date-time":"2022-06-19T00:00:00Z","timestamp":1655596800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100007129","name":"Natural Science Foundation of Shandong Province","doi-asserted-by":"publisher","award":["ZR2021MF007"],"award-info":[{"award-number":["ZR2021MF007"]}],"id":[{"id":"10.13039\/501100007129","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Neural Comput &amp; Applic"],"published-print":{"date-parts":[[2022,11]]},"DOI":"10.1007\/s00521-022-07457-1","type":"journal-article","created":{"date-parts":[[2022,6,19]],"date-time":"2022-06-19T18:02:35Z","timestamp":1655661755000},"page":"18561-18577","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Boundary intermittent stabilization for delay reaction\u2013diffusion cellular neural networks"],"prefix":"10.1007","volume":"34","author":[{"given":"Xing-Yu","family":"Li","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qing-Ling","family":"Fan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiao-Zhen","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4122-9832","authenticated-orcid":false,"given":"Kai-Ning","family":"Wu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,6,19]]},"reference":[{"issue":"6","key":"7457_CR1","doi-asserted-by":"publisher","first-page":"82","DOI":"10.1109\/MSP.2012.2205597","volume":"29","author":"G Hinton","year":"2012","unstructured":"Hinton G, Deng L, Yu D, Dahl G, Mohamed A, Jaitly N, Senior A, Vanhoucke V, Nguyen P, Sainath T, Kingsbury B (2012) Deep neural networks for acoustic modeling in speech recognition. IEEE Singal Process Mag 29(6):82\u201397","journal-title":"IEEE Singal Process Mag"},{"issue":"4","key":"7457_CR2","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1080\/13658810210137004","volume":"16","author":"X Li","year":"2002","unstructured":"Li X, Yeh A (2002) Neural-network-based cellular automata for simulating multiple land use changes using GIS. Int J Geogr Inf Sci 16(4):323\u2013343","journal-title":"Int J Geogr Inf Sci"},{"issue":"7356","key":"7457_CR3","doi-asserted-by":"publisher","first-page":"368","DOI":"10.1038\/nature10262","volume":"475","author":"L Qian","year":"2011","unstructured":"Qian L, Winfree E, Bruck J (2011) Neural network computation with DNA strand displacement cascades. Nature 475(7356):368\u2013372","journal-title":"Nature"},{"issue":"4","key":"7457_CR4","doi-asserted-by":"publisher","first-page":"781","DOI":"10.1109\/36.917895","volume":"39","author":"A Tatem","year":"2001","unstructured":"Tatem A, Lewis H, Atkinson P, Nixon M (2001) Super-resolution target identification from remotely sensed images using a Hopfield neural network. IEEE Trans Geosci Remote Sens 39(4):781\u2013796","journal-title":"IEEE Trans Geosci Remote Sens"},{"issue":"9","key":"7457_CR5","doi-asserted-by":"publisher","first-page":"1601","DOI":"10.1016\/S0893-6080(98)00080-X","volume":"11","author":"J Cao","year":"1998","unstructured":"Cao J, Zhou D (1998) Stability analysis of delayed cellular neural networks. Neural Netw 11(9):1601\u20131605","journal-title":"Neural Netw"},{"issue":"1","key":"7457_CR6","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1007\/s00521-012-0826-4","volume":"23","author":"Q Han","year":"2013","unstructured":"Han Q, Liao X, Li C (2013) Analysis of associative memories based on stability of cellular neural networks with time delay. Neural Comput Appl 23(1):237\u2013244","journal-title":"Neural Comput Appl"},{"issue":"6","key":"7457_CR7","doi-asserted-by":"publisher","first-page":"1639","DOI":"10.1109\/TNN.2006.881058","volume":"17","author":"J Wu","year":"2006","unstructured":"Wu J, Lian K (2006) Cellular neural field and its convergence analysis. IEEE Trans Neural Netw 17(6):1639\u20131641","journal-title":"IEEE Trans Neural Netw"},{"issue":"8","key":"7457_CR8","doi-asserted-by":"publisher","first-page":"2313","DOI":"10.1007\/s00521-016-2194-y","volume":"28","author":"Z Huang","year":"2017","unstructured":"Huang Z (2017) Almost periodic solutions for fuzzy cellular neural networks with time-varying delays. Neural Comput Appl 28(8):2313\u20132320","journal-title":"Neural Comput Appl"},{"issue":"12","key":"7457_CR9","doi-asserted-by":"publisher","first-page":"1309","DOI":"10.1007\/s00521-016-2641-9","volume":"29","author":"C Rajivganthi","year":"2018","unstructured":"Rajivganthi C, Rihan F, Lakshmanan S, Muthukumar P (2018) Finite-time stability analysis for fractional-order Cohen-Grossberg BAM neural networks with time delays. Neural Comput Appl 29(12):1309\u20131320","journal-title":"Neural Comput Appl"},{"issue":"1","key":"7457_CR10","doi-asserted-by":"publisher","first-page":"140","DOI":"10.1109\/TNN.2007.903154","volume":"19","author":"Z Yuan","year":"2008","unstructured":"Yuan Z, Huang L, Hu D, Liu B (2008) Convergence of nonautonomous Cohen-Grossberg-type neural networks with variable delays. IEEE Trans Neural Netw 19(1):140\u2013147","journal-title":"IEEE Trans Neural Netw"},{"issue":"8","key":"7457_CR11","doi-asserted-by":"publisher","first-page":"977","DOI":"10.1016\/S0893-6080(01)00059-4","volume":"14","author":"T Chen","year":"2001","unstructured":"Chen T (2001) Global exponential stability of delayed Hopfield neural networks. Neural Netw 14(8):977\u2013980","journal-title":"Neural Netw"},{"issue":"8","key":"7457_CR12","doi-asserted-by":"publisher","first-page":"1205","DOI":"10.1007\/s00521-010-0470-9","volume":"20","author":"W Liu","year":"2011","unstructured":"Liu W, Fu C, Hu H (2011) Global exponential stability of a class of Hopfield neural networks with delays. Neural Comput Appl 20(8):1205\u20131209","journal-title":"Neural Comput Appl"},{"issue":"8","key":"7457_CR13","doi-asserted-by":"publisher","first-page":"1889","DOI":"10.1109\/TNNLS.2016.2552640","volume":"28","author":"X Hu","year":"2017","unstructured":"Hu X, Feng G, Duan S, Liu L (2017) A memristive multilayer cellular neural network with applications to image processing. IEEE Trans Neural Netw Learn Syst 28(8):1889\u20131901","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"issue":"6","key":"7457_CR14","doi-asserted-by":"publisher","first-page":"487","DOI":"10.1109\/81.153647","volume":"39","author":"T Roska","year":"1992","unstructured":"Roska T, Wu C, Balsi M, Chua L (1992) Stability and dynamics of delay-type general and cellular neural networks. IEEE Trans Circults Syst I-Regul Pap 39(6):487\u2013490","journal-title":"IEEE Trans Circults Syst I-Regul Pap"},{"key":"7457_CR15","doi-asserted-by":"publisher","first-page":"819","DOI":"10.1016\/j.apm.2020.07.021","volume":"89","author":"O Nikan","year":"2021","unstructured":"Nikan O, Tenreiro Machado J, Golbabai A (2021) Numerical solution of time-fractional fourth-order reaction\u2013diffusion model arising in composite environments. Appl Math Model 89:819\u2013836","journal-title":"Appl Math Model"},{"issue":"12","key":"7457_CR16","doi-asserted-by":"publisher","first-page":"5231","DOI":"10.1109\/TNNLS.2020.2964843","volume":"31","author":"J Wang","year":"2020","unstructured":"Wang J, Qiu S, Chen W, Wu H, Huang T (2020) Recent advances on dynamical behaviors of coupled neural networks with and without reaction\u2013diffusion terms. IEEE Trans Neural Netw Learn Syst 31(12):5231\u20135244","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"issue":"1","key":"7457_CR17","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1007\/s00521-011-0695-2","volume":"22","author":"C Liu","year":"2013","unstructured":"Liu C, Li C, Huang T, Li C (2013) Stability of Hopfield neural networks with time delays and variable-time impulses. Neural Comput Appl 22(1):195\u2013202","journal-title":"Neural Comput Appl"},{"issue":"6","key":"7457_CR18","doi-asserted-by":"publisher","first-page":"1796","DOI":"10.1109\/TSMCB.2012.2230441","volume":"43","author":"Z Wu","year":"2013","unstructured":"Wu Z, Shi P, Su H, Chu J (2013) Stochastic synchronization of Markovian jump neural networks with time-varying delay using sampled data. IEEE Trans Cybern 43(6):1796\u20131806","journal-title":"IEEE Trans Cybern"},{"key":"7457_CR19","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1016\/j.neunet.2013.10.001","volume":"48","author":"S Wen","year":"2013","unstructured":"Wen S, Bao G, Zeng Z, Chen Y, Huang T (2013) Global exponential synchronization of memristor-based recurrent neural networks with time-varying delays. Neural Netw 48:195\u2013203","journal-title":"Neural Netw"},{"issue":"5","key":"7457_CR20","doi-asserted-by":"publisher","first-page":"1239","DOI":"10.1109\/TNN.2002.1031957","volume":"13","author":"S Arik","year":"2002","unstructured":"Arik S (2002) An analysis of global asymptotic stability of delayed cellular neural networks. IEEE Trans Neural Netw 13(5):1239\u20131242","journal-title":"IEEE Trans Neural Netw"},{"issue":"2","key":"7457_CR21","doi-asserted-by":"publisher","first-page":"268","DOI":"10.1109\/TCSI.2002.808213","volume":"50","author":"X Liao","year":"2003","unstructured":"Liao X, Wang J (2003) Algebraic criteria for global exponential stability of cellular neural networks with multiple time delays. IEEE Trans Circuits Syst I-Fundam Theory Appl 50(2):268\u2013275","journal-title":"IEEE Trans Circuits Syst I-Fundam Theory Appl"},{"issue":"1","key":"7457_CR22","first-page":"17","volume":"135","author":"S Mohamad","year":"2003","unstructured":"Mohamad S, Gopalsamy K (2003) Exponential stability of continuous-time and discrete-time cellular neural networks with delays. Appl Math Comput 135(1):17\u201338","journal-title":"Appl Math Comput"},{"issue":"3","key":"7457_CR23","doi-asserted-by":"publisher","first-page":"947","DOI":"10.1109\/TNN.2007.891628","volume":"18","author":"H Zhang","year":"2007","unstructured":"Zhang H, Wang Z (2007) Global asymptotic stability of delayed cellular neural networks. IEEE Trans Neural Netw 18(3):947\u2013950","journal-title":"IEEE Trans Neural Netw"},{"key":"7457_CR24","doi-asserted-by":"publisher","first-page":"S97","DOI":"10.1007\/s00521-016-2295-7","volume":"28","author":"Y Yu","year":"2017","unstructured":"Yu Y (2017) Finite-time stability on a class of SICNNs with neutral proportional delays. Neural Comput Appl 28:S97\u2013S105","journal-title":"Neural Comput Appl"},{"issue":"2","key":"7457_CR25","doi-asserted-by":"publisher","first-page":"653","DOI":"10.1016\/j.chaos.2006.01.044","volume":"33","author":"X Lou","year":"2007","unstructured":"Lou X, Cui B (2007) Boundedness and exponential stability for nonautonomous cellular neural networks with reaction\u2013diffusion terms. Chaos Solitons Fractals 33(2):653\u2013662","journal-title":"Chaos Solitons Fractals"},{"key":"7457_CR26","doi-asserted-by":"crossref","unstructured":"Rao R, Zhong S(2017) Stability analysis of impulsive stochastic reaction-diffusion cellular neural network with distributed delay via fixed point theory. Complexity","DOI":"10.1155\/2017\/6292597"},{"issue":"2","key":"7457_CR27","doi-asserted-by":"publisher","first-page":"1101","DOI":"10.1016\/j.nonrwa.2007.12.002","volume":"10","author":"L Wang","year":"2009","unstructured":"Wang L, Zhang R, Wang Y (2009) Global exponential stability of reaction\u2013diffusion cellular neural networks with S-type distributed time delays. Nonlinear Anal-Real World Appl 10(2):1101\u20131113","journal-title":"Nonlinear Anal-Real World Appl"},{"issue":"3\u20134","key":"7457_CR28","doi-asserted-by":"publisher","first-page":"1109","DOI":"10.1007\/s00521-012-1040-0","volume":"23","author":"G Yang","year":"2013","unstructured":"Yang G, Kao Y, Li W, Sun X (2013) Exponential stability of impulsive stochastic fuzzy cellular neural networks with mixed delays and reaction\u2013diffusion terms. Neural Comput Appl 23(3\u20134):1109\u20131121","journal-title":"Neural Comput Appl"},{"issue":"9","key":"7457_CR29","doi-asserted-by":"publisher","first-page":"3533","DOI":"10.1016\/j.apm.2008.11.017","volume":"33","author":"Q Song","year":"2009","unstructured":"Song Q, Wang Z (2009) Dynamical behaviors of fuzzy reaction\u2013diffusion periodic cellular neural networks with variable coefficients and delays. Appl Math Model 33(9):3533\u20133545","journal-title":"Appl Math Model"},{"issue":"7","key":"7457_CR30","doi-asserted-by":"publisher","first-page":"3045","DOI":"10.1109\/TCYB.2019.2926115","volume":"50","author":"Z Liu","year":"2020","unstructured":"Liu Z, Wen G, Yu X, Guan Z, Huang T (2020) Delayed impulsive control for consensus of multi-agent systems with switching commucation graphs. IEEE Trans Cybern 50(7):3045\u20133055","journal-title":"IEEE Trans Cybern"},{"issue":"5","key":"7457_CR31","doi-asserted-by":"publisher","first-page":"783","DOI":"10.1109\/TSMC.2016.2524063","volume":"47","author":"Z Liu","year":"2017","unstructured":"Liu Z, Yu X, Guan Z, Hu B, Li C (2017) Pulse-Modulated intermittent control in consensus of multi-agent systems. IEEE Trans Syst Man Cybern Syst 47(5):783\u2013793","journal-title":"IEEE Trans Syst Man Cybern Syst"},{"key":"7457_CR32","doi-asserted-by":"publisher","first-page":"269","DOI":"10.1016\/j.neunet.2020.09.009","volume":"132","author":"X Liu","year":"2021","unstructured":"Liu X, Li Z, Wu K (2021) Boundary Mittag-Leffler stabilization of fractional reaction\u2013diffusion cellular neural networks. Neural Netw 132:269\u2013280","journal-title":"Neural Netw"},{"issue":"1","key":"7457_CR33","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1023\/A:1017999917259","volume":"11","author":"T Kobayashi","year":"2001","unstructured":"Kobayashi T (2001) Adaptive stabilization of a class of reaction\u2013diffusion systems. Dyn Control 11(1):47\u201356","journal-title":"Dyn Control"},{"key":"7457_CR34","first-page":"52","volume":"329","author":"K Wu","year":"2018","unstructured":"Wu K, Sun H, Yang B, Lim C (2018) Finite-time boundary control for delay reaction\u2013diffusion systems. Appl Math Comput 329:52\u201363","journal-title":"Appl Math Comput"},{"issue":"5","key":"7457_CR35","doi-asserted-by":"publisher","first-page":"2085","DOI":"10.1109\/TCST.2018.2849072","volume":"27","author":"J Wang","year":"2019","unstructured":"Wang J, Liu Y, Sun C (2019) Adaptive neural boundary control design for nonlinear flexible distributed parameter systems. IEEE Trans Control Syst Technol 27(5):2085\u20132099","journal-title":"IEEE Trans Control Syst Technol"},{"key":"7457_CR36","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1016\/j.neucom.2016.02.050","volume":"197","author":"K Wu","year":"2016","unstructured":"Wu K, Tian T, Wang L, Wang W (2016) Asymptotical synchronization for a class of coupled time-delay partial differential systems via boundary control. Neurocomputing 197:113\u2013118","journal-title":"Neurocomputing"},{"key":"7457_CR37","doi-asserted-by":"publisher","first-page":"47889","DOI":"10.1109\/ACCESS.2018.2867343","volume":"6","author":"C Yang","year":"2016","unstructured":"Yang C, Huang T, Li Z, Zhang A, Qiu J, Alsaadi F (2016) Boundary control for exponential stabilization of nonlinear distributed parameter systems modeled by PIDEs. IEEE Access 6:47889\u201347896","journal-title":"IEEE Access"},{"issue":"3","key":"7457_CR38","doi-asserted-by":"publisher","first-page":"1763","DOI":"10.1007\/s11071-018-4455-z","volume":"94","author":"K Wu","year":"2018","unstructured":"Wu K, Wang J, Lim C (2018) Synchronization of stochastic reaction\u2013diffusion systems via boundary control. Nonlinear Dyn 94(3):1763\u20131773","journal-title":"Nonlinear Dyn"},{"key":"7457_CR39","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2021.109667","volume":"129","author":"Y Cheng","year":"2021","unstructured":"Cheng Y, Wu Y, Guo BZ (2021) Absolute boundary stabilization for an axially moving Kirchhoff beam. Automatica 129:109667","journal-title":"Automatica"},{"issue":"1","key":"7457_CR40","doi-asserted-by":"publisher","DOI":"10.1063\/1.2430394","volume":"17","author":"C Li","year":"2007","unstructured":"Li C, Liao X, Huang T (2007) Exponential stabilization of chaotic systems with delay by periodically intermittent control. Chaos 17(1):013103","journal-title":"Chaos"},{"issue":"7","key":"7457_CR41","doi-asserted-by":"publisher","first-page":"1431","DOI":"10.1109\/TNNLS.2014.2345125","volume":"26","author":"G Zhang","year":"2015","unstructured":"Zhang G, Shen Y (2015) Exponential stabilization of memristor-based chaotic neural networks with time-varying delays via intermittent control. IEEE Trans Neural Netw Learn Syst 26(7):1431\u20131441","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"key":"7457_CR42","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1016\/j.neunet.2015.08.002","volume":"71","author":"W Zhang","year":"2015","unstructured":"Zhang W, Li C, Huang T, Xiao M (2015) Synchronization of neural networks with stochastic perturbation via aperiodically intermittent control. Neural Netw 71:105\u2013111","journal-title":"Neural Netw"},{"key":"7457_CR43","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.neunet.2014.03.009","volume":"55","author":"G Zhang","year":"2014","unstructured":"Zhang G, Shen Y (2014) Exponential synchronization of delayed memristor-based chaotic neural networks via periodically intermittent control. Neural Netw 55:1\u201310","journal-title":"Neural Netw"},{"issue":"7","key":"7457_CR44","doi-asserted-by":"publisher","first-page":"2651","DOI":"10.1007\/s00521-018-3671-2","volume":"32","author":"Y Dong","year":"2020","unstructured":"Dong Y, Guo L, Hao J (2020) Robust exponential stabilization for uncertain neutral neural networks with interval time-varying delays by periodically intermittent control. Neural Comput Appl 32(7):2651\u20132664","journal-title":"Neural Comput Appl"},{"key":"7457_CR45","doi-asserted-by":"crossref","unstructured":"Tucsnak M, Weiss G (2009) Observation and control for operator semigroups. Birkhauser Verlag AG","DOI":"10.1007\/978-3-7643-8994-9"},{"key":"7457_CR46","first-page":"52","volume":"329","author":"K Wu","year":"2018","unstructured":"Wu K, Sun H, Yang B, Lim C (2018) Finite-time boundary control for delay reaction\u2013diffusion systems. Appl Math Comput 329:52\u201363","journal-title":"Appl Math Comput"},{"key":"7457_CR47","doi-asserted-by":"crossref","unstructured":"Boyd S, Laurent E, Ghaoui L, Feron E, Balakrishnan V (1994) Linear matrix inequalities in system and control theory. Soc Ind Appl Math","DOI":"10.1137\/1.9781611970777"},{"key":"7457_CR48","doi-asserted-by":"publisher","first-page":"6757","DOI":"10.1007\/s00521-018-3498-x","volume":"31","author":"H Li","year":"2019","unstructured":"Li H, Zhang W, Li C, Zhang W (2019) Global asymptotical stability for a class of non-autonomous impulsive inertial neural networks with unbounded time-varying delay. Neural Comput Appl 31:6757\u20136766","journal-title":"Neural Comput Appl"}],"container-title":["Neural Computing and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-022-07457-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00521-022-07457-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-022-07457-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,10,21]],"date-time":"2022-10-21T02:10:13Z","timestamp":1666318213000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00521-022-07457-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,6,19]]},"references-count":48,"journal-issue":{"issue":"21","published-print":{"date-parts":[[2022,11]]}},"alternative-id":["7457"],"URL":"https:\/\/doi.org\/10.1007\/s00521-022-07457-1","relation":{},"ISSN":["0941-0643","1433-3058"],"issn-type":[{"value":"0941-0643","type":"print"},{"value":"1433-3058","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,6,19]]},"assertion":[{"value":"1 November 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 May 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 June 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that there is no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}