{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T15:52:05Z","timestamp":1772293925645,"version":"3.50.1"},"reference-count":32,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2018,12,3]],"date-time":"2018-12-03T00:00:00Z","timestamp":1543795200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Neural Process Lett"],"published-print":{"date-parts":[[2019,10]]},"DOI":"10.1007\/s11063-018-9961-y","type":"journal-article","created":{"date-parts":[[2018,12,3]],"date-time":"2018-12-03T08:45:04Z","timestamp":1543826704000},"page":"1831-1843","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Weighted Pseudo Almost Periodic Shunting Inhibitory Cellular Neural Networks with Multi-proportional Delays"],"prefix":"10.1007","volume":"50","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6003-3416","authenticated-orcid":false,"given":"Zhibin","family":"Chen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Aiping","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,12,3]]},"reference":[{"issue":"1551","key":"9961_CR1","doi-asserted-by":"publisher","first-page":"447","DOI":"10.1098\/rspa.1971.0078","volume":"322","author":"JR Ockendon","year":"1971","unstructured":"Ockendon JR, Tayler AB (1971) The dynamics of a current collection system for an electric locomotive. Proc R Soc Lond Ser A Math Phys Eng Sci 322(1551):447\u2013468","journal-title":"Proc R Soc Lond Ser A Math Phys Eng Sci"},{"issue":"3","key":"9961_CR2","doi-asserted-by":"publisher","first-page":"271","DOI":"10.1093\/imamat\/8.3.271","volume":"8","author":"L Fox","year":"1971","unstructured":"Fox L, Ockendon DF, Tayler AB (1971) On a functional-differential equations. J Inst Math Appl 8(3):271\u2013307","journal-title":"J Inst Math Appl"},{"key":"9961_CR3","first-page":"319","volume":"46","author":"GA Derfel","year":"1990","unstructured":"Derfel GA (1990) Kato problem for functional-differential equations and difference Schrodinger operator. Oper Theory 46:319\u2013321","journal-title":"Oper Theory"},{"key":"9961_CR4","doi-asserted-by":"publisher","unstructured":"Zhou L (2011) On the global dissipativity of a class of cellular neural networks with multi-pantograph delays. Adv Artif Neural Syst. https:\/\/doi.org\/10.1155\/2011\/941426:1-7","DOI":"10.1155\/2011\/941426:1-7"},{"key":"9961_CR5","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1007\/s11063-016-9516-z","volume":"45","author":"Y Yu","year":"2017","unstructured":"Yu Y (2017) Exponential stability of pseudo almost periodic solutions for cellular neural networks with multi-proportional delays. Neural Process Lett 45:141\u2013151","journal-title":"Neural Process Lett"},{"issue":"3","key":"9961_CR6","doi-asserted-by":"publisher","first-page":"651","DOI":"10.1007\/s11063-015-9486-6","volume":"44","author":"L Zhou","year":"2016","unstructured":"Zhou L, Zhao Z (2016) Exponential stability of a class of competitive neural networks with multi-proportional delays. Neural Process Lett 44(3):651\u2013663","journal-title":"Neural Process Lett"},{"issue":"1","key":"9961_CR7","doi-asserted-by":"publisher","first-page":"396","DOI":"10.1016\/j.neucom.2016.09.038","volume":"219","author":"L Zhou","year":"2017","unstructured":"Zhou L, Liu X (2017) Mean-square exponential input-to-state stability of stochastic recurrent neural networks with multi-proportional delays. Neurocomputing 219(1):396\u2013403","journal-title":"Neurocomputing"},{"key":"9961_CR8","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1016\/j.amc.2014.11.044","volume":"251","author":"LV Hiena","year":"2015","unstructured":"Hiena LV, Son DT (2015) Finite-time stability of a class of non-autonomous neural networks with heterogeneous proportional delays. Appl Math Comput 251:14\u201323","journal-title":"Appl Math Comput"},{"key":"9961_CR9","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1007\/s11063-017-9708-1","volume":"48","author":"Y Tang","year":"2018","unstructured":"Tang Y (2018) Pseudo almost periodic shunting inhibitory cellular neural networks with multi-proportional delays. Neural Process Lett 48:167\u2013177","journal-title":"Neural Process Lett"},{"key":"9961_CR10","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1007\/s11063-017-9631-5","volume":"47","author":"A Zhang","year":"2018","unstructured":"Zhang A (2018) Almost periodic solutions for SICNNs with neutral type proportional delays and D operators. Neural Process Lett 47:57\u201370","journal-title":"Neural Process Lett"},{"key":"9961_CR11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.amc.2016.03.018","volume":"285","author":"Y Yu","year":"2016","unstructured":"Yu Y (2016) Global exponential convergence for a class of HCNNs with neutral time-proportional delays. Appl Math Comput 285:1\u20137","journal-title":"Appl Math Comput"},{"key":"9961_CR12","doi-asserted-by":"publisher","first-page":"1323","DOI":"10.1007\/s13042-016-0507-1","volume":"8","author":"Z Huang","year":"2017","unstructured":"Huang Z (2017) Almost periodic solutions for fuzzy cellular neural networks with multi-proportional delays. Int J Mach Learn Cybern 8:1323\u20131331","journal-title":"Int J Mach Learn Cybern"},{"key":"9961_CR13","doi-asserted-by":"crossref","first-page":"6536","DOI":"10.1016\/j.amc.2011.12.026","volume":"218","author":"NS Al-Islam","year":"2012","unstructured":"Al-Islam NS, Alsulami SM, Diagana T (2012) Existence of weighted pseudo anti-periodic solutions to some non-autonomous differential equations. Appl Math Comput 218:6536\u20136548","journal-title":"Appl Math Comput"},{"issue":"24","key":"9961_CR14","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1016\/j.neucom.2018.09.065","volume":"325","author":"C Huang","year":"2019","unstructured":"Huang C, Liu B (2019) New studies on dynamic analysis of inertial neural networks involving non-reduced order method. Neurocomputing 325(24):283\u2013287","journal-title":"Neurocomputing"},{"key":"9961_CR15","doi-asserted-by":"publisher","first-page":"865","DOI":"10.1007\/s00521-016-2582-3","volume":"29","author":"Q Zhou","year":"2018","unstructured":"Zhou Q, Shao J (2018) Weighted pseudo anti-periodic SICNNs with mixed delays. Neural Comput Appl 29:865\u2013872","journal-title":"Neural Comput Appl"},{"issue":"10","key":"9961_CR16","doi-asserted-by":"publisher","first-page":"643","DOI":"10.1016\/j.crma.2006.10.008","volume":"343","author":"T Diagana","year":"2006","unstructured":"Diagana T (2006) Weighted pseudo almost periodic functions and applications. C R Acad Sci Paris Ser I 343(10):643\u2013646","journal-title":"C R Acad Sci Paris Ser I"},{"key":"9961_CR17","doi-asserted-by":"publisher","first-page":"2250","DOI":"10.1016\/j.na.2007.01.054","volume":"68","author":"T Diagana","year":"2008","unstructured":"Diagana T (2008) Weighted pseudo-almost periodic solutions to some differential equations. Nonlinear Anal 68:2250\u20132260","journal-title":"Nonlinear Anal"},{"key":"9961_CR18","doi-asserted-by":"publisher","unstructured":"Xu Y (2017) Weighted pseudo-almost periodic delayed cellular neural networks. Neural Comput Appl. https:\/\/doi.org\/10.1007\/s00521-016-2820-8","DOI":"10.1007\/s00521-016-2820-8"},{"key":"9961_CR19","doi-asserted-by":"publisher","first-page":"507","DOI":"10.1007\/s11063-017-9595-5","volume":"46","author":"Y Xu","year":"2017","unstructured":"Xu Y (2017) Exponential stability of weighted pseudo almost periodic solutions for HCNNs with mixed delays. Neural Process Lett 46:507\u2013519","journal-title":"Neural Process Lett"},{"key":"9961_CR20","doi-asserted-by":"publisher","unstructured":"Yang G, Wan W, (2018) Weighted pseudo almost periodic solutions for cellular neural networks with multi-proportional delays. Neural Process Lett. https:\/\/doi.org\/10.1007\/s11063-018-9851-3","DOI":"10.1007\/s11063-018-9851-3"},{"key":"9961_CR21","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4342-7","volume-title":"Introduction to functional differential equations","author":"JK Hale","year":"1993","unstructured":"Hale JK, Verduyn Lunel SM (1993) Introduction to functional differential equations. Springer, New York"},{"key":"9961_CR22","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0070324","volume-title":"Almost periodic differential equations. Lecture notes in mathematics","author":"AM Fink","year":"1974","unstructured":"Fink AM (1974) Almost periodic differential equations. Lecture notes in mathematics, vol 377. Springer, Berlin"},{"key":"9961_CR23","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1016\/j.apm.2018.07.007","volume":"64","author":"L Yao","year":"2018","unstructured":"Yao L (2018) Dynamics of Nicholson\u2019s blowflies models with a nonlinear density-dependent mortality. Appl Math Model 64:185\u2013195","journal-title":"Appl Math Model"},{"issue":"1","key":"9961_CR24","doi-asserted-by":"publisher","first-page":"559","DOI":"10.1016\/j.nonrwa.2012.07.016","volume":"14","author":"B Liu","year":"2013","unstructured":"Liu B (2013) Global exponential stability for BAM neural networks with time-varying delays in the leakage terms. Nonlinear Anal Real World Appl 14(1):559\u2013566","journal-title":"Nonlinear Anal Real World Appl"},{"key":"9961_CR25","doi-asserted-by":"publisher","first-page":"84","DOI":"10.1016\/j.neunet.2016.07.009","volume":"82","author":"C Huang","year":"2016","unstructured":"Huang C, Cao J, Cao J (2016) Stability analysis of switched cellular neural networks: a mode-dependent average dwell time approach. Neural Netw 82:84\u201399","journal-title":"Neural Netw"},{"key":"9961_CR26","doi-asserted-by":"publisher","first-page":"889","DOI":"10.1088\/0951-7715\/22\/4\/011","volume":"22","author":"J Lu","year":"2009","unstructured":"Lu J, Ho DWC, Wu L (2009) Exponential stabilization of switched stochastic dynamical networks. Nonlinearity 22:889\u2013911","journal-title":"Nonlinearity"},{"key":"9961_CR27","doi-asserted-by":"publisher","first-page":"2101","DOI":"10.1016\/j.jde.2013.12.015","volume":"256","author":"C Huang","year":"2014","unstructured":"Huang C, Yang Z, Yi T, Zou X (2014) On the basins of attraction for a class of delay differential equations with non-monotone bistable nonlinearities. J Differ Equ 256:2101\u20132114","journal-title":"J Differ Equ"},{"key":"9961_CR28","doi-asserted-by":"publisher","first-page":"1250176","DOI":"10.1142\/S0218127412501763","volume":"22","author":"J Lu","year":"2012","unstructured":"Lu J, Wang Z, Cao J, Ho DWC (2012) Pinning impulsive stabilization of nonlinear dynamical networks with time-varying delay. Int J Bifurc Chaos 22:1250176","journal-title":"Int J Bifurc Chaos"},{"key":"9961_CR29","doi-asserted-by":"publisher","first-page":"1617","DOI":"10.1109\/TNN.2009.2027810","volume":"20","author":"J Lu","year":"2009","unstructured":"Lu J, Ho DWC, Wang Z (2009) Pinning stabilization of linearly coupled stochastic neural networks via minimum number of controllers. IEEE Trans Neural Netw 20:1617\u20131629","journal-title":"IEEE Trans Neural Netw"},{"key":"9961_CR30","doi-asserted-by":"publisher","first-page":"1847","DOI":"10.1007\/s11071-016-3157-7","volume":"87","author":"L Li","year":"2017","unstructured":"Li L, Ho DWC, Lu J (2017) Event-based network consensus with communication delays. Nonlinear Dyn 87:1847\u20131858","journal-title":"Nonlinear Dyn"},{"key":"9961_CR31","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.neunet.2015.12.008","volume":"76","author":"L Li","year":"2016","unstructured":"Li L, Ho DWC, Cao J, Lu J (2016) Pinning cluster synchronization in an array of coupled neural networks under event-based mechanism. Neural Netw 76:1\u201312","journal-title":"Neural Netw"},{"key":"9961_CR32","doi-asserted-by":"publisher","first-page":"6520","DOI":"10.1016\/j.jfranklin.2018.06.021","volume":"355","author":"Y Li","year":"2018","unstructured":"Li Y, Lou J, Wang Z, Alsaadi FE (2018) Synchronization of dynamical networks with nonlinearly coupling function under hybrid pinning impulsive controllers. J Frankl Inst 355:6520\u20136530","journal-title":"J Frankl Inst"}],"container-title":["Neural Processing Letters"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11063-018-9961-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11063-018-9961-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11063-018-9961-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,9,7]],"date-time":"2022-09-07T10:37:57Z","timestamp":1662547077000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11063-018-9961-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,12,3]]},"references-count":32,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2019,10]]}},"alternative-id":["9961"],"URL":"https:\/\/doi.org\/10.1007\/s11063-018-9961-y","relation":{},"ISSN":["1370-4621","1573-773X"],"issn-type":[{"value":"1370-4621","type":"print"},{"value":"1573-773X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,12,3]]},"assertion":[{"value":"3 December 2018","order":1,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Compliance with Ethical Standards"}},{"value":"We confirm that we have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}