{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,6,9]],"date-time":"2023-06-09T08:27:14Z","timestamp":1686299234571},"reference-count":47,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2014,12,13]],"date-time":"2014-12-13T00:00:00Z","timestamp":1418428800000},"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 Comput &amp; Applic"],"published-print":{"date-parts":[[2015,7]]},"DOI":"10.1007\/s00521-014-1784-9","type":"journal-article","created":{"date-parts":[[2014,12,12]],"date-time":"2014-12-12T04:55:17Z","timestamp":1418360117000},"page":"1073-1084","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Square-mean almost periodic solution for stochastic Hopfield neural networks with time-varying delays on timescales"],"prefix":"10.1007","volume":"26","author":[{"given":"Yongkun","family":"Li","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Li","family":"Yang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wanqin","family":"Wu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2014,12,13]]},"reference":[{"key":"1784_CR1","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1016\/j.cam.2003.11.014","volume":"169","author":"SH Chen","year":"2004","unstructured":"Chen SH, Zhang Q, Wang CP (2004) Existence and stability of equilibria of the continuous-time Hopfield neural network. J Comput Appl Math 169:117\u2013125","journal-title":"J Comput Appl Math"},{"key":"1784_CR2","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1016\/S0893-6080(03)00077-7","volume":"17","author":"HY Zhao","year":"2004","unstructured":"Zhao HY (2004) Global asymptotic stability of Hopfield neural network involving distributed delays. Neural Netw 17:47\u201353","journal-title":"Neural Netw"},{"key":"1784_CR3","doi-asserted-by":"crossref","first-page":"1513","DOI":"10.1016\/j.apm.2008.02.006","volume":"33","author":"J Zhou","year":"2009","unstructured":"Zhou J, Li SY, Yang ZG (2009) Global exponential stability of Hopfield neural networks with distributed delays. Appl Math Model 33:1513\u20131520","journal-title":"Appl Math Model"},{"key":"1784_CR4","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1016\/j.physleta.2005.06.008","volume":"343","author":"XF Yang","year":"2005","unstructured":"Yang XF, Liao XF, Evans DJ, Tang YY (2005) Existence and stability of periodic solution in impulsive Hopfield neural networks with finite distributed delays. Phys Lett A 343:108\u2013116","journal-title":"Phys Lett A"},{"key":"1784_CR5","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1016\/j.physleta.2005.12.014","volume":"352","author":"H Xiang","year":"2006","unstructured":"Xiang H, Yan KM, Wang BY (2006) Existence and global exponential stability of periodic solution for delayed high-order Hopfield-type neural networks. Phys Lett A 352:341\u2013349","journal-title":"Phys Lett A"},{"key":"1784_CR6","doi-asserted-by":"crossref","first-page":"2455","DOI":"10.1016\/j.neucom.2008.11.010","volume":"72","author":"HJ Jiang","year":"2009","unstructured":"Jiang HJ, Teng ZD (2009) Boundedness, periodic solutions and global stability for cellular neural networks with variable coefficients and infinite delays. Neurocomputing 72:2455\u20132463","journal-title":"Neurocomputing"},{"key":"1784_CR7","doi-asserted-by":"crossref","first-page":"4890","DOI":"10.1016\/j.amc.2010.11.025","volume":"217","author":"E Kaslik","year":"2011","unstructured":"Kaslik E, Sivasundaram S (2011) Multiple periodic solutions in impulsive hybrid neural networks with delays. Appl Math Comput 217:4890\u20134899","journal-title":"Appl Math Comput"},{"key":"1784_CR8","doi-asserted-by":"crossref","first-page":"196","DOI":"10.1016\/j.neucom.2005.05.002","volume":"68","author":"BW Liu","year":"2005","unstructured":"Liu BW, Huang LH (2005) Existence and exponential stability of almost periodic solutions for Hopfield neural networks with delays. Neurocomputing 68:196\u2013207","journal-title":"Neurocomputing"},{"key":"1784_CR9","doi-asserted-by":"crossref","first-page":"528","DOI":"10.1016\/j.aml.2008.06.025","volume":"22","author":"B Xiao","year":"2009","unstructured":"Xiao B (2009) Existence and uniqueness of almost periodic solutions for a class of Hopfield neural networks with neutral delays. Appl Math Lett 22:528\u2013533","journal-title":"Appl Math Lett"},{"key":"1784_CR10","doi-asserted-by":"crossref","first-page":"5850","DOI":"10.1016\/j.na.2009.05.008","volume":"71","author":"CZ Bai","year":"2009","unstructured":"Bai CZ (2009) Existence and stability of almost periodic solutions of Hopfield neural networks with continuously distributed delays. Nonlinear Anal 71:5850\u20135859","journal-title":"Nonlinear Anal"},{"key":"1784_CR11","doi-asserted-by":"crossref","first-page":"623","DOI":"10.1016\/j.amc.2010.01.095","volume":"216","author":"PL Shi","year":"2010","unstructured":"Shi PL, Dong LZ (2010) Existence and exponential stability of anti-periodic solutions of Hopfield neural networks with impulses. Appl Math Comput 216:623\u2013630","journal-title":"Appl Math Comput"},{"key":"1784_CR12","first-page":"3014","volume":"12","author":"LJ Pan","year":"2011","unstructured":"Pan LJ, Cao Jinde (2011) Anti-periodic solution for delayed cellular neural networks with impulsive effects. Nonlinear Anal Real World Appl 12:3014\u20133027","journal-title":"Nonlinear Anal Real World Appl"},{"key":"1784_CR13","volume-title":"Neural networks","author":"S Haykin","year":"1994","unstructured":"Haykin S (1994) Neural networks. Prentice-Hall, NJ"},{"issue":"5","key":"1784_CR14","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1016\/S0016-0032(01)00016-3","volume":"338","author":"S Blythe","year":"2001","unstructured":"Blythe S, Mao X, Liao X (2001) Stability of stochastic delay neural networks. J Frankl Inst 338(5):481\u2013495","journal-title":"J Frankl Inst"},{"key":"1784_CR15","doi-asserted-by":"crossref","first-page":"1119","DOI":"10.1016\/j.nonrwa.2005.10.004","volume":"7","author":"ZD Wang","year":"2006","unstructured":"Wang ZD, Shu HS, Fang J, Liu XH (2006) Robust stability for stochastic Hopfield neural networks with time delays. Nonlinear Anal Real World Appl 7:1119\u20131128","journal-title":"Nonlinear Anal Real World Appl"},{"key":"1784_CR16","doi-asserted-by":"crossref","first-page":"316","DOI":"10.1016\/j.jmaa.2006.05.041","volume":"328","author":"XY Lou","year":"2007","unstructured":"Lou XY, Cui BT (2007) Delay-dependent stochastic stability of delayed Hopfield neural networks with Markovian jump parameters. J Math Anal Appl 328:316\u2013326","journal-title":"J Math Anal Appl"},{"key":"1784_CR17","doi-asserted-by":"crossref","first-page":"1349","DOI":"10.1016\/j.nonrwa.2006.06.010","volume":"8","author":"JH Zhang","year":"2007","unstructured":"Zhang JH, Shi P, Qiu JQ (2007) Novel robust stability criteria for uncertain stochastic Hopfield neural networks with time-varying delays. Nonlinear Anal Real World Appl 8:1349\u20131357","journal-title":"Nonlinear Anal Real World Appl"},{"key":"1784_CR18","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1016\/j.amc.2007.09.025","volume":"199","author":"QH Zhou","year":"2008","unstructured":"Zhou QH, Wan L (2008) Exponential stability of stochastic delayed Hopfield neural networks. Appl Math Comput 199:84\u201389","journal-title":"Appl Math Comput"},{"key":"1784_CR19","doi-asserted-by":"crossref","first-page":"3503","DOI":"10.1016\/j.fss.2009.09.015","volume":"160","author":"L Sheng","year":"2009","unstructured":"Sheng L, Gao M, Yang HZ (2009) Delay-dependent robust stability for uncertain stochastic fuzzy Hopfield neural networks with time-varying delays. Fuzzy Sets Syst 160:3503\u20133517","journal-title":"Fuzzy Sets Syst"},{"key":"1784_CR20","doi-asserted-by":"crossref","first-page":"4370","DOI":"10.1016\/j.amc.2009.12.068","volume":"215","author":"XD Li","year":"2010","unstructured":"Li XD (2010) Global robust stability for stochastic interval neural networks with continuously distributed delays of neutral type. Appl Math Comput 215:4370\u20134384","journal-title":"Appl Math Comput"},{"key":"1784_CR21","doi-asserted-by":"crossref","first-page":"435","DOI":"10.1016\/j.cnsns.2010.03.003","volume":"16","author":"XL Fu","year":"2011","unstructured":"Fu XL, Li XD (2011) LMI conditions for stability of impulsive stochastic Cohen\u2013Grossberg neural networks with mixed delays. Commun Nonlinear Sci Numer Simul 16:435\u2013454","journal-title":"Commun Nonlinear Sci Numer Simul"},{"key":"1784_CR22","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1007\/BF03323153","volume":"18","author":"S Hilger","year":"1990","unstructured":"Hilger S (1990) Analysis on measure chains: a unified approach to continuous and discrete calculus. Result Math 18:18\u201356","journal-title":"Result Math"},{"key":"1784_CR23","doi-asserted-by":"crossref","first-page":"2455","DOI":"10.1016\/j.apm.2008.07.011","volume":"33","author":"G Zhang","year":"2009","unstructured":"Zhang G, Dong WL, Li QL, Liang HY (2009) Positive solutions for higher oder nonlinear neutral dynamic equations on time scales. Appl Math Model 33:2455\u20132463","journal-title":"Appl Math Model"},{"key":"1784_CR24","doi-asserted-by":"crossref","first-page":"1621","DOI":"10.1016\/j.neucom.2008.08.010","volume":"72","author":"YK Li","year":"2009","unstructured":"Li YK, Chen X, Zhao L (2009) Stability and existence of periodic solutions to delayed Cohen\u2013Grossberg BAM neural networks with impulses on time scales. Neurocomputing 72:1621\u20131630","journal-title":"Neurocomputing"},{"key":"1784_CR25","doi-asserted-by":"crossref","first-page":"571","DOI":"10.1016\/j.aml.2010.01.013","volume":"23","author":"FY Zheng","year":"2010","unstructured":"Zheng FY, Zhou Z, Ma CQ (2010) Periodic solutions for a delayed neural network model on a special time scale. Appl Math Lett 23:571\u2013575","journal-title":"Appl Math Lett"},{"key":"1784_CR26","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1016\/j.neunet.2011.02.001","volume":"24","author":"ZQ Zhang","year":"2011","unstructured":"Zhang ZQ, Liu KY (2011) Existence and global exponential stability of a periodic solution to interval general bidirectional associative memory (BAM) neural networks with multiple delays on time scales. Neural Netw 24:427\u2013439","journal-title":"Neural Netw"},{"key":"1784_CR27","doi-asserted-by":"crossref","unstructured":"Li YK (2013) Periodic solutions of nonautonomous cellular neural networks with impulses and delays on time scales. IMA J Math Control Inf. doi: 10.1093\/imamci\/dnt012","DOI":"10.1093\/imamci\/dnt012"},{"key":"1784_CR28","doi-asserted-by":"crossref","first-page":"3258","DOI":"10.1016\/j.cnsns.2011.11.034","volume":"17","author":"YK Li","year":"2012","unstructured":"Li YK, Wang C (2012) Almost periodic solutions of shunting inhibitory cellular neural networks on time scales. Commun Nonlinear Sci Numer Simul 17:3258\u20133266","journal-title":"Commun Nonlinear Sci Numer Simul"},{"key":"1784_CR29","doi-asserted-by":"crossref","unstructured":"Li YK, Yang L (2013) Almost periodic solutions for neutral-type BAM neural networks with delays on time scales. J Appl Math. Article ID 942309.","DOI":"10.1155\/2013\/942309"},{"key":"1784_CR30","doi-asserted-by":"crossref","first-page":"3326","DOI":"10.1016\/j.cnsns.2010.11.004","volume":"16","author":"YK Li","year":"2011","unstructured":"Li YK, Shu JY (2011) Anti-periodic solutions to impulsive shunting inhibitory cellular neural networks with distributed delays on time scales. Commun Nonlinear Sci Numer Simul 16:3326\u20133336","journal-title":"Commun Nonlinear Sci Numer Simul"},{"key":"1784_CR31","doi-asserted-by":"crossref","first-page":"1127","DOI":"10.1080\/00207720903308371","volume":"42","author":"YK Li","year":"2011","unstructured":"Li YK, Yang L, Wu WQ (2011) Anti-periodic solutions for a class of Cohen\u2013Grossberg neural networks with time-varying delays on time scales. Int J Syst Sci 42:1127\u20131132","journal-title":"Int J Syst Sci"},{"key":"1784_CR32","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1080\/07362994.2011.564441","volume":"29","author":"D Grow","year":"2011","unstructured":"Grow D, Sanyal S (2011) Brownian motion indexed by a time scale. Stoch Anal Appl 29:457\u2013472","journal-title":"Stoch Anal Appl"},{"key":"1784_CR33","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1016\/j.jmaa.2013.04.075","volume":"406","author":"M Bohner","year":"2013","unstructured":"Bohner M, Wintz N (2013) The Kalman filter for linear systems on time scales. J Math Anal Appl 406:419\u2013436","journal-title":"J Math Anal Appl"},{"issue":"86","key":"1784_CR34","first-page":"1","volume":"2012","author":"C Lungan","year":"2012","unstructured":"Lungan C, Lupulescu V (2012) Random dynamical systems on time scales. Electron J Differ Equ 2012(86):1\u201314","journal-title":"Electron J Differ Equ"},{"issue":"57","key":"1784_CR35","first-page":"1","volume":"2013","author":"M Bohner","year":"2013","unstructured":"Bohner M, Stanzhytskyi OM, Bratochkina AO (2013) Stochastic dynamic equations on general time scales. Electron J Differ Equ 2013(57):1\u201315","journal-title":"Electron J Differ Equ"},{"key":"1784_CR36","unstructured":"Sanyal S (2008) Stochastic dynamic equations, Ph.D. Dissertation, Missouri University of Science and Technology, Rolla, Missouri, USA."},{"key":"1784_CR37","doi-asserted-by":"crossref","first-page":"1677","DOI":"10.1016\/j.spl.2012.05.008","volume":"82","author":"D Grow","year":"2012","unstructured":"Grow D, Sanyal S (2012) The quadratic variation of Brownian motion on a time scale. Stat Probab Lett 82:1677\u20131680","journal-title":"Stat Probab Lett"},{"issue":"2","key":"1784_CR38","first-page":"317","volume":"38","author":"NH Du","year":"2013","unstructured":"Du NH, Dieu NH (2013) Stochastic dynamic equations on time scales. Acta Math 38(2):317\u2013338","journal-title":"Acta Math"},{"issue":"11","key":"1784_CR39","first-page":"1057","volume":"29","author":"NH Du","year":"2011","unstructured":"Du NH, Dieu NH (2011) The first attempt on the stochastic calculus on time scale. Stoch Anal Appl 29(11):1057\u20131080","journal-title":"Stoch Anal Appl"},{"issue":"2","key":"1784_CR40","first-page":"77","volume":"2","author":"G David","year":"2013","unstructured":"David G, Suman S (2013) Existence and uniqueness for stochastic dynamic equations. Int J Stat Probab 2(2):77\u201388","journal-title":"Int J Stat Probab"},{"key":"1784_CR41","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-0201-1","volume-title":"Dynamic equations on time scales: an introduction with applications","author":"M Bohner","year":"2001","unstructured":"Bohner M, Peterson A (2001) Dynamic equations on time scales: an introduction with applications. Birkh\u00e4user, Boston"},{"key":"1784_CR42","doi-asserted-by":"crossref","first-page":"1","DOI":"10.14232\/ejqtde.2009.4.1","volume":"1","author":"M Ad\u0131var","year":"2009","unstructured":"Ad\u0131var M, Raffoul YN (2009) Existence of periodic solutions in totally nonlinear delay dynamic equations. Electron J Qual Theory Differ Equ 1:1\u201320","journal-title":"Electron J Qual Theory Differ Equ"},{"key":"1784_CR43","unstructured":"Li YK, Wang C (2011) Uniformly almost periodic functions and almost periodic solutions to dynamic equations on time scales. Abs Appl Anal. Article ID 341520."},{"key":"1784_CR44","doi-asserted-by":"crossref","unstructured":"Lizama C, Mesquita JG, Ponce R (2014) A connection between almost periodic functions defined on time scales and $${\\mathbb{R}}$$ R . Appl Anal. doi: 10.1080\/00036811.2013.875161 .","DOI":"10.1080\/00036811.2013.875161"},{"key":"1784_CR45","doi-asserted-by":"crossref","first-page":"104","DOI":"10.1016\/j.jmaa.2009.10.072","volume":"364","author":"F Wu","year":"2010","unstructured":"Wu F, Hu S, Liu Y (2010) Positive solution and its asymptotic behavior of stochastic functional Kolmogorov-type system. J Math Anal Appl 364:104\u2013118","journal-title":"J Math Anal Appl"},{"issue":"10","key":"1784_CR46","doi-asserted-by":"crossref","first-page":"3689","DOI":"10.1090\/S0002-9939-10-10377-3","volume":"138","author":"M Fu","year":"2010","unstructured":"Fu M, Liu Z (2010) Square-mean almost automorphic solutions for some stochastic differential equations. Proc Am Math Soc 138(10):3689\u20133701","journal-title":"Proc Am Math Soc"},{"issue":"7","key":"1784_CR47","doi-asserted-by":"crossref","first-page":"819","DOI":"10.1080\/00036810701397788","volume":"86","author":"PH Bezandry","year":"2007","unstructured":"Bezandry PH, Diagana T (2007) Existence of almost periodic solutions to some stochastic differential equations. Appl Anal 86(7):819\u2013827","journal-title":"Appl Anal"}],"container-title":["Neural Computing and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-014-1784-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00521-014-1784-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-014-1784-9","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,29]],"date-time":"2019-05-29T02:21:17Z","timestamp":1559096477000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00521-014-1784-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,12,13]]},"references-count":47,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2015,7]]}},"alternative-id":["1784"],"URL":"https:\/\/doi.org\/10.1007\/s00521-014-1784-9","relation":{},"ISSN":["0941-0643","1433-3058"],"issn-type":[{"value":"0941-0643","type":"print"},{"value":"1433-3058","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,12,13]]}}}