{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,18]],"date-time":"2025-10-18T10:51:03Z","timestamp":1760784663484,"version":"3.37.3"},"reference-count":47,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2019,5,24]],"date-time":"2019-05-24T00:00:00Z","timestamp":1558656000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,5,24]],"date-time":"2019-05-24T00:00:00Z","timestamp":1558656000000},"content-version":"vor","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":[[2019,8]]},"DOI":"10.1007\/s11063-019-10048-2","type":"journal-article","created":{"date-parts":[[2019,5,24]],"date-time":"2019-05-24T13:07:01Z","timestamp":1558703221000},"page":"297-320","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Pseudo Almost Periodic Solution of Recurrent Neural Networks with D Operator on Time Scales"],"prefix":"10.1007","volume":"50","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8252-9017","authenticated-orcid":false,"given":"Chaouki","family":"Aouiti","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"El Abed","family":"Assali","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Imen","family":"Ben Gharbia","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2019,5,24]]},"reference":[{"key":"10048_CR1","first-page":"1","volume":"99","author":"S Wen","year":"2018","unstructured":"Wen S, Hu R, Yang Y, Huang T, Zeng Z, Song YD (2018) Memristor-based echo state network with online least mean square. IEEE Trans Syst Man Cybern Syst 99:1\u201310","journal-title":"IEEE Trans Syst Man Cybern Syst"},{"key":"10048_CR2","doi-asserted-by":"publisher","unstructured":"Wen S, Xiao S, Yan Z, Zeng Z, Huang T (2018) Adjusting learning rate of memristor-based multilayer neural networks via fuzzy method. IEEE Trans Comput Aided Des Integr Circuits Syst. \n                    https:\/\/doi.org\/10.1109\/TCAD.2018.2834436","DOI":"10.1109\/TCAD.2018.2834436"},{"key":"10048_CR3","doi-asserted-by":"publisher","DOI":"10.1109\/TCSVT.2018.2867934","author":"S Wen","year":"2018","unstructured":"Wen S, Liu W, Yang Y, Huang T, Zeng Z (2018) Generating realistic videos from keyframes with concatenated GANs. IEEE Trans Circuits Syst Video Technol. \n                    https:\/\/doi.org\/10.1109\/TCSVT.2018.2867934","journal-title":"IEEE Trans Circuits Syst Video Technol"},{"issue":"8","key":"10048_CR4","doi-asserted-by":"publisher","first-page":"2554","DOI":"10.1073\/pnas.79.8.2554","volume":"79","author":"JJ Hopfield","year":"1982","unstructured":"Hopfield JJ (1982) Neural networks and physical systems with emergent collective computational abilities. Proc Natl Acad Sci 79(8):2554\u20132558","journal-title":"Proc Natl Acad Sci"},{"key":"10048_CR5","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfranklin.2019.01.028","author":"C Aouiti","year":"2019","unstructured":"Aouiti C, Gharbia IB, Cao J, Alsaedi A (2019) Dynamics of impulsive neutral-type BAM neural networks. J Frankl Inst. \n                    https:\/\/doi.org\/10.1016\/j.jfranklin.2019.01.028","journal-title":"J Frankl Inst"},{"key":"10048_CR6","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1016\/j.chaos.2017.12.022","volume":"107","author":"C Aouiti","year":"2018","unstructured":"Aouiti C, Gharbia IB, Cao J, M\u2019hamdi MS, Alsaedi A (2018) Existence and global exponential stability of pseudo almost periodic solution for neutral delay BAM neural networks with time-varying delay in leakage terms. Chaos Solitons Fractals 107:111\u2013127","journal-title":"Chaos Solitons Fractals"},{"key":"10048_CR7","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1016\/j.neucom.2018.11.020","volume":"332","author":"AM Alimi","year":"2019","unstructured":"Alimi AM, Aouiti C, Assali EA (2019) Finite-time and fixed-time synchronization of a class of inertial neural networks with multi-proportional delays and its application to secure communication. Neurocomputing 332:29\u201343","journal-title":"Neurocomputing"},{"issue":"2","key":"10048_CR8","doi-asserted-by":"publisher","first-page":"417","DOI":"10.1109\/TCSI.2004.841574","volume":"52","author":"J Cao","year":"2005","unstructured":"Cao J, Wang J (2005) Global asymptotic and robust stability of recurrent neural networks with time delays. IEEE Trans Circuits Syst I Regul Pap 52(2):417\u2013426","journal-title":"IEEE Trans Circuits Syst I Regul Pap"},{"issue":"2","key":"10048_CR9","doi-asserted-by":"publisher","first-page":"457","DOI":"10.1109\/72.991431","volume":"13","author":"J Cao","year":"2002","unstructured":"Cao J, Wang L (2002) Exponential stability and periodic oscillatory solution in BAM networks with delays. IEEE Trans Neural Netw 13(2):457\u2013463","journal-title":"IEEE Trans Neural Netw"},{"key":"10048_CR10","doi-asserted-by":"publisher","first-page":"1645","DOI":"10.1007\/s11063-018-9791-y","volume":"48","author":"C Aouiti","year":"2018","unstructured":"Aouiti C, Miaadi F (2018) Finite-time stabilization of neutral Hopfield neural networks with mixed delays. Neural Process Lett. 48:1645\u20131669. \n                    https:\/\/doi.org\/10.1007\/s11063-018-9791-y","journal-title":"Neural Process Lett."},{"key":"10048_CR11","doi-asserted-by":"publisher","first-page":"274","DOI":"10.1016\/j.neucom.2018.01.061","volume":"321","author":"AM Alimi","year":"2018","unstructured":"Alimi AM, Aouiti C, Ch\u00e9rif F, Dridi F, M\u2019hamdi MS (2018) Dynamics and oscillations of generalized high-order Hopfield neural networks with mixed delays. Neurocomputing 321:274\u2013295. \n                    https:\/\/doi.org\/10.1016\/j.neucom.2018.01.061","journal-title":"Neurocomputing"},{"key":"10048_CR12","doi-asserted-by":"publisher","unstructured":"Aouiti C, Miaadi F (2018) Pullback attractor for neutral Hopfield neural networks with time delay in the leakage term and mixed time delays. Neural Comput Appl. \n                    https:\/\/doi.org\/10.1007\/s00521-017-3314-z","DOI":"10.1007\/s00521-017-3314-z"},{"issue":"6","key":"10048_CR13","doi-asserted-by":"publisher","first-page":"868","DOI":"10.1109\/TNNLS.2012.2236352","volume":"24","author":"X Li","year":"2013","unstructured":"Li X, Song S (2013) Impulsive control for existence, uniqueness, and global stability of periodic solutions of recurrent neural networks with discrete and continuously distributed delays. IEEE Trans Neural Netw Learn Syst 24(6):868\u2013877","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"issue":"1","key":"10048_CR14","doi-asserted-by":"publisher","first-page":"012203","DOI":"10.1007\/s11432-017-9097-1","volume":"61","author":"X Li","year":"2018","unstructured":"Li X, Song S, Wu J (2018) Impulsive control of unstable neural networks with unbounded time-varying delays. Sci China Inf Sci 61(1):012203","journal-title":"Sci China Inf Sci"},{"key":"10048_CR15","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2018.2874982","author":"Q Xiao","year":"2018","unstructured":"Xiao Q, Huang T, Zeng Z (2018) Global exponential stability and synchronization for discrete-time inertial neural networks with time delays: a timescale approach. IEEE Trans Neural Netw Learn Syst. \n                    https:\/\/doi.org\/10.1109\/TNNLS.2018.2874982","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"issue":"1","key":"10048_CR16","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1016\/j.chaos.2004.04.002","volume":"23","author":"J Cao","year":"2005","unstructured":"Cao J, Huang DS, Qu Y (2005) Global robust stability of delayed recurrent neural networks. Chaos Solitons Fractals 23(1):221\u2013229","journal-title":"Chaos Solitons Fractals"},{"issue":"2","key":"10048_CR17","doi-asserted-by":"publisher","first-page":"487","DOI":"10.1007\/s11063-017-9601-y","volume":"46","author":"C Aouiti","year":"2017","unstructured":"Aouiti C, M\u2019hamdi MS, Ch\u00e9rif F (2017) New results for impulsive recurrent neural networks with time-varying coefficients and mixed delays. Neural Process Lett 46(2):487\u2013506","journal-title":"Neural Process Lett"},{"key":"10048_CR18","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2017.12.028","author":"Q Huang","year":"2017","unstructured":"Huang Q, Cao J (2017) Stability analysis of inertial Cohen\u2013Grossberg neural networks with Markovian jumping parameters. Neurocomputing. \n                    https:\/\/doi.org\/10.1016\/j.neucom.2017.12.028","journal-title":"Neurocomputing"},{"issue":"1","key":"10048_CR19","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1007\/s11063-016-9515-0","volume":"45","author":"C Aouiti","year":"2017","unstructured":"Aouiti C, M\u2019hamdi MS, Touati A (2017) Pseudo almost automorphic solutions of recurrent neural networks with time-varying coefficients and mixed delays. Neural Process Lett 45(1):121\u2013140","journal-title":"Neural Process Lett"},{"key":"10048_CR20","doi-asserted-by":"publisher","first-page":"1109","DOI":"10.1007\/s13042-016-0633-9","volume":"9","author":"Z Chen","year":"2017","unstructured":"Chen Z (2017) Global exponential stability of anti-periodic solutions for neutral type CNNs with $$D$$ operator. Int J Mach Learn Cybern 9:1109\u20131115. \n                    https:\/\/doi.org\/10.1007\/s13042-016-0633-9","journal-title":"Int J Mach Learn Cybern"},{"key":"10048_CR21","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1002\/mma.3976","volume":"40","author":"B Liu","year":"2016","unstructured":"Liu B (2016) Finite-time stability of CNNs with neutral proportional delays and time-varying leakage delays. Math Methods Appl Sci 40:167\u2013174. \n                    https:\/\/doi.org\/10.1002\/mma.3976","journal-title":"Math Methods Appl Sci"},{"key":"10048_CR22","doi-asserted-by":"publisher","first-page":"477","DOI":"10.1007\/s00521-016-2558-3","volume":"29","author":"C Aouiti","year":"2016","unstructured":"Aouiti C (2016) Oscillation of impulsive neutral delay generalized high-order Hopfield neural networks. Neural Comput Appl 29:477\u2013495. \n                    https:\/\/doi.org\/10.1007\/s00521-016-2558-3","journal-title":"Neural Comput Appl"},{"issue":"3\u20134","key":"10048_CR23","doi-asserted-by":"publisher","first-page":"267","DOI":"10.1016\/j.physleta.2006.12.013","volume":"364","author":"Z Gui","year":"2007","unstructured":"Gui Z, Ge W, Yang X (2007) Periodic oscillation for a Hopfield neural networks with neutral delays. Phys Lett A 364(3\u20134):267\u2013273","journal-title":"Phys Lett A"},{"key":"10048_CR24","doi-asserted-by":"publisher","first-page":"445","DOI":"10.1016\/j.neucom.2014.07.020","volume":"148","author":"B Liu","year":"2015","unstructured":"Liu B (2015) Pseudo almost periodic solutions for neutral type CNNs with continuously distributed leakage delays. Neurocomputing 148:445\u2013454","journal-title":"Neurocomputing"},{"key":"10048_CR25","doi-asserted-by":"publisher","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. \n                    https:\/\/doi.org\/10.1016\/j.amc.2016.03.018","journal-title":"Appl Math Comput"},{"issue":"2","key":"10048_CR26","doi-asserted-by":"publisher","first-page":"401","DOI":"10.1007\/s11063-016-9529-7","volume":"45","author":"L Yao","year":"2017","unstructured":"Yao L (2017) Global exponential convergence of neutral type shunting inhibitory cellular neural networks with D operator. Neural Process Lett 45(2):401\u2013409","journal-title":"Neural Process Lett"},{"issue":"4","key":"10048_CR27","doi-asserted-by":"publisher","first-page":"795","DOI":"10.1080\/0952813X.2016.1259268","volume":"29","author":"A Zhang","year":"2017","unstructured":"Zhang A (2017) Pseudo almost periodic solutions for neutral type SICNNs with D operator. J Exp Theor Artif Intell 29(4):795\u2013807","journal-title":"J Exp Theor Artif Intell"},{"key":"10048_CR28","doi-asserted-by":"publisher","first-page":"142","DOI":"10.1016\/j.aml.2015.08.014","volume":"52","author":"T Candan","year":"2016","unstructured":"Candan T (2016) Existence of positive periodic solutions of first order neutral differential equations with variable coefficients. Appl Math Lett 52:142\u2013148","journal-title":"Appl Math Lett"},{"issue":"1","key":"10048_CR29","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1007\/s00521-016-2403-8","volume":"29","author":"L Yao","year":"2018","unstructured":"Yao L (2018) Global convergence of CNNs with neutral type delays and D operator. Neural Comput Appl 29(1):105\u2013109","journal-title":"Neural Comput Appl"},{"key":"10048_CR30","doi-asserted-by":"publisher","first-page":"1109","DOI":"10.1007\/s13042-016-0633-9","volume":"9","author":"Z Chen","year":"2017","unstructured":"Chen Z (2017) Global exponential stability of anti-periodic solutions for neutral type CNNs with D operator. Int J Mach Learn Cybern 9:1109\u20131115. \n                    https:\/\/doi.org\/10.1007\/s13042-016-0633-9","journal-title":"Int J Mach Learn Cybern"},{"issue":"1\u20132","key":"10048_CR31","doi-asserted-by":"publisher","first-page":"18","DOI":"10.1007\/BF03323153","volume":"18","author":"S Hilger","year":"1990","unstructured":"Hilger S (1990) Analysis on measure chains\u2014a unified approach to continuous and discrete calculus. Results Math 18(1\u20132):18\u201356","journal-title":"Results Math"},{"volume-title":"Advances in dynamic equations on time scales","year":"2002","key":"10048_CR32","unstructured":"Bohner M, Peterson AC (eds) (2002) Advances in dynamic equations on time scales. Springer, Berlin"},{"key":"10048_CR33","unstructured":"Agarwal RP (2002) Dynamic equations on time scales: a survey, Special Issue on \u201cDynamic Equations on Time Scales\u201d, edited by RP Agarwal, M. Bohner, and D. O\u2019Regan. Preprint in Ulmer Seminare 5:1\u201326"},{"issue":"16\u201318","key":"10048_CR34","doi-asserted-by":"publisher","first-page":"3582","DOI":"10.1016\/j.neucom.2008.06.004","volume":"71","author":"A Chen","year":"2008","unstructured":"Chen A, Du D (2008) Global exponential stability of delayed BAM network on time scale. Neurocomputing 71(16\u201318):3582\u20133588","journal-title":"Neurocomputing"},{"issue":"6","key":"10048_CR35","doi-asserted-by":"publisher","first-page":"1915","DOI":"10.1007\/s13042-016-0570-7","volume":"8","author":"Y Li","year":"2017","unstructured":"Li Y, Meng X, Xiong L (2017) Pseudo almost periodic solutions for neutral type high-order Hopfield neural networks with mixed time-varying delays and leakage delays on time scales. Int J Mach Learn Cybern 8(6):1915\u20131927","journal-title":"Int J Mach Learn Cybern"},{"issue":"17","key":"10048_CR36","doi-asserted-by":"publisher","first-page":"3142","DOI":"10.1016\/j.neucom.2011.04.008","volume":"74","author":"B Zhou","year":"2011","unstructured":"Zhou B, Song Q, Wang H (2011) Global exponential stability of neural networks with discrete and distributed delays and general activation functions on time scales. Neurocomputing 74(17):3142\u20133150","journal-title":"Neurocomputing"},{"key":"10048_CR37","doi-asserted-by":"publisher","DOI":"10.1007\/s40840-017-0595-4","author":"X Yu","year":"2017","unstructured":"Yu X, Wang Q (2017) Weighted pseudo-almost periodic solutions for shunting inhibitory cellular neural networks on time scales. Bull Malays Math Sci Soc. \n                    https:\/\/doi.org\/10.1007\/s40840-017-0595-4","journal-title":"Bull Malays Math Sci Soc"},{"key":"10048_CR38","doi-asserted-by":"publisher","first-page":"62","DOI":"10.1006\/jmaa.1994.1005","volume":"151","author":"CY Zhang","year":"1994","unstructured":"Zhang CY (1994) Pseudo almost periodic solutions of some differential equations. J Math Anal Appl 151:62\u201376","journal-title":"J Math Anal Appl"},{"key":"10048_CR39","first-page":"639","volume":"237","author":"J Gao","year":"2014","unstructured":"Gao J, Wang QR, Zhang LW (2014) Existence and stability of almost-periodic solutions for cellular neural networks with time-varying delays in leakage terms on time scales. Appl Math Comput 237:639\u2013649","journal-title":"Appl Math Comput"},{"key":"10048_CR40","doi-asserted-by":"publisher","first-page":"921","DOI":"10.1016\/j.neucom.2015.08.047","volume":"173","author":"B Du","year":"2016","unstructured":"Du B, Liu Y, Batarfi HA, Alsaadi FE (2016) Almost periodic solution for a neutral-type neural networks with distributed leakage delays on time scales. Neurocomputing 173:921\u2013929","journal-title":"Neurocomputing"},{"key":"10048_CR41","volume-title":"Dynamic equations on time scales: an introduction with applications","author":"M Bohner","year":"2012","unstructured":"Bohner M, Peterson A (2012) Dynamic equations on time scales: an introduction with applications. Springer, Berlin"},{"issue":"3","key":"10048_CR42","doi-asserted-by":"publisher","first-page":"603","DOI":"10.1007\/s11063-015-9483-9","volume":"44","author":"Y Li","year":"2016","unstructured":"Li Y, Yang L, Li B (2016) Existence and stability of pseudo almost periodic solution for neutral type high-order Hopfield neural networks with delays in leakage terms on time scales. Neural Process Lett 44(3):603\u2013623","journal-title":"Neural Process Lett"},{"key":"10048_CR43","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1016\/j.neunet.2015.11.003","volume":"74","author":"A Wu","year":"2016","unstructured":"Wu A, Zeng Z (2016) Boundedness, Mittag\u2013Leffler stability and asymptotical $$\\omega $$-periodicity of fractional-order fuzzy neural networks. Neural Netw 74:73\u201384","journal-title":"Neural Netw"},{"issue":"15","key":"10048_CR44","doi-asserted-by":"publisher","first-page":"1661","DOI":"10.1016\/j.physleta.2011.02.068","volume":"375","author":"A Wu","year":"2011","unstructured":"Wu A, Zhang J, Zeng Z (2011) Dynamic behaviors of a class of memristor-based Hopfield networks. Phys Lett A 375(15):1661\u20131665","journal-title":"Phys Lett A"},{"key":"10048_CR45","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1016\/j.neucom.2017.03.015","volume":"244","author":"Q Song","year":"2017","unstructured":"Song Q, Shu H, Zhao Z, Liu Y, Alsaadi FE (2017) Lagrange stability analysis for complex-valued neural networks with leakage delay and mixed time-varying delays. Neurocomputing 244:33\u201341","journal-title":"Neurocomputing"},{"key":"10048_CR46","doi-asserted-by":"publisher","first-page":"2762","DOI":"10.1016\/j.neucom.2017.11.041","volume":"275","author":"Q Song","year":"2018","unstructured":"Song Q, Yu Q, Zhao Z, Liu Y, Alsaadi FE (2018) Dynamics of complex-valued neural networks with variable coefficients and proportional delays. Neurocomputing 275:2762\u20132768","journal-title":"Neurocomputing"},{"key":"10048_CR47","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1016\/j.neunet.2018.03.008","volume":"103","author":"Q Song","year":"2018","unstructured":"Song Q, Yu Q, Zhao Z, Liu Y, Alsaadi FE (2018) Boundedness and global robust stability analysis of delayed complex-valued neural networks with interval parameter uncertainties. Neural Netw 103:55\u201362","journal-title":"Neural Netw"}],"container-title":["Neural Processing Letters"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11063-019-10048-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11063-019-10048-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11063-019-10048-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,22]],"date-time":"2020-05-22T23:13:29Z","timestamp":1590189209000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11063-019-10048-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,5,24]]},"references-count":47,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2019,8]]}},"alternative-id":["10048"],"URL":"https:\/\/doi.org\/10.1007\/s11063-019-10048-2","relation":{},"ISSN":["1370-4621","1573-773X"],"issn-type":[{"type":"print","value":"1370-4621"},{"type":"electronic","value":"1573-773X"}],"subject":[],"published":{"date-parts":[[2019,5,24]]},"assertion":[{"value":"24 May 2019","order":1,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}