{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,16]],"date-time":"2026-04-16T16:40:54Z","timestamp":1776357654238,"version":"3.51.2"},"reference-count":45,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2020,4,6]],"date-time":"2020-04-06T00:00:00Z","timestamp":1586131200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,4,6]],"date-time":"2020-04-06T00:00:00Z","timestamp":1586131200000},"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":["Comp. Appl. Math."],"published-print":{"date-parts":[[2020,5]]},"DOI":"10.1007\/s40314-020-01148-0","type":"journal-article","created":{"date-parts":[[2020,4,6]],"date-time":"2020-04-06T08:04:41Z","timestamp":1586160281000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":29,"title":["Dynamics behavior for second-order neutral Clifford differential equations: inertial neural networks with mixed delays"],"prefix":"10.1007","volume":"39","author":[{"given":"Chaouki","family":"Aouiti","sequence":"first","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":[[2020,4,6]]},"reference":[{"issue":"6","key":"1148_CR1","doi-asserted-by":"publisher","first-page":"573","DOI":"10.1007\/s11571-016-9405-1","volume":"10","author":"C Aouiti","year":"2016","unstructured":"Aouiti C (2016) Neutral impulsive shunting inhibitory cellular neural networks with time-varying coefficients and leakage delays. Cogn Neurodyn 10(6):573\u2013591","journal-title":"Cogn Neurodyn"},{"issue":"9","key":"1148_CR2","doi-asserted-by":"publisher","first-page":"477","DOI":"10.1007\/s00521-016-2558-3","volume":"29","author":"C Aouiti","year":"2018","unstructured":"Aouiti C (2018) Oscillation of impulsive neutral delay generalized high-order Hopfield neural networks. Neural Comput Appl 29(9):477\u2013495","journal-title":"Neural Comput Appl"},{"issue":"3","key":"1148_CR3","doi-asserted-by":"publisher","first-page":"1459","DOI":"10.1007\/s11063-018-9880-y","volume":"49","author":"C Aouiti","year":"2019","unstructured":"Aouiti C, Dridi F (2019) New results on impulsive Cohen\u2013Grossberg neural networks. Neural Process Lett 49(3):1459\u20131483","journal-title":"Neural Process Lett"},{"issue":"9","key":"1148_CR4","doi-asserted-by":"publisher","first-page":"5527","DOI":"10.1007\/s00521-018-3378-4","volume":"31","author":"C Aouiti","year":"2019","unstructured":"Aouiti C, Dridi F (2019) Piecewise asymptotically almost automorphic solutions for impulsive non-autonomous high-order Hopfield neural networks with mixed delays. Neural Comput Appl 31(9):5527\u20135545","journal-title":"Neural Comput Appl"},{"key":"1148_CR5","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, Ben Gharbia I, 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"},{"issue":"1","key":"1148_CR6","doi-asserted-by":"publisher","first-page":"297","DOI":"10.1007\/s11063-019-10048-2","volume":"50","author":"C Aouiti","year":"2019","unstructured":"Aouiti C, Assali EA, Gharbia IB (2019) Pseudo almost periodic solution of recurrent neural networks with D operator on time scales. Neural Process Lett 50(1):297\u2013320","journal-title":"Neural Process Lett"},{"key":"1148_CR7","doi-asserted-by":"publisher","first-page":"292","DOI":"10.1016\/j.neucom.2019.04.077","volume":"357","author":"C Aouiti","year":"2019","unstructured":"Aouiti C, Assali EA, Gharbia IB, El Foutayeni Y (2019) Existence and exponential stability of piecewise pseudo almost periodic solution of neutral-type inertial neural networks with mixed delay and impulsive perturbations. Neurocomputing 357:292\u2013309","journal-title":"Neurocomputing"},{"key":"1148_CR8","doi-asserted-by":"crossref","unstructured":"Aouiti C, Abed Assali E (2019) Effect of fuzziness on the stability of inertial neural networks with mixed delay via non-reduced-order method. Int J Comput Math Comput Syst Theory 1\u201320","DOI":"10.1080\/23799927.2019.1685006"},{"key":"1148_CR9","unstructured":"Aouiti C, Assali EA, Ch\u00e9rif F, Zeglaoui A (2019) Fixed-time synchronization of competitive neural networks with proportional delays and impulsive effect. Neural Comput Appl 1\u201310"},{"key":"1148_CR10","unstructured":"Aouiti C, Sakthivel R, Touati F (2019) Global dissipativity of high-order Hopfield bidirectional associative memory neural networks with mixed delays. Neural Comput Appl 1\u201315"},{"key":"1148_CR11","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1007\/BF02543859","volume":"46","author":"H Bohr","year":"1925","unstructured":"Bohr H (1925) Zur Theorie der fastperiodischen Funktionen. II. Acta Math 46:101\u2013214","journal-title":"Acta Math"},{"key":"1148_CR12","doi-asserted-by":"crossref","unstructured":"Bohr H, Zur Theorie der Fastperiodischen Funktionen I (1925) III. Acta Math 45:29\u2013127","DOI":"10.1007\/BF02395468"},{"key":"1148_CR13","unstructured":"Buchholz S (2005) A theory of neural computation with Clifford algebras (Doctoral dissertation, Christian-Albrechts Universit\u00e4t Kiel)"},{"issue":"3","key":"1148_CR14","doi-asserted-by":"publisher","first-page":"189","DOI":"10.2478\/jaiscr-2019-0003","volume":"9","author":"Y Cao","year":"2019","unstructured":"Cao Y, Samidurai R, Sriraman R (2019) Stability and dissipativity analysis for neutral type stochastic Markovian jump static neural networks with time delays. J Artif Intell Soft Comput Res 9(3):189\u2013204","journal-title":"J Artif Intell Soft Comput Res"},{"key":"1148_CR15","doi-asserted-by":"publisher","first-page":"207","DOI":"10.1016\/j.matcom.2019.05.011","volume":"171","author":"Y Cao","year":"2020","unstructured":"Cao Y, Sriraman R, Shyamsundarraj N, Samidurai R (2020) Robust stability of uncertain stochastic complex-valued neural networks with additive time-varying delays. Math Comput Simul 171:207\u2013220","journal-title":"Math Comput Simul"},{"key":"1148_CR16","doi-asserted-by":"publisher","first-page":"36","DOI":"10.1016\/j.matcom.2019.03.002","volume":"171","author":"Y Cao","year":"2020","unstructured":"Cao Y, Sriraman R, Samidurai R (2020) Stability and stabilization analysis of nonlinear time-delay systems with randomly occurring controller gain fluctuation. Math Comput Simul 171:36\u201351","journal-title":"Math Comput Simul"},{"key":"1148_CR17","unstructured":"Chevalley CCAO (1954) The algebraic theory of spinors. New York, pp 65\u2013192"},{"key":"1148_CR18","volume-title":"Almost periodic type functions and ergodicity","author":"Z Chuanyi","year":"2003","unstructured":"Chuanyi Z (2003) Almost periodic type functions and ergodicity. Springer, Berlin"},{"key":"1148_CR19","doi-asserted-by":"publisher","first-page":"350","DOI":"10.2307\/2369379","volume":"1","author":"WK Clifford","year":"1878","unstructured":"Clifford WK (1878) Applications of Grassmann\u2019s extensive algebra. Am J Math 1:350\u2013358","journal-title":"Am J Math"},{"key":"1148_CR20","volume-title":"Clifford algebra to geometric calculus: a unified language for mathematics and physics","author":"D Hestenes","year":"2012","unstructured":"Hestenes D, Sobczyk G (2012) Clifford algebra to geometric calculus: a unified language for mathematics and physics, vol 5. Springer, Berlin"},{"issue":"2","key":"1148_CR21","doi-asserted-by":"publisher","first-page":"377","DOI":"10.1007\/s00006-013-0378-4","volume":"23","author":"E Hitzer","year":"2013","unstructured":"Hitzer E, Nitta T, Kuroe Y (2013) Applications of Clifford\u2019s geometric algebra. Adv Appl Clifford Algebras 23(2):377\u2013404","journal-title":"Adv Appl Clifford Algebras"},{"key":"1148_CR22","doi-asserted-by":"publisher","unstructured":"Karthick SA, Sakthivel R, Aouiti C, Leelamani A (2019) Memory feedback finite-time control for memristive neutral-type neural networks with quantization. Chin J Phys. https:\/\/doi.org\/10.1016\/j.cjph.2019.09.016","DOI":"10.1016\/j.cjph.2019.09.016"},{"issue":"2","key":"1148_CR23","doi-asserted-by":"publisher","first-page":"523","DOI":"10.1007\/s11063-016-9540-z","volume":"45","author":"Y Ke","year":"2017","unstructured":"Ke Y, Miao C (2017) Anti-periodic solutions of inertial neural networks with time delays. Neural Process Lett 45(2):523\u2013538","journal-title":"Neural Process Lett"},{"key":"1148_CR24","doi-asserted-by":"publisher","first-page":"106","DOI":"10.1016\/j.neunet.2019.10.007","volume":"122","author":"R Kumar","year":"2020","unstructured":"Kumar R, Das S, Cao Y (2020) Effects of infinite occurrence of hybrid impulses with quasi-synchronization of parameter mismatched neural networks. Neural Netw 122:106\u2013116","journal-title":"Neural Netw"},{"issue":"12","key":"1148_CR25","first-page":"4370","volume":"215","author":"X Li","year":"2010","unstructured":"Li X (2010) Global robust stability for stochastic interval neural networks with continuously distributed delays of neutral type. Appl Math Comput 215(12):4370\u20134384","journal-title":"Appl Math Comput"},{"issue":"5\u20136","key":"1148_CR26","doi-asserted-by":"publisher","first-page":"643","DOI":"10.1016\/j.mcm.2010.04.011","volume":"52","author":"X Li","year":"2010","unstructured":"Li X, Bohner M (2010) Exponential synchronization of chaotic neural networks with mixed delays and impulsive effects via output coupling with delay feedback. Math Comput Modell 52(5\u20136):643\u2013653","journal-title":"Math Comput Modell"},{"issue":"7","key":"1148_CR27","doi-asserted-by":"publisher","first-page":"1709","DOI":"10.1088\/0951-7715\/23\/7\/010","volume":"23","author":"X Li","year":"2010","unstructured":"Li X, Cao J (2010) Delay-dependent stability of neural networks of neutral type with time delay in the leakage term. Nonlinearity 23(7):1709","journal-title":"Nonlinearity"},{"key":"1148_CR28","doi-asserted-by":"publisher","first-page":"150213","DOI":"10.1109\/ACCESS.2019.2947647","volume":"7","author":"B Li","year":"2019","unstructured":"Li B, Li Y (2019) Existence and global exponential stability of pseudo almost periodic solution for Clifford-valued neutral high-order hopfield neural networks with leakage delays. IEEE Access 7:150213\u2013150225","journal-title":"IEEE Access"},{"issue":"3","key":"1148_CR29","doi-asserted-by":"publisher","first-page":"337","DOI":"10.1140\/epjb\/e2004-00327-2","volume":"41","author":"C Li","year":"2004","unstructured":"Li C, Chen G, Liao X, Yu J (2004) Hopf bifurcation and chaos in a single inertial neuron model with time delay. Eur Phys J B Condens Matter Complex Syst 41(3):337\u2013343","journal-title":"Eur Phys J B Condens Matter Complex Syst"},{"issue":"2","key":"1148_CR30","doi-asserted-by":"publisher","first-page":"767","DOI":"10.1007\/s11071-015-2526-y","volume":"84","author":"Y Liu","year":"2016","unstructured":"Liu Y, Xu P, Lu J, Liang J (2016) Global stability of Clifford-valued recurrent neural networks with time delays. Nonlinear Dyn 84(2):767\u2013777","journal-title":"Nonlinear Dyn"},{"key":"1148_CR31","doi-asserted-by":"crossref","unstructured":"Li Y, Xiang J (2019) Global asymptotic almost periodic synchronization of Clifford-valued CNNs with discrete delays. Complexity","DOI":"10.1155\/2019\/6982109"},{"issue":"9","key":"1148_CR32","doi-asserted-by":"publisher","first-page":"3990","DOI":"10.1016\/j.jfranklin.2018.01.051","volume":"355","author":"R Manivannan","year":"2018","unstructured":"Manivannan R, Cao Y (2018) Design of generalized dissipativity state estimator for static neural networks including state time delays and leakage delays. J Franklin Inst 355(9):3990\u20134014","journal-title":"J Franklin Inst"},{"key":"1148_CR33","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-36216-3","volume-title":"Clifford algebras and Lie theory","author":"E Meinrenken","year":"2013","unstructured":"Meinrenken E (2013) Clifford algebras and Lie theory, vol 58. Springer, Berlin\/Heidelberg"},{"issue":"2","key":"1148_CR34","doi-asserted-by":"publisher","first-page":"495","DOI":"10.1016\/j.chaos.2004.05.023","volume":"23","author":"JH Park","year":"2005","unstructured":"Park JH, Kwon OM (2005) A novel criterion for delayed feedback control of time-delay chaotic systems. Chaos Solitons Fractals 23(2):495\u2013501","journal-title":"Chaos Solitons Fractals"},{"issue":"3","key":"1148_CR35","doi-asserted-by":"publisher","first-page":"1174","DOI":"10.1016\/j.chaos.2008.04.049","volume":"41","author":"JH Park","year":"2009","unstructured":"Park JH, Kwon OM (2009) Global stability for neural networks of neutral-type with interval time-varying delays. Chaos Solitons Fractals 41(3):1174\u20131181","journal-title":"Chaos Solitons Fractals"},{"issue":"1","key":"1148_CR36","first-page":"236","volume":"196","author":"JH Park","year":"2008","unstructured":"Park JH, Kwon OM, Lee SM (2008) LMI optimization approach on stability for delayed neural networks of neutral-type. Appl Math Comput 196(1):236\u2013244","journal-title":"Appl Math Comput"},{"key":"1148_CR37","unstructured":"Pearson JK, Bisset DL (1992) Back propagation in a Clifford algebra. Artif Neural Netw 2"},{"key":"1148_CR38","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511470912","volume-title":"Clifford algebras and the classical groups","author":"IR Porteous","year":"1995","unstructured":"Porteous IR (1995) Clifford algebras and the classical groups, vol 50. Cambridge University Press, Cambridge"},{"key":"1148_CR39","unstructured":"Riesz M (1958) Clifford numbers and spinors. Lecture Series No. 38. The Institute for Fluid Dynamics and Applied Mathematics, University of Maryland"},{"issue":"4","key":"1148_CR40","doi-asserted-by":"publisher","first-page":"1633","DOI":"10.3934\/dcds.2013.33.1633","volume":"33","author":"A Ruiz-Herrera","year":"2013","unstructured":"Ruiz-Herrera A (2013) Chaos in delay differential equations with applications in population dynamics. Discrete. Cont. Dyn. Syst 33(4):1633\u20131644","journal-title":"Discrete. Cont. Dyn. Syst"},{"key":"1148_CR41","doi-asserted-by":"crossref","unstructured":"St\u00e9p\u00e1n G (1999) Delay, nonlinear oscillations and shimmying wheels. In: IUTAM Symposium on New Applications of Nonlinear and Chaotic Dynamics in Mechanics. Springer, Dordrecht, pp 373\u2013386","DOI":"10.1007\/978-94-011-5320-1_38"},{"issue":"1","key":"1148_CR42","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1016\/j.chaos.2003.10.018","volume":"21","author":"J Sun","year":"2004","unstructured":"Sun J (2004) Delay-dependent stability criteria for time-delay chaotic systems via time-delay feedback control. Chaos Solitons Fractals 21(1):143\u2013150","journal-title":"Chaos Solitons Fractals"},{"issue":"4","key":"1148_CR43","doi-asserted-by":"publisher","first-page":"545","DOI":"10.1017\/S1446181100009664","volume":"46","author":"J Yan","year":"2005","unstructured":"Yan J, Zhao A, Peng L (2005) Oscillation of impulsive delay differential equations and applications to population dynamics. ANZIAM J 46(4):545\u2013554","journal-title":"ANZIAM J"},{"issue":"14","key":"1148_CR44","first-page":"1","volume":"2012","author":"E Yankson","year":"2012","unstructured":"Yankson E (2012) Positive periodic solutions for second-order neutral differential equations with functional delay. Electron J Differ Equ 2012(14):1\u20136","journal-title":"Electron J Differ Equ"},{"issue":"1","key":"1148_CR45","doi-asserted-by":"publisher","first-page":"62","DOI":"10.1006\/jmaa.1994.1005","volume":"181","author":"CY Zhang","year":"1994","unstructured":"Zhang CY (1994) Pseudo almost periodic solutions of some differential equations. J Math Anal Appl 181(1):62\u201376","journal-title":"J Math Anal Appl"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-020-01148-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s40314-020-01148-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-020-01148-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,5]],"date-time":"2021-04-05T23:20:36Z","timestamp":1617664836000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s40314-020-01148-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,4,6]]},"references-count":45,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2020,5]]}},"alternative-id":["1148"],"URL":"https:\/\/doi.org\/10.1007\/s40314-020-01148-0","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"value":"2238-3603","type":"print"},{"value":"1807-0302","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,4,6]]},"assertion":[{"value":"20 January 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 March 2020","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 March 2020","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 April 2020","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"120"}}