{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,15]],"date-time":"2025-12-15T19:46:51Z","timestamp":1765828011977,"version":"3.37.3"},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"11","license":[{"start":{"date-parts":[[2021,4,8]],"date-time":"2021-04-08T00:00:00Z","timestamp":1617840000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,4,8]],"date-time":"2021-04-08T00:00:00Z","timestamp":1617840000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61773404","61271355"],"award-info":[{"award-number":["61773404","61271355"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Circuits Syst Signal Process"],"published-print":{"date-parts":[[2021,11]]},"DOI":"10.1007\/s00034-021-01717-6","type":"journal-article","created":{"date-parts":[[2021,4,8]],"date-time":"2021-04-08T12:03:10Z","timestamp":1617883390000},"page":"5280-5308","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["Synchronization of a Riemann\u2013Liouville Fractional Time-Delayed Neural Network with Two Inertial Terms"],"prefix":"10.1007","volume":"40","author":[{"given":"Shuailei","family":"Zhang","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3419-5988","authenticated-orcid":false,"given":"Meilan","family":"Tang","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8573-7014","authenticated-orcid":false,"given":"Xinge","family":"Liu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,4,8]]},"reference":[{"key":"1717_CR1","doi-asserted-by":"publisher","first-page":"410","DOI":"10.1016\/j.physleta.2005.04.095","volume":"341","author":"S Arik","year":"2005","unstructured":"S. Arik, Z. Orman, Global stability analysis of Cohen\u2013Grossberg neural networks with time-varying delays. Phys. Lett. A. 341, 410\u2013421 (2005)","journal-title":"Phys. Lett. A."},{"key":"1717_CR2","doi-asserted-by":"publisher","first-page":"464","DOI":"10.1016\/0167-2789(86)90152-1","volume":"23","author":"KL Babcock","year":"1986","unstructured":"K.L. Babcock, R.M. Westervelt, Stability and dynamics of simple electronic neural networks with added inertia. Phys. D. 23, 464\u2013469 (1986)","journal-title":"Phys. D."},{"key":"1717_CR3","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.neunet.2013.11.016","volume":"51","author":"J Chen","year":"2014","unstructured":"J. Chen, Z. Zeng, P. Jiang, Global Mittag-Leffler stability and synchronization of memrister-based fractional-order neural networks. Neural Netw. 51, 1\u20138 (2014)","journal-title":"Neural Netw."},{"key":"1717_CR4","doi-asserted-by":"publisher","first-page":"190","DOI":"10.1016\/j.neucom.2012.11.034","volume":"111","author":"L Chen","year":"2013","unstructured":"L. Chen, Y. Chai, R. Wu, T. Ma, H. Zhai, Dynamic analysis of a class of fractional-order neural networks with delay. Neurocomputing 111, 190\u2013194 (2013)","journal-title":"Neurocomputing"},{"key":"1717_CR5","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1016\/j.neunet.2015.07.012","volume":"71","author":"L Chen","year":"2015","unstructured":"L. Chen, R. Wu, J. Cao, J.B. Liu, Stability and synchronization of memrister-based fractional-order delayed neural networks. Neural Netw. 71, 37\u201344 (2015)","journal-title":"Neural Netw."},{"key":"1717_CR6","doi-asserted-by":"publisher","first-page":"85","DOI":"10.1016\/j.cam.2018.01.007","volume":"339","author":"SA David","year":"2018","unstructured":"S.A. David, D.D. Quintino, C.M.C. Inacio, J.A.T. Machado, Fractional dynamic behavior in ethanol prices series. J. Comput. Appl. Math. 339, 85\u201393 (2018)","journal-title":"J. Comput. Appl. Math."},{"key":"1717_CR7","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/978-3-642-14574-2","volume-title":"The Analysis of Fractional Differential Equations","author":"K Diethelm","year":"2010","unstructured":"K. Diethelm, The Analysis of Fractional Differential Equations (Springer, New York, 2010), pp. 1\u201330"},{"key":"1717_CR8","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1016\/j.neunet.2020.01.024","volume":"125","author":"S Ding","year":"2020","unstructured":"S. Ding, Z. Wang, Event-triggered synchronization of discrete-time neural networks: a switching approach. Neural Netw. 125, 31\u201340 (2020)","journal-title":"Neural Netw."},{"key":"1717_CR9","first-page":"1","volume":"99","author":"S Ding","year":"2020","unstructured":"S. Ding, Z. Wang, H. Zhang, Intermittent control for quasisynchronization of delayed discrete-time neural networks. IEEE Trans. Cybern. 99, 1\u201312 (2020)","journal-title":"IEEE Trans. Cybern."},{"key":"1717_CR10","doi-asserted-by":"publisher","first-page":"270","DOI":"10.1016\/j.neucom.2019.03.005","volume":"340","author":"Y Gu","year":"2019","unstructured":"Y. Gu, H. Wang, Y. Yu, Stability and synchronization for Riemman\u2013Liouville fractional-order time-delayed inertial neural networks. Neurocomputing 340, 270\u2013280 (2019)","journal-title":"Neurocomputing"},{"issue":"051002","key":"1717_CR11","first-page":"1","volume":"14","author":"Y Gu","year":"2019","unstructured":"Y. Gu, H. Wang, Y. Yu, Synchronization for incommensurate Riemann\u2013Liouville fractional-order time-delayed competitive neural networks with different time scales and known or unknown parameters. J. Comput. Nonlinear Dyn. 14(051002), 1\u201311 (2019)","journal-title":"J. Comput. Nonlinear Dyn."},{"key":"1717_CR12","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1016\/j.neucom.2018.05.098","volume":"313","author":"T Hu","year":"2018","unstructured":"T. Hu, X. Zhang, S. Zhong, Global asymptotic synchronization of nonidentical fractional-order neural networks. Neurocomputing 313, 39\u201346 (2018)","journal-title":"Neurocomputing"},{"key":"1717_CR13","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1016\/j.neucom.2018.09.065","volume":"325","author":"C Huang","year":"2019","unstructured":"C. Huang, B. Liu, New studies on dynamic analysis of inertial neural networks involving non-reduced order method. Neurocomputing 325, 283\u2013287 (2019)","journal-title":"Neurocomputing"},{"key":"1717_CR14","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1016\/j.amc.2015.01.004","volume":"256","author":"MD Ji","year":"2015","unstructured":"M.D. Ji, Y. He, M. Wu, C.K. Zhang, Further results on exponential stability of neural networks with time-varying delay. Appl. Math. Comput. 256, 175\u2013182 (2015)","journal-title":"Appl. Math. Comput."},{"key":"1717_CR15","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1016\/j.neunet.2017.09.009","volume":"96","author":"XY Li","year":"2017","unstructured":"X.Y. Li, X.T. Li, C. Hu, Some new results on stability and synchronization for delayed inertial neural networks based on non-reduced order method. Neural Netw. 96, 91\u2013100 (2017)","journal-title":"Neural Netw."},{"key":"1717_CR16","doi-asserted-by":"publisher","first-page":"11285","DOI":"10.1016\/j.jfranklin.2019.07.027","volume":"356","author":"K Liang","year":"2019","unstructured":"K. Liang, W. Li, Exponential synchronization in inertial Cohen\u2013Grossberg neural networks with time delays. J. Frank. Inst. 356, 11285\u201311304 (2019)","journal-title":"J. Frank. Inst."},{"key":"1717_CR17","doi-asserted-by":"publisher","first-page":"2279","DOI":"10.1109\/TSMC.2017.2651059","volume":"47","author":"P Liu","year":"2017","unstructured":"P. Liu, Z. Zeng, J. Wang, Multiple mittag-leffler stability of fractional-order recurrent neural networks. IEEE Trans. Syst. Man Cybern. Syst. 47, 2279\u20132288 (2017)","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."},{"key":"1717_CR18","doi-asserted-by":"publisher","first-page":"32","DOI":"10.1016\/j.aml.2016.10.002","volume":"65","author":"S Liu","year":"2017","unstructured":"S. Liu, X.F. Zhou, X. Li, W. Jiang, Asymptotical stability of Riemann\u2013Liouville fractional singular systems with multiple time-varying delays. Appl. Math. Lett. 65, 32\u201339 (2017)","journal-title":"Appl. Math. Lett."},{"key":"1717_CR19","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1016\/j.neunet.2008.10.001","volume":"22","author":"Y Liu","year":"2009","unstructured":"Y. Liu, Z. Wang, X. Liu, Asymptotic stability for neural networks with mixed time-delays: the discrete-time case. Neural Netw. 22, 67\u201374 (2009)","journal-title":"Neural Netw."},{"key":"1717_CR20","doi-asserted-by":"publisher","first-page":"1447","DOI":"10.1080\/00207170110067116","volume":"74","author":"YS Moon","year":"2004","unstructured":"Y.S. Moon, P.Y. Park, W.H. Kwon, Y.S. Lee, Delay dependent robust stabilization of uncertain state-delayed systems. Int. J. Control 74, 1447\u20131455 (2004)","journal-title":"Int. J. Control"},{"key":"1717_CR21","doi-asserted-by":"publisher","first-page":"821","DOI":"10.1103\/PhysRevLett.64.821","volume":"64","author":"LM Pecora","year":"1990","unstructured":"L.M. Pecora, T.L. Carroll, Synchronization in chaotic system. Phys. Rev. Lett. 64, 821\u2013824 (1990)","journal-title":"Phys. Rev. Lett."},{"key":"1717_CR22","first-page":"62","volume-title":"Fractional Differential Equations","author":"I Podlubny","year":"1999","unstructured":"I. Podlubny, Fractional Differential Equations (Academic Press, San Diego, 1999), pp. 62\u201374"},{"key":"1717_CR23","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1016\/j.amc.2019.04.062","volume":"359","author":"A Pratap","year":"2019","unstructured":"A. Pratap, R. Raja, J. Cao, C.P. Lim, O. Bagdasar, Stability and pinning synchronization analysis of fractional order delayed Cohen\u2013Grossberg neural networks with discontinuous activations. Appl. Math. Comput. 359, 241\u2013260 (2019)","journal-title":"Appl. Math. Comput."},{"key":"1717_CR24","doi-asserted-by":"publisher","first-page":"2212","DOI":"10.1016\/j.jfranklin.2019.01.017","volume":"356","author":"A Pratap","year":"2019","unstructured":"A. Pratap, R. Raja, J. Cao, G. Rajchakit, Habib M. Fardoun, Stability and synchronization criteria for fractional order competitive neural networks with time delays: an asymptotic expansion of Mittag Leffler function. J. Frank. Inst. 356, 2212\u20132239 (2019)","journal-title":"J. Frank. Inst."},{"issue":"109491","key":"1717_CR25","first-page":"1","volume":"131","author":"A Pratap","year":"2020","unstructured":"A. Pratap, R. Raja, J. Cao, Fathalla A. Rihan, Aly R. Seadawy, Quasi-pinning synchronization and stabilization of fractional order BAM neural networks with delays and discontinuous neuron activations. Chaos, Solitons Frac. 131(109491), 1\u201322 (2020)","journal-title":"Chaos, Solitons Frac."},{"key":"1717_CR26","doi-asserted-by":"publisher","first-page":"487","DOI":"10.1007\/s00521-016-2697-6","volume":"30","author":"S Tyagi","year":"2018","unstructured":"S. Tyagi, S. Abbas, M. Kirane, Global asymptotic and exponential synchronization of ring neural network with reaction-diffusion term and unbounded delay. Neural Comput. Appl. 30, 487\u2013501 (2018)","journal-title":"Neural Comput. Appl."},{"key":"1717_CR27","doi-asserted-by":"publisher","first-page":"134","DOI":"10.1016\/j.physa.2015.03.089","volume":"434","author":"F Wang","year":"2015","unstructured":"F. Wang, Y. Yang, M. Hu, X. Xu, Projective cluster synchronization of fractional-order coupled-delay complex network via adaptive pinning control. Phys. A. 434, 134\u2013143 (2015)","journal-title":"Phys. A."},{"key":"1717_CR28","doi-asserted-by":"publisher","first-page":"12","DOI":"10.1016\/j.neucom.2018.08.089","volume":"346","author":"F Wang","year":"2019","unstructured":"F. Wang, X. Liu, M. Tang, L. Chen, Further results on stability and synchronization of fractional-order Hopfield neural networks. Neurocomputing 346, 12\u201319 (2019)","journal-title":"Neurocomputing"},{"key":"1717_CR29","doi-asserted-by":"publisher","first-page":"98","DOI":"10.1016\/j.neunet.2014.03.012","volume":"55","author":"H Wang","year":"2014","unstructured":"H. Wang, Y. Yu, G. Wen, Stability analysis of fractional-order Hopfield neural networks with time delays. Neural Netw. 55, 98\u2013109 (2014)","journal-title":"Neural Netw."},{"key":"1717_CR30","doi-asserted-by":"publisher","first-page":"2385","DOI":"10.1007\/s12555-016-0315-0","volume":"15","author":"SP Xiao","year":"2017","unstructured":"S.P. Xiao, H.H. Lian, H.B. Zeng, G. Chen, W.H. Zheng, Analysis on robust passivity of uncertain neural networks with time-varying delays via free-matrix-based integral inequality. Int. J. Control Autom. 15, 2385\u20132394 (2017)","journal-title":"Int. J. Control Autom."},{"key":"1717_CR31","doi-asserted-by":"publisher","first-page":"82","DOI":"10.1016\/j.neucom.2018.01.036","volume":"285","author":"Y Yang","year":"2018","unstructured":"Y. Yang, Y. He, Y. Wang, M. Wu, Stability analysis of fractional-order neural networks: an LMI approach. Neurocomputing 285, 82\u201393 (2018)","journal-title":"Neurocomputing"},{"key":"1717_CR32","doi-asserted-by":"publisher","first-page":"5926","DOI":"10.1007\/s00034-020-01451-5","volume":"39","author":"X Yao","year":"2020","unstructured":"X. Yao, M. Tang, F. Wang, Z. Ye, X. Liu, New results on stability for a class of fractional-order static neural networks. Circ. Syst. Signal Process. 39, 5926\u20135950 (2020)","journal-title":"Circ. Syst. Signal Process."},{"key":"1717_CR33","doi-asserted-by":"publisher","first-page":"1776","DOI":"10.1016\/j.neucom.2011.02.015","volume":"74","author":"J Yu","year":"2011","unstructured":"J. Yu, C. Hu, H. Jiang, Z. Teng, Exponential synchronization of Cohen\u2013Grossberg neural networks via periodically intermittent control. Neurocomputing 74, 1776\u20131782 (2011)","journal-title":"Neurocomputing"},{"key":"1717_CR34","doi-asserted-by":"crossref","first-page":"792","DOI":"10.1016\/j.amc.2015.07.074","volume":"269","author":"C Zhang","year":"2015","unstructured":"C. Zhang, F. Deng, Y. Peng, Adaptive synchronization of Cohen\u2013Grossberg neural network with mixed time-varying delays and stochastic perturbation. Appl. Math. Comput. 269, 792\u2013801 (2015)","journal-title":"Appl. Math. Comput."},{"key":"1717_CR35","doi-asserted-by":"publisher","first-page":"533","DOI":"10.1109\/TNN.2009.2014160","volume":"20","author":"XM Zhang","year":"2009","unstructured":"X.M. Zhang, Q.L. Han, New Lyapunov\u2013Krasovskii functionals for global asymptotic stability of delayed neural networks. IEEE Trans. Neural Netw. 20, 533\u2013539 (2009)","journal-title":"IEEE Trans. Neural Netw."},{"key":"1717_CR36","doi-asserted-by":"publisher","first-page":"1180","DOI":"10.1109\/TNN.2011.2147331","volume":"22","author":"XM Zhang","year":"2011","unstructured":"X.M. Zhang, Q.L. Han, Global asymptotic stability for a class of generalized neural networks with interval time-varying delay. IEEE Trans. Neural Netw. 22, 1180\u20131192 (2011)","journal-title":"IEEE Trans. Neural Netw."},{"key":"1717_CR37","doi-asserted-by":"publisher","first-page":"242","DOI":"10.1016\/j.cam.2017.09.045","volume":"339","author":"Y Zhang","year":"2018","unstructured":"Y. Zhang, Y. Yu, X. Cui, Dynamical behaviors analysis of memristor-based fractional-order complex-valued neural networks with time delay. Appl. Math. Comput. 339, 242\u2013258 (2018)","journal-title":"Appl. Math. Comput."}],"container-title":["Circuits, Systems, and Signal Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00034-021-01717-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00034-021-01717-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00034-021-01717-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,1]],"date-time":"2023-11-01T20:58:43Z","timestamp":1698872323000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00034-021-01717-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,4,8]]},"references-count":37,"journal-issue":{"issue":"11","published-print":{"date-parts":[[2021,11]]}},"alternative-id":["1717"],"URL":"https:\/\/doi.org\/10.1007\/s00034-021-01717-6","relation":{},"ISSN":["0278-081X","1531-5878"],"issn-type":[{"type":"print","value":"0278-081X"},{"type":"electronic","value":"1531-5878"}],"subject":[],"published":{"date-parts":[[2021,4,8]]},"assertion":[{"value":"2 July 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 March 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 March 2021","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 April 2021","order":4,"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 they have no conflicts of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"All data generated or analyzed during this study are included in this published article.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Data availability statements"}}]}}