{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,29]],"date-time":"2025-12-29T18:53:32Z","timestamp":1767034412523,"version":"3.37.3"},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2024,9,19]],"date-time":"2024-09-19T00:00:00Z","timestamp":1726704000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,9,19]],"date-time":"2024-09-19T00:00:00Z","timestamp":1726704000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100005046","name":"Natural Science Foundation of Heilongjiang Province","doi-asserted-by":"publisher","award":["YQ2021F014"],"award-info":[{"award-number":["YQ2021F014"]}],"id":[{"id":"10.13039\/501100005046","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Basic Research Foundation for Outstanding Young Teachers in Heilongjiang Provincial Universities of China","award":["YQJH2023141"],"award-info":[{"award-number":["YQJH2023141"]}]},{"name":"Fundamental Research Funds in Heilongjiang Provincial Universities of China","award":["2022-KYYWF-1099"],"award-info":[{"award-number":["2022-KYYWF-1099"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12401343"],"award-info":[{"award-number":["12401343"]}],"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":[[2025,1]]},"DOI":"10.1007\/s00034-024-02856-2","type":"journal-article","created":{"date-parts":[[2024,9,19]],"date-time":"2024-09-19T18:02:34Z","timestamp":1726768954000},"page":"128-140","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Concise Exponential Stability Conditions for BAM Quaternion Memristive Neural Networks Affected by Mixed Delays"],"prefix":"10.1007","volume":"44","author":[{"given":"Zhiwei","family":"Zhang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaona","family":"Yang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hongwei","family":"Guan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7023-7351","authenticated-orcid":false,"given":"Xian","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,9,19]]},"reference":[{"issue":"4","key":"2856_CR1","doi-asserted-by":"publisher","first-page":"1940","DOI":"10.1007\/s00034-021-01894-4","volume":"41","author":"A Arbi","year":"2022","unstructured":"A. Arbi, N. Tahri, C. Jammazi, C. Huang, J. Cao, Almost anti-periodic solution of inertial neural networks with leakage and time-varying delays on timescales. Circ., Syst. Signal Process. 41(4), 1940\u20131956 (2022)","journal-title":"Circ., Syst. Signal Process."},{"key":"2856_CR2","first-page":"127633","volume":"439","author":"Y Chen","year":"2023","unstructured":"Y. Chen, Y. Xue, X. Yang, X. Zhang, A direct analysis method to Lagrangian global exponential stability for quaternion memristive neural networks with mixed delays. Appl. Math. Comput. 439, 127633 (2023)","journal-title":"Appl. Math. Comput."},{"issue":"1","key":"2856_CR3","doi-asserted-by":"publisher","first-page":"405","DOI":"10.1109\/TNNLS.2022.3174880","volume":"35","author":"J Cheng","year":"2024","unstructured":"J. Cheng, L. Liang, H. Yan, J. Cao, S. Tang, K. Shi, Proportional-integral observer-based state estimation for Markov memristive neural networks with sensor saturations. IEEE Trans. Neural Netw. Learn. Syst. 35(1), 405\u2013416 (2024)","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"issue":"6","key":"2856_CR4","doi-asserted-by":"publisher","first-page":"5367","DOI":"10.1109\/TCYB.2020.3031309","volume":"52","author":"K Deng","year":"2022","unstructured":"K. Deng, S. Zhu, W. Dai, C. Yang, S. Wen, New criteria on stability of dynamic memristor delayed cellular neural networks. IEEE Trans. Cybern. 52(6), 5367\u20135379 (2022)","journal-title":"IEEE Trans. Cybern."},{"key":"2856_CR5","first-page":"125401","volume":"385","author":"Z Dong","year":"2020","unstructured":"Z. Dong, X. Wang, X. Zhang, A nonsingular M-matrix-based global exponential stability analysis of higher-order delayed discrete-time Cohen-Grossberg neural networks. Appl. Math. Comput. 385, 125401 (2020)","journal-title":"Appl. Math. Comput."},{"key":"2856_CR6","first-page":"101291","volume":"47","author":"Z Dong","year":"2023","unstructured":"Z. Dong, X. Wang, X. Zhang, M. Hu, T.N. Dinh, Global exponential synchronization of discrete-time high-order switched neural networks and its application to multi-channel audio encryption. Nonlinear Anal.: Hybrid Syst. 47, 101291 (2023)","journal-title":"Nonlinear Anal.: Hybrid Syst."},{"issue":"18","key":"2856_CR7","doi-asserted-by":"publisher","first-page":"8098","DOI":"10.1002\/rnc.5210","volume":"30","author":"XR Ji","year":"2020","unstructured":"X.R. Ji, J.Q. Lu, J.G. Lou, J.L. Qiu, K.B. Shi, A unified criterion for global exponential stability of quaternion-valued neural networks with hybrid impulses. Int. J. Robust Nonlinear Control 30(18), 8098\u20138116 (2020)","journal-title":"Int. J. Robust Nonlinear Control"},{"issue":"23","key":"2856_CR8","doi-asserted-by":"publisher","first-page":"4947","DOI":"10.1364\/AO.26.004947","volume":"26","author":"B Kosko","year":"1987","unstructured":"B. Kosko, Adaptive bidirectional associative memories. Appl. Optics 26(23), 4947\u20134960 (1987)","journal-title":"Appl. Optics"},{"key":"2856_CR9","doi-asserted-by":"publisher","first-page":"729","DOI":"10.1016\/j.ins.2022.12.053","volume":"623","author":"Q Li","year":"2023","unstructured":"Q. Li, L. Zhou, Global polynomial stabilization of proportional delayed inertial memristive neural networks. Inf. Sci. 623, 729\u2013747 (2023)","journal-title":"Inf. Sci."},{"key":"2856_CR10","doi-asserted-by":"publisher","first-page":"2147","DOI":"10.1007\/s00034-024-02701-6","volume":"43","author":"W Li","year":"2024","unstructured":"W. Li, X. Zhang, C. Liu, X. Yang, Global exponential stability conditions for discrete-time BAM neural networks affected by impulses and time-varying delays. Circ., Syst. Signal Process. 43, 2147\u20132170 (2024)","journal-title":"Circ., Syst. Signal Process."},{"issue":"12","key":"2856_CR11","doi-asserted-by":"publisher","first-page":"6374","DOI":"10.1109\/TNNLS.2018.2830789","volume":"29","author":"X Li","year":"2018","unstructured":"X. Li, F. Li, X. Zhang, C. Yang, W. Gui, Exponential stability analysis for delayed semi-Markovian recurrent neural networks: a homogeneous polynomial approach. IEEE Trans. Neural Netw. Learn. Syst. 29(12), 6374\u20136384 (2018)","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"2856_CR12","doi-asserted-by":"publisher","first-page":"461","DOI":"10.1016\/j.neucom.2022.05.085","volume":"500","author":"Y-G Li","year":"2022","unstructured":"Y.-G. Li, G.-H. Yang, Optimal innovation-based deception attacks with side information against remote state estimation in cyber-physical systems. Neurocomputing 500, 461\u2013470 (2022)","journal-title":"Neurocomputing"},{"key":"2856_CR13","doi-asserted-by":"publisher","first-page":"134","DOI":"10.1016\/j.matcom.2020.03.002","volume":"174","author":"J Liu","year":"2020","unstructured":"J. Liu, J. Jian, B. Wang, Stability analysis for BAM quaternion-valued inertial neural networks with time delay via nonlinear measure approach. Math. Comput. Simul. 174, 134\u2013152 (2020)","journal-title":"Math. Comput. Simul."},{"issue":"7","key":"2856_CR14","doi-asserted-by":"publisher","first-page":"3777","DOI":"10.1007\/s00034-022-01980-1","volume":"41","author":"H Liu","year":"2022","unstructured":"H. Liu, W. Qian, Y. Zhao, New optimization approach of state estimation for neural networks with mixed delays. Circ., Syst. Signal Process. 41(7), 3777\u20133797 (2022)","journal-title":"Circ., Syst. Signal Process."},{"issue":"3","key":"2856_CR15","doi-asserted-by":"publisher","first-page":"1022","DOI":"10.1109\/TNNLS.2019.2916597","volume":"31","author":"Y Liu","year":"2020","unstructured":"Y. Liu, Y. Zheng, J. Lu, J. Cao, L. Rutkowski, Constrained quaternion-variable convex optimization: a quaternion-valued recurrent neural network approach. IEEE Trans. Neural Netw. Learn. Syst. 31(3), 1022\u20131035 (2020)","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"2856_CR16","doi-asserted-by":"publisher","first-page":"206","DOI":"10.1016\/j.neucom.2022.08.059","volume":"509","author":"X Mao","year":"2022","unstructured":"X. Mao, X. Wang, H. Qin, Stability analysis of quaternion-valued BAM neural networks fractional-order model with impulses and proportional delays. Neurocomputing 509, 206\u2013220 (2022)","journal-title":"Neurocomputing"},{"issue":"4","key":"2856_CR17","doi-asserted-by":"publisher","first-page":"2957","DOI":"10.1007\/s10462-019-09752-1","volume":"53","author":"T Parcollet","year":"2020","unstructured":"T. Parcollet, M. Morchid, G. Linares, A survey of quaternion neural networks. Artif. Intell. Rev. 53(4), 2957\u20132982 (2020)","journal-title":"Artif. Intell. Rev."},{"key":"2856_CR18","doi-asserted-by":"publisher","first-page":"508","DOI":"10.1016\/j.matcom.2021.02.023","volume":"201","author":"G Rajchakit","year":"2022","unstructured":"G. Rajchakit, R. Sriraman, C.P. Lim, B. Unyong, Existence, uniqueness and global stability of Clifford-valued neutral-type neural networks with time delays. Math. Comput. Simul. 201, 508\u2013527 (2022)","journal-title":"Math. Comput. Simul."},{"key":"2856_CR19","first-page":"126309","volume":"407","author":"G Rajchakit","year":"2021","unstructured":"G. Rajchakit, R. Sriraman, P. Vignesh, C.P. Lim, Impulsive effects on Clifford-valued neural networks with time-varying delays: an asymptotic stability analysis. Appl. Math. Comput. 407, 126309 (2021)","journal-title":"Appl. Math. Comput."},{"issue":"1","key":"2856_CR20","first-page":"363","volume":"68","author":"XN Song","year":"2021","unstructured":"X.N. Song, J.T. Man, S. Song, C.K. Ahn, Finite\/fixed-time anti-synchronization of inconsistent Markovian quaternion-valued memristive neural networks with reaction-diffusion terms. IEEE Trans. Circ. Syst.I: Regul. Papers 68(1), 363\u2013375 (2021)","journal-title":"IEEE Trans. Circ. Syst.I: Regul. Papers"},{"key":"2856_CR21","doi-asserted-by":"publisher","first-page":"106279","DOI":"10.1016\/j.neunet.2024.106279","volume":"175","author":"K Tu","year":"2024","unstructured":"K. Tu, Y. Xue, X. Zhang, Observer-based resilient dissipativity control for discrete-time memristor-based neural networks with unbounded or bounded time-varying delays. Neural Netw. 175, 106279 (2024)","journal-title":"Neural Netw."},{"issue":"10","key":"2856_CR22","first-page":"4063","volume":"31","author":"K Udhayakumar","year":"2019","unstructured":"K. Udhayakumar, X. Li, R. Rajan, Quasi-synchronization and bifurcation results on fractional-order quaternion-valued neural networks. IEEE Trans. Neural Netw. Learn. Syst. 31(10), 4063\u20134072 (2019)","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"2856_CR23","first-page":"126092","volume":"401","author":"K Udhayakumar","year":"2021","unstructured":"K. Udhayakumar, R. Rakkiyappan, X. Li, J. Cao, Mutiple $$\\psi $$-type stability of fractional-order quaternion-valued neural networks. Appl. Math. Comput. 401, 126092 (2021)","journal-title":"Appl. Math. Comput."},{"key":"2856_CR24","doi-asserted-by":"crossref","first-page":"125680","DOI":"10.1016\/j.cam.2021.113383","volume":"390","author":"H Wang","year":"2021","unstructured":"H. Wang, G. Wei, S. Wen, T. Huang, Impulsive disturbance on stability analysis of delayed quaternion-valued neural networks. Appl. Math. Comput. 390, 125680 (2021)","journal-title":"Appl. Math. Comput."},{"issue":"11","key":"2856_CR25","doi-asserted-by":"publisher","first-page":"6693","DOI":"10.1109\/TSMC.2023.3286095","volume":"53","author":"J Wang","year":"2023","unstructured":"J. Wang, X. Wang, X. Zhang, S. Zhu, Global $$h$$-synchronization of high-order delayed inertial neural networks via direct SORS approach. IEEE Trans. Syst., Man, Cybern.: Syst. 53(11), 6693\u20136704 (2023)","journal-title":"IEEE Trans. Syst., Man, Cybern.: Syst."},{"key":"2856_CR26","doi-asserted-by":"publisher","first-page":"62","DOI":"10.1016\/j.ins.2022.05.103","volume":"607","author":"J Wang","year":"2022","unstructured":"J. Wang, X. Zhang, X. Wang, X. Yang, $${L}_{2}-{L}_{\\infty }$$ state estimation of the high-order inertial neural network with time-varying delay: Non-reduced order strategy. Inf. Sci. 607, 62\u201378 (2022)","journal-title":"Inf. Sci."},{"key":"2856_CR27","doi-asserted-by":"publisher","first-page":"119865","DOI":"10.1016\/j.ins.2023.119865","volume":"654","author":"X Wang","year":"2024","unstructured":"X. Wang, X. Liang, X. Zhang, Y. Xue, $$L_p$$ synchronization of shunting inhibitory cellular neural networks with multiple proportional delays. Inf. Sci. 654, 119865 (2024)","journal-title":"Inf. Sci."},{"issue":"10","key":"2856_CR28","doi-asserted-by":"publisher","first-page":"4924","DOI":"10.1109\/TCYB.2020.3034374","volume":"51","author":"X Wang","year":"2021","unstructured":"X. Wang, J.H. Park, H. Liu, X. Zhang, Cooperative output-feedback secure control of distributed linear cyber-physical systems resist intermittent DoS attacks. IEEE Trans. Cybern. 51(10), 4924\u20134933 (2021)","journal-title":"IEEE Trans. Cybern."},{"issue":"5","key":"2856_CR29","doi-asserted-by":"publisher","first-page":"1921","DOI":"10.1109\/TCYB.2019.2901542","volume":"50","author":"X Wang","year":"2020","unstructured":"X. Wang, G.H. Yang, Fault-tolerant consensus tracking control for linear multiagent systems under switching directed network. IEEE Trans. Cybern. 50(5), 1921\u20131930 (2020)","journal-title":"IEEE Trans. Cybern."},{"issue":"6","key":"2856_CR30","doi-asserted-by":"publisher","first-page":"3587","DOI":"10.1109\/TSMC.2019.2931091","volume":"51","author":"R Wei","year":"2021","unstructured":"R. Wei, J. Cao, M. Abdel-Aty, Fixed-time synchronization of second-order MNNs in quaternion field. IEEE Trans. Syst., Man, Cybern.: Syst. 51(6), 3587\u20133598 (2021)","journal-title":"IEEE Trans. Syst., Man, Cybern.: Syst."},{"key":"2856_CR31","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1016\/j.neunet.2023.07.004","volume":"166","author":"Y Xu","year":"2023","unstructured":"Y. Xu, C. Yang, L. Zhou, L. Ma, S. Zhu, Adaptive event-triggered synchronization of neural networks under stochastic cyber-attacks with application to Chua\u2019s circuit. Neural Netw. 166, 11\u201321 (2023)","journal-title":"Neural Netw."},{"issue":"10","key":"2856_CR32","doi-asserted-by":"publisher","first-page":"6652","DOI":"10.1109\/TSMC.2022.3148715","volume":"52","author":"Y Xue","year":"2022","unstructured":"Y. Xue, C. Liu, X. Zhang, State bounding description and reachable set estimation for discrete-time genetic regulatory networks with time-varying delays and bounded disturbances. IEEE Trans. Syst., Man, Cybern.: Syst. 52(10), 6652\u20136661 (2022)","journal-title":"IEEE Trans. Syst., Man, Cybern.: Syst."},{"key":"2856_CR33","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1016\/j.ins.2023.02.082","volume":"632","author":"Y Yan","year":"2023","unstructured":"Y. Yan, T. Li, H. Yang, J. Wang, C.L.P. Chen, Fuzzy finite-time consensus control for uncertain nonlinear multi-agent systems with input delay. Inf. Sci. 632, 51\u201368 (2023)","journal-title":"Inf. Sci."},{"issue":"7","key":"2856_CR34","doi-asserted-by":"publisher","first-page":"1989","DOI":"10.1109\/TCYB.2017.2726015","volume":"48","author":"X Zhang","year":"2018","unstructured":"X. Zhang, X. Fan, L. Wu, Reduced- and full-order observers for delayed genetic regulatory networks. IEEE Trans. Cybern. 48(7), 1989\u20132000 (2018)","journal-title":"IEEE Trans. Cybern."},{"issue":"2","key":"2856_CR35","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1109\/TNNLS.2016.2618899","volume":"29","author":"X Zhang","year":"2018","unstructured":"X. Zhang, Y. Han, L. Wu, Y. Wang, State estimation for delayed genetic regulatory networks with reaction-diffusion terms. IEEE Trans. Neural Netw. Learn. Syst. 29(2), 299\u2013309 (2018)","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"issue":"2","key":"2856_CR36","doi-asserted-by":"publisher","first-page":"308","DOI":"10.1109\/LED.2017.2782752","volume":"39","author":"X Zhang","year":"2017","unstructured":"X. Zhang, W. Wang, Q. Liu, X. Zhao, J. Wei, R. Cao, Z. Yao, X. Zhu, F. Zhang, H. Lv et al., An artificial neuron based on a threshold switching memristor. IEEE Electron Device Lett. 39(2), 308\u2013311 (2017)","journal-title":"IEEE Electron Device Lett."},{"issue":"2","key":"2856_CR37","doi-asserted-by":"publisher","first-page":"1847","DOI":"10.1109\/TNNLS.2022.3185617","volume":"35","author":"Y Zhang","year":"2022","unstructured":"Y. Zhang, Y. He, F. Long, C.-K. Zhang, Mixed-delay-based augmented functional for sampled-data synchronization of delayed neural networks with communication delay. IEEE Trans. Neural Netw. Learn. Syst. 35(2), 1847\u20131856 (2022)","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"issue":"9","key":"2856_CR38","doi-asserted-by":"publisher","first-page":"7165","DOI":"10.1002\/mma.9962","volume":"47","author":"Z Zhang","year":"2024","unstructured":"Z. Zhang, X. Liang, J. Lan, X. Zhang, Global exponential stability of quaternion bidirectional associative memory neural networks with multiple delays. Math. Methods Appl. Sci. 47(9), 7165\u20137181 (2024)","journal-title":"Math. Methods Appl. Sci."}],"container-title":["Circuits, Systems, and Signal Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00034-024-02856-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00034-024-02856-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00034-024-02856-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,20]],"date-time":"2025-01-20T13:33:17Z","timestamp":1737379997000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00034-024-02856-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,9,19]]},"references-count":38,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2025,1]]}},"alternative-id":["2856"],"URL":"https:\/\/doi.org\/10.1007\/s00034-024-02856-2","relation":{},"ISSN":["0278-081X","1531-5878"],"issn-type":[{"type":"print","value":"0278-081X"},{"type":"electronic","value":"1531-5878"}],"subject":[],"published":{"date-parts":[[2024,9,19]]},"assertion":[{"value":"13 February 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 August 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 August 2024","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 September 2024","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 have no Conflict of interest to declare.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}