{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T18:05:26Z","timestamp":1769191526433,"version":"3.49.0"},"reference-count":33,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2019,8,1]],"date-time":"2019-08-01T00:00:00Z","timestamp":1564617600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,8,1]],"date-time":"2019-08-01T00:00:00Z","timestamp":1564617600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61803247"],"award-info":[{"award-number":["61803247"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100010909","name":"Young Scientists Fund","doi-asserted-by":"publisher","award":["61802243"],"award-info":[{"award-number":["61802243"]}],"id":[{"id":"10.13039\/501100010909","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61273311"],"award-info":[{"award-number":["61273311"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61173094"],"award-info":[{"award-number":["61173094"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Project Funded by China Postdoctoral Science Foundation","award":["2018M640948"],"award-info":[{"award-number":["2018M640948"]}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"crossref","award":["GK201903003"],"award-info":[{"award-number":["GK201903003"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Shaanxi Postdoctoral Science Foundation","award":["2018BSHEDZZ129"],"award-info":[{"award-number":["2018BSHEDZZ129"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Circuits Syst Signal Process"],"published-print":{"date-parts":[[2020,3]]},"DOI":"10.1007\/s00034-019-01225-8","type":"journal-article","created":{"date-parts":[[2019,8,1]],"date-time":"2019-08-01T09:02:55Z","timestamp":1564650175000},"page":"1353-1371","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Exponential Stabilization Control of Delayed Quaternion-Valued Memristive Neural Networks: Vector Ordering Approach"],"prefix":"10.1007","volume":"39","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4817-9906","authenticated-orcid":false,"given":"Ruoxia","family":"Li","sequence":"first","affiliation":[]},{"given":"Xingbao","family":"Gao","sequence":"additional","affiliation":[]},{"given":"Jinde","family":"Cao","sequence":"additional","affiliation":[]},{"given":"Kai","family":"Zhang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,8,1]]},"reference":[{"issue":"3","key":"1225_CR1","doi-asserted-by":"publisher","first-page":"1350052","DOI":"10.1142\/S0218127413500521","volume":"23","author":"A Ascoli","year":"2013","unstructured":"A. Ascoli, F. Corinto, Memristor models in a chaotic neural circuit. Int. J. Bifurc. Chaos 23(3), 1350052 (2013)","journal-title":"Int. J. Bifurc. Chaos"},{"key":"1225_CR2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-69512-4","volume-title":"Differential Inclusions","author":"J Aubin","year":"1984","unstructured":"J. Aubin, A. Cellina, Differential Inclusions (Springer, Berlin, 1984)"},{"key":"1225_CR3","first-page":"2769","volume":"29","author":"X Chen","year":"2018","unstructured":"X. Chen, Q. Song, Z. Li, Z. Zhao, Y. Liu, Stability analysis of continuous-time and discrete-time quaternion-valued neural networks with linear threshold neurons. IEEE Trans. Neural Netw. Learn. Syst. 29, 2769\u20132781 (2018)","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"1225_CR4","first-page":"186","volume":"113","author":"S Choe","year":"2004","unstructured":"S. Choe, J. Faraway, Modeling head and hand orientation during motion using quaternions. J. Aerosp. 113, 186\u2013192 (2004)","journal-title":"J. Aerosp."},{"key":"1225_CR5","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1109\/70.127239","volume":"8","author":"J Chou","year":"1992","unstructured":"J. Chou, Quaternions kinematic and dynamic differential equations. IEEE Trans. Robot. Autom. 8, 53\u201364 (1992)","journal-title":"IEEE Trans. Robot. Autom."},{"key":"1225_CR6","doi-asserted-by":"publisher","first-page":"507","DOI":"10.1109\/TCT.1971.1083337","volume":"18","author":"L Chua","year":"1971","unstructured":"L. Chua, Memristor\u2014the missing circuit element. IEEE Trans. Circuit Theory 18, 507\u2013519 (1971)","journal-title":"IEEE Trans. Circuit Theory"},{"key":"1225_CR7","doi-asserted-by":"publisher","first-page":"4989","DOI":"10.1016\/j.jfranklin.2017.05.011","volume":"354","author":"S Ding","year":"2017","unstructured":"S. Ding, Z. Wang, H. Niu, H. Zhang, Stop and go adaptive strategy for synchronization of delayed memristive recurrent neural networks with unknown synaptic weights. J. Frankl. Inst. 354, 4989\u20135010 (2017)","journal-title":"J. Frankl. Inst."},{"key":"1225_CR8","doi-asserted-by":"publisher","first-page":"704","DOI":"10.1109\/TNNLS.2013.2280556","volume":"25","author":"Z Guo","year":"2014","unstructured":"Z. Guo, J. Wang, Z. Yan, Attractivity analysis of memristor-based cellular neural networks with time-varying delays. IEEE Trans. Neural Netw. Learn. Syst. 25, 704\u2013717 (2014)","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"1225_CR9","volume-title":"Lectures on Quaternions","author":"W Hamilton","year":"1853","unstructured":"W. Hamilton, Lectures on Quaternions (Hodges and Smith, Dublin, 1853)"},{"key":"1225_CR10","first-page":"821","volume":"17","author":"T Huang","year":"2017","unstructured":"T. Huang, C. Li, X. Liao, Synchronization of a class of coupled chaotic delayed systems with parameter mismatch. Chaos 17, 821\u2013439 (2017)","journal-title":"Chaos"},{"key":"1225_CR11","doi-asserted-by":"publisher","first-page":"411","DOI":"10.4018\/978-1-60566-214-5.ch016","volume-title":"Complex-Valued Neural Networks: Utilizing High-Dimensional Parameters","author":"T Isokawa","year":"2009","unstructured":"T. Isokawa, N. Matsui, H. Nishimura, Quaternionic neural networks: fundamental properties and applications, in Complex-Valued Neural Networks: Utilizing High-Dimensional Parameters, ed. by T. Nitta (Pennsylvania, IGI global, 2009), pp. 411\u2013439"},{"issue":"11","key":"1225_CR12","doi-asserted-by":"publisher","first-page":"3605","DOI":"10.1142\/S0218127409025031","volume":"19","author":"M Itoh","year":"2009","unstructured":"M. Itoh, L.O. Chua, Memristor cellular automata and memristor discrete-time cellular neural networks. Int. J. Bifurc. Chaos 19(11), 3605\u20133656 (2009)","journal-title":"Int. J. Bifurc. Chaos"},{"key":"1225_CR13","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-54265-7","volume-title":"Set-Valued Optimization: An Introduction with Applications","author":"A Khan","year":"2015","unstructured":"A. Khan, C. Tammer, C. Zalinescu, Set-Valued Optimization: An Introduction with Applications (Springer, Berlin, 2015)"},{"key":"1225_CR14","doi-asserted-by":"publisher","first-page":"2924","DOI":"10.1109\/TNNLS.2016.2609148","volume":"28","author":"R Li","year":"2017","unstructured":"R. Li, J. Cao, Finite-time stability analysis for Markovian jump memristive neural networks with partly unknown transition probabilities. IEEE Trans. Neural Netw. Learn. Syst. 28, 2924\u20132935 (2017)","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"issue":"9","key":"1225_CR15","doi-asserted-by":"publisher","first-page":"4201","DOI":"10.1109\/TNNLS.2017.2755697","volume":"29","author":"Y Liu","year":"2018","unstructured":"Y. Liu, D. Zhang, J. Lou, J. Lu, J. Cao, Stability analysis of quaternion-valued neural networks: decomposition and direct approaches. IEEE Trans. Neural Netw. Learn. Syst. 29(9), 4201\u20134211 (2018)","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"1225_CR16","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2019.2916597","author":"Y Liu","year":"2019","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. (2019). \nhttps:\/\/doi.org\/10.1109\/TNNLS.2019.2916597","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"1225_CR17","first-page":"149","volume":"15","author":"N Matsui","year":"2004","unstructured":"N. Matsui, T. Isokawa, H. Kusamichi, F. Peper, H. Nishimura, Quaternion neural network with geometrical operators. J. Intell. Fuzzy Syst. Appl. Eng. Technol. 15, 149\u2013164 (2004)","journal-title":"J. Intell. Fuzzy Syst. Appl. Eng. Technol."},{"key":"1225_CR18","unstructured":"R. Mukundan, Quaternions: from classical mechanics to computer graphics and beyond, in Proceedings of the 7th Asian Technology Conference in Mathematics (2002), pp. 97\u2013105"},{"issue":"3","key":"1225_CR19","doi-asserted-by":"publisher","first-page":"903","DOI":"10.1109\/TCST.2017.2699158","volume":"26","author":"H Pan","year":"2018","unstructured":"H. Pan, X. Jing, W. Sun, H. Gao, A bioinspired dynamics-based adaptive tracking control for nonlinear suspension systems. IEEE Trans. Control Syst. Technol. 26(3), 903\u2013914 (2018)","journal-title":"IEEE Trans. Control Syst. Technol."},{"issue":"2","key":"1225_CR20","doi-asserted-by":"publisher","first-page":"868","DOI":"10.1109\/TASE.2015.2414652","volume":"13","author":"H Pan","year":"2016","unstructured":"H. Pan, W. Sun, H. Gao, X. Jing, Disturbance observer-based adaptive tracking control with actuator saturation and its application. IEEE Trans. Autom. Sci. Eng. 13(2), 868\u2013875 (2016)","journal-title":"IEEE Trans. Autom. Sci. Eng."},{"issue":"1","key":"1225_CR21","doi-asserted-by":"publisher","first-page":"1430001","DOI":"10.1142\/S0218127414300018","volume":"24","author":"M Scarabello","year":"2014","unstructured":"M. Scarabello, M. Messias, Bifurcations leading to nonlinear oscillations in a 3D piecewise linear memristor oscillator. Int. J. Bifurc. Chaos 24(1), 1430001 (2014)","journal-title":"Int. J. Bifurc. Chaos"},{"key":"1225_CR22","doi-asserted-by":"publisher","first-page":"5430","DOI":"10.1109\/TNNLS.2018.2801297","volume":"29","author":"Q Song","year":"2018","unstructured":"Q. Song, X. Chen, Multistability analysis of quaternion-valued neural networks with time delays. IEEE Trans. Neural Netw. Learn. Syst. 29, 5430\u20135440 (2018)","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"1225_CR23","doi-asserted-by":"publisher","first-page":"80","DOI":"10.1038\/nature06932","volume":"453","author":"D Strukov","year":"2008","unstructured":"D. Strukov, G. Snider, D. Stewart, R. Williams, The missing memristor found. Nature 453, 80\u201383 (2008)","journal-title":"Nature"},{"key":"1225_CR24","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1016\/j.neunet.2017.01.006","volume":"89","author":"Z Tu","year":"2017","unstructured":"Z. Tu, J. Cao, A. Alsaedi, T. Hayat, Global dissipativity analysis for delayed quaternion-valued neural networks. Neural Netw. 89, 97\u2013104 (2017)","journal-title":"Neural Netw."},{"key":"1225_CR25","doi-asserted-by":"publisher","first-page":"1193","DOI":"10.1109\/TNN.2011.2157358","volume":"22","author":"B Ujang","year":"2011","unstructured":"B. Ujang, C. Took, D. Mandic, Quaternion-valued nonlinear adaptive filtering. IEEE Trans. Neural Netw. 22, 1193\u20131206 (2011)","journal-title":"IEEE Trans. Neural Netw."},{"issue":"8","key":"1225_CR26","doi-asserted-by":"publisher","first-page":"1250205","DOI":"10.1142\/S0218127412502057","volume":"22","author":"L Wang","year":"2012","unstructured":"L. Wang, E. Drakakis, S. Duan, P. He, X. Liao, Memristor model and its application for chaos generation. Int. J. Bifurc. Chaos 22(8), 1250205 (2012)","journal-title":"Int. J. Bifurc. Chaos"},{"key":"1225_CR27","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1007\/s00034-011-9282-0","volume":"31","author":"Q Wang","year":"2012","unstructured":"Q. Wang, B. Du, J. Lam, M. Chen, Stability analysis of Markovian jump systems with multiple delay components and polytopic uncertainties. Circuits Syst. Signal Process. 31, 143\u2013162 (2012)","journal-title":"Circuits Syst. Signal Process."},{"key":"1225_CR28","doi-asserted-by":"publisher","first-page":"379","DOI":"10.1007\/s11063-016-9531-0","volume":"45","author":"H Wei","year":"2017","unstructured":"H. Wei, R. Li, C. Chen, Z. Tu, Stability analysis of fractional order complex-valued memristive neural networks with time delays. Neural Process. Lett. 45, 379\u2013399 (2017)","journal-title":"Neural Process. Lett."},{"key":"1225_CR29","doi-asserted-by":"publisher","first-page":"48","DOI":"10.1016\/j.neunet.2014.10.011","volume":"63","author":"S Wen","year":"2015","unstructured":"S. Wen, T. Huang, Z. Zeng, Y. Chen, P. Li, Circuit design and exponential stabilization of memristive neural networks. Neural Netw. 63, 48\u201356 (2015)","journal-title":"Neural Netw."},{"issue":"12","key":"1225_CR30","doi-asserted-by":"publisher","first-page":"1919","DOI":"10.1109\/TNNLS.2012.2219554","volume":"23","author":"A Wu","year":"2012","unstructured":"A. Wu, Z. Zeng, Exponential stabilization of memristive neural networks with time delays. IEEE Trans. Neural Netw. Learn. Syst. 23(12), 1919\u20131929 (2012)","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"1225_CR31","doi-asserted-by":"publisher","first-page":"3377","DOI":"10.1109\/TCYB.2015.2505903","volume":"46","author":"X Yang","year":"2015","unstructured":"X. Yang, D.W.C. Ho, Synchronization of delayed memristive neural networks: robust analysis approach. IEEE Trans. Cybern. 46, 3377\u20133387 (2015)","journal-title":"IEEE Trans. Cybern."},{"key":"1225_CR32","doi-asserted-by":"publisher","first-page":"162","DOI":"10.1016\/j.neunet.2015.12.003","volume":"75","author":"S Yang","year":"2016","unstructured":"S. Yang, C. Li, T. Huang, Exponential stabilization and synchronization for fuzzy model of memristive neural networks by periodically intermittent control. Neural Netw. 75, 162\u2013172 (2016)","journal-title":"Neural Netw."},{"key":"1225_CR33","doi-asserted-by":"publisher","first-page":"2065","DOI":"10.1007\/s00034-013-9735-8","volume":"33","author":"S Zhu","year":"2014","unstructured":"S. Zhu, W. Luo, Y. Shen, Robustness analysis for connection weight matrices of global exponential stability of stochastic delayed recurrent neural networks. Circuits Syst. Signal Process. 33, 2065\u20132083 (2014)","journal-title":"Circuits Syst. Signal Process."}],"container-title":["Circuits, Systems, and Signal Processing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00034-019-01225-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00034-019-01225-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00034-019-01225-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,7,31]],"date-time":"2020-07-31T00:08:06Z","timestamp":1596154086000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00034-019-01225-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,8,1]]},"references-count":33,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2020,3]]}},"alternative-id":["1225"],"URL":"https:\/\/doi.org\/10.1007\/s00034-019-01225-8","relation":{},"ISSN":["0278-081X","1531-5878"],"issn-type":[{"value":"0278-081X","type":"print"},{"value":"1531-5878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,8,1]]},"assertion":[{"value":"14 March 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 July 2019","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 July 2019","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 August 2019","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}