{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,19]],"date-time":"2025-10-19T15:46:03Z","timestamp":1760888763913},"reference-count":43,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2012,11,27]],"date-time":"2012-11-27T00:00:00Z","timestamp":1353974400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Circuits Syst Signal Process"],"published-print":{"date-parts":[[2013,8]]},"DOI":"10.1007\/s00034-012-9523-x","type":"journal-article","created":{"date-parts":[[2012,11,26]],"date-time":"2012-11-26T18:54:37Z","timestamp":1353956077000},"page":"1907-1929","source":"Crossref","is-referenced-by-count":17,"title":["Pinning Cluster Synchronization for Delayed Dynamical Networks via Kronecker Product"],"prefix":"10.1007","volume":"32","author":[{"given":"Tao","family":"Li","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ting","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xin","family":"Yang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shumin","family":"Fei","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2012,11,27]]},"reference":[{"issue":"2","key":"9523_CR1","doi-asserted-by":"crossref","first-page":"520","DOI":"10.1016\/j.amc.2008.12.026","volume":"208","author":"S.J. Choi","year":"2009","unstructured":"S.J. Choi, S.M. Lee, S.C. Won, J.H. Park, Improved delay-dependent stability criteria for uncertain Lur\u2019e systems with sector and slope restricted nonlinearities and time-varying delays. Appl. Math. Comput. 208(2), 520\u2013530 (2009)","journal-title":"Appl. Math. Comput."},{"issue":"2\u20134","key":"9523_CR2","doi-asserted-by":"crossref","first-page":"567","DOI":"10.1016\/j.mcm.2010.03.056","volume":"52","author":"Y. Chen","year":"2010","unstructured":"Y. Chen, M.Y. Li, Z.F. Cheng, Global anti-synchronization of master\u2013slave chaotic modified Chua\u2019s circuits coupled by linear feedback control. Math. Comput. Model. 52(2\u20134), 567\u2013573 (2010)","journal-title":"Math. Comput. Model."},{"issue":"21","key":"9523_CR3","doi-asserted-by":"crossref","first-page":"2099","DOI":"10.1016\/j.physleta.2011.04.015","volume":"375","author":"L.P. Chen","year":"2011","unstructured":"L.P. Chen, Y. Chai, R.C. Wu, Lag projective synchronization in fractional-order chaotic (hyperchaotic) systems. Phys. Lett. A 375(21), 2099\u20132110 (2011)","journal-title":"Phys. Lett. A"},{"issue":"4","key":"9523_CR4","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1016\/j.neunet.2009.03.006","volume":"22","author":"J.D. Cao","year":"2009","unstructured":"J.D. Cao, L.L. Li, Cluster synchronization in an array of hybrid coupled neural networks with delay. Neural Netw. 22(4), 335\u2013342 (2009)","journal-title":"Neural Netw."},{"issue":"35","key":"9523_CR5","doi-asserted-by":"crossref","first-page":"2381","DOI":"10.1016\/j.physleta.2012.05.060","volume":"376","author":"L.P. Chen","year":"2012","unstructured":"L.P. Chen, Y. Chai, R.C. Wu, J. Sun, Cluster synchronization in fractional-order complex dynamical networks. Phys. Lett. A 376(35), 2381\u20132388 (2012)","journal-title":"Phys. Lett. A"},{"issue":"1","key":"9523_CR6","first-page":"14","volume":"82","author":"D.W. Dong","year":"2012","unstructured":"D.W. Dong, H.G. Zhang, Z.S. Wang, Novel synchronization analysis for complex networks with hybrid coupling by handling multitude Kronecker product terms. Neurocomputing 82(1), 14\u201320 (2012)","journal-title":"Neurocomputing"},{"issue":"17","key":"9523_CR7","doi-asserted-by":"crossref","first-page":"1565","DOI":"10.1016\/j.physleta.2009.03.003","volume":"373","author":"W.L. Guo","year":"2009","unstructured":"W.L. Guo, F. Austin, S.H. Chen, W. Sun, Pinning synchronization of the complex networks with non-delayed and delayed coupling. Phys. Lett. A 373(17), 1565\u20131572 (2009)","journal-title":"Phys. Lett. A"},{"issue":"3","key":"9523_CR8","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1007\/s11063-012-9213-5","volume":"35","author":"D.W. Gong","year":"2012","unstructured":"D.W. Gong, H.G. Zhang, Z.S. Wang, Pinning synchronization for a general complex networks with multiple time-varying coupling delays. Neural Process. Lett. 35(3), 221\u2013231 (2012)","journal-title":"Neural Process. Lett."},{"issue":"11","key":"9523_CR9","doi-asserted-by":"crossref","first-page":"4159","DOI":"10.1142\/S021812740701969X","volume":"17","author":"H. Huang","year":"2007","unstructured":"H. Huang, J.D. Cao, Master\u2013slave synchronization of Lur\u2019e systems based on time-varying delay feedback control. Int. J. Bifur. Chaos 17(11), 4159\u20134166 (2007)","journal-title":"Int. J. Bifur. Chaos"},{"issue":"4","key":"9523_CR10","doi-asserted-by":"crossref","first-page":"571","DOI":"10.1109\/TNN.2009.2039803","volume":"21","author":"W.L. He","year":"2010","unstructured":"W.L. He, J.D. Cao, Exponential synchronization of hybrid coupled networks with delayed coupling. IEEE Trans. Neural Netw. 21(4), 571\u2013583 (2010)","journal-title":"IEEE Trans. Neural Netw."},{"issue":"6","key":"9523_CR11","doi-asserted-by":"crossref","first-page":"1396","DOI":"10.1109\/TCSI.2010.2097691","volume":"58","author":"X.Z. Jin","year":"2011","unstructured":"X.Z. Jin, G.H. Yang, Adaptive synchronization of a class of uncertain complex networks against network deterioration. IEEE Trans. Circuits Syst. I 58(6), 1396\u20131409 (2011)","journal-title":"IEEE Trans. Circuits Syst. I"},{"issue":"9","key":"9523_CR12","doi-asserted-by":"crossref","first-page":"1345","DOI":"10.1109\/TNNLS.2012.2202246","volume":"23","author":"X.Z. Jin","year":"2012","unstructured":"X.Z. Jin, G.H. Yang, W.W. Che, Adaptive pinning control of deteriorated nonlinear coupling networks with circuit realization. IEEE Trans. Neural Netw. Learn. Syst 23(9), 1345\u20131355 (2012)","journal-title":"IEEE Trans. Neural Netw. Learn. Syst"},{"issue":"2","key":"9523_CR13","doi-asserted-by":"crossref","first-page":"316","DOI":"10.1016\/j.cnsns.2012.07.011","volume":"18","author":"X.Z. Jin","year":"2013","unstructured":"X.Z. Jin, G.H. Yang, Adaptive pinning synchronization of a class of nonlinearly coupled complex networks. Commun. Nonlinear Sci. Numer. Simul. 18(2), 316\u2013326 (2013)","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"issue":"1","key":"9523_CR14","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1109\/TSMCB.2009.2024408","volume":"40","author":"H.R. Karimi","year":"2010","unstructured":"H.R. Karimi, H.J. Gao, New delay-dependent exponential H \u221e synchronization for uncertain neural networks with mixed time delays. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 40(1), 173\u2013185 (2010)","journal-title":"IEEE Trans. Syst. Man Cybern., Part B, Cybern."},{"issue":"3","key":"9523_CR15","first-page":"149","volume":"232","author":"H.J. Li","year":"2009","unstructured":"H.J. Li, D. Yue, Synchronization stability of general complex dynamical networks with time-varying delays: a piecewise analysis method. J. Comput. Appl. Math. 232(3), 149\u2013158 (2009)","journal-title":"J. Comput. Appl. Math."},{"issue":"9","key":"9523_CR16","doi-asserted-by":"crossref","first-page":"973","DOI":"10.1080\/00207720902752173","volume":"40","author":"J.L. Liang","year":"2009","unstructured":"J.L. Liang, Z.D. Wang, P. Li, Robust synchronisation of delayed neural networks with both linear and non-linear couplings. Int. J. Syst. Sci. 40(9), 973\u2013984 (2009)","journal-title":"Int. J. Syst. Sci."},{"issue":"1","key":"9523_CR17","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1016\/j.cnsns.2010.04.008","volume":"16","author":"T. Li","year":"2011","unstructured":"T. Li, A.G. Song, S.M. Fei, Global synchronization in arrays of coupled Lurie systems with both time-delay and hybrid coupling. Commun. Nonlinear Sci. Numer. Simul. 16(1), 10\u201320 (2011)","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"issue":"2","key":"9523_CR18","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1109\/TNNLS.2011.2179312","volume":"23","author":"J.Q. Lu","year":"2012","unstructured":"J.Q. Lu, J. Kurths, J.D. Cao, N. Mahdavi, C. Huang, Synchronization control for nonlinear stochastic dynamical networks: pinning impulsive strategy. IEEE Trans. Neural Netw. Learn. Syst 23(2), 285\u2013292 (2012)","journal-title":"IEEE Trans. Neural Netw. Learn. Syst"},{"issue":"5","key":"9523_CR19","doi-asserted-by":"crossref","first-page":"846","DOI":"10.1016\/j.neucom.2010.11.006","volume":"74","author":"L.L. Li","year":"2011","unstructured":"L.L. Li, J.D. Cao, Cluster synchronization in an array of coupled stochastic delayed neural networks via pinning control. Neurocomputing 74(5), 846\u2013856 (2011)","journal-title":"Neurocomputing"},{"issue":"2","key":"9523_CR20","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1049\/iet-cta.2011.0147","volume":"6","author":"J. Liu","year":"2012","unstructured":"J. Liu, J. Zhang, Note on stability of discrete-time time-varying delay systems. IET Control Theory Appl. 6(2), 335\u2013339 (2012)","journal-title":"IET Control Theory Appl."},{"issue":"3","key":"9523_CR21","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1109\/81.222798","volume":"40","author":"V. Perez-Munuzuri","year":"1993","unstructured":"V. Perez-Munuzuri, V. Perez-Villar, L.O. Chua, Autowaves for image processing on a two-dimensional CNN array of excitable nonlinear circuits: flat and wrinkled labyrinths. IEEE Trans. Circuits Syst. I 40(3), 174\u2013181 (1993)","journal-title":"IEEE Trans. Circuits Syst. I"},{"issue":"23","key":"9523_CR22","first-page":"11634","volume":"218","author":"M.J. Park","year":"2012","unstructured":"M.J. Park, O.M. Kwon, J.H. Park, S.M. Lee, E.J. Cha, Synchronization criteria of fuzzy complex dynamical networks with interval time-varying delays. Appl. Math. Comput. 218(23), 11634\u201311647 (2012)","journal-title":"Appl. Math. Comput."},{"issue":"23","key":"9523_CR23","doi-asserted-by":"crossref","first-page":"11634","DOI":"10.1016\/j.amc.2012.05.046","volume":"218","author":"M.J. Park","year":"2012","unstructured":"M.J. Park, O.M. Kwon, J.H. Park, S.M. Lee, E.J. Cha, Synchronization criteria of fuzzy complex dynamical networks with interval time-varying delays. Appl. Math. Comput. 218(23), 11634\u201311647 (2012)","journal-title":"Appl. Math. Comput."},{"key":"9523_CR24","doi-asserted-by":"crossref","unstructured":"Q. Song, F. Liu, J.D. Cao, W.W. Yu, Pinning-controllability analysis of complex networks: an M-matrix\u00a0approach. IEEE Trans. Circ. Syst.-I. Available online (2012)","DOI":"10.1109\/TCSI.2012.2190573"},{"issue":"6","key":"9523_CR25","doi-asserted-by":"crossref","first-page":"690","DOI":"10.1002\/rnc.1725","volume":"22","author":"Q. Song","year":"2012","unstructured":"Q. Song, J.D. Cao, F. Liu, Pinning-controlled synchronization of hybrid-coupled complex dynamical networks with mixed time-delays. Int. J. Robust Nonlinear Control 22(6), 690\u2013706 (2012)","journal-title":"Int. J. Robust Nonlinear Control"},{"issue":"2","key":"9523_CR26","doi-asserted-by":"crossref","first-page":"466","DOI":"10.1016\/j.automatica.2009.11.002","volume":"46","author":"J. Sun","year":"2012","unstructured":"J. Sun, G.P. Liu, J. Chen, D. Rees, Improved delay-range-dependent stability criteria for linear systems with time-varying delays. Automatica 46(2), 466\u2013470 (2012)","journal-title":"Automatica"},{"key":"9523_CR27","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1007\/978-3-642-49967-8_5","volume-title":"Information Processing in the Cortex: Experiments and Theory","author":"E. Vaadia","year":"1992","unstructured":"E. Vaadia, A. Acrtsen, Coding and computation in the cortex: singleneuron activity and cooperative phenomena, in Information Processing in the Cortex: Experiments and Theory (Springer, Berlin, 1992), pp. 81\u2013121"},{"key":"9523_CR28","doi-asserted-by":"crossref","first-page":"494","DOI":"10.1109\/81.404064","volume":"42","author":"C.W. Wu","year":"1995","unstructured":"C.W. Wu, L. Chua, Application of graph theory to the synchronization in an array of coupled nonlinear oscillators. IEEE Trans. Circuits Syst. I 42, 494\u2013497 (1995)","journal-title":"IEEE Trans. Circuits Syst. I"},{"issue":"14","key":"9523_CR29","doi-asserted-by":"crossref","first-page":"1559","DOI":"10.1016\/j.physleta.2011.02.052","volume":"375","author":"X.J. Wu","year":"2011","unstructured":"X.J. Wu, H.T. Lu, Cluster synchronization in the adaptive complex dynamical networks via a novel approach. Phys. Lett. A 375(14), 1559\u20131565 (2011)","journal-title":"Phys. Lett. A"},{"issue":"5","key":"9523_CR30","doi-asserted-by":"crossref","DOI":"10.1088\/1674-1056\/ad1c5b","volume":"21","author":"S.G. Wang","year":"2012","unstructured":"S.G. Wang, H.X. Yao, Pinning synchronization of the time-varying delay coupled complex networks with time-varying delayed dynamical nodes. Chin. Phys. B 21(5), 050508 (2012)","journal-title":"Chin. Phys. B"},{"issue":"15","key":"9523_CR31","first-page":"168","volume":"89","author":"X.J. Wu","year":"2012","unstructured":"X.J. Wu, H.T. Lu, Hybrid synchronization of the general delayed and non-delayed complex dynamical networks via pinning control. Neurocomputing 89(15), 168\u2013177 (2012)","journal-title":"Neurocomputing"},{"issue":"12","key":"9523_CR32","doi-asserted-by":"crossref","first-page":"4202","DOI":"10.1016\/j.cnsns.2010.02.001","volume":"15","author":"Z.Y. Wang","year":"2010","unstructured":"Z.Y. Wang, L.H. Huang, Y.N. Wang, Y. Zou, Synchronization analysis of networks with both delayed and non-delayed couplings via adaptive pinning control method. Commun. Nonlinear Sci. Numer. Simul. 15(12), 4202\u20134208 (2010)","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"9523_CR33","doi-asserted-by":"crossref","first-page":"2997","DOI":"10.1016\/j.cnsns.2011.10.036","volume":"17","author":"S.G. Wang","year":"2012","unstructured":"S.G. Wang, H.X. Yao, S. Zheng, Y. Xie, A novel criterion for cluster synchronization of complex dynamical networks with coupling time-varying delays. Commun. Nonlinear Sci. Numer. Simul. 17, 2997\u20133004 (2012)","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"9523_CR34","author":"S.G. Wang","year":"2012","unstructured":"S.G. Wang, H.X. Yao, M.P. Sun, Cluster synchronization of time-varying delays coupled complex networks with nonidentical dynamical nodes. J. Appl. Math. (2012). doi: 10.1155\/2012\/958405","journal-title":"J. Appl. Math."},{"key":"9523_CR35","doi-asserted-by":"crossref","first-page":"829","DOI":"10.1109\/TCSI.2008.2003373","volume":"56","author":"W. Wu","year":"2009","unstructured":"W. Wu, W. Zhou, T.P. Chen, Cluster synchronization of linearly coupled complex networks under pinning control. IEEE Trans. Circuits Syst. I 56, 829\u2013839 (2009)","journal-title":"IEEE Trans. Circuits Syst. I"},{"issue":"3","key":"9523_CR36","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1016\/j.neucom.2011.11.014","volume":"83","author":"T. Wang","year":"2012","unstructured":"T. Wang, T. Li, X. Yang, S.M. Fei, Cluster synchronization for delayed Lur\u2019e dynamical networks based on pinning control. Neurocomputing 83(3), 72\u201382 (2012)","journal-title":"Neurocomputing"},{"issue":"7","key":"9523_CR37","doi-asserted-by":"crossref","first-page":"1165","DOI":"10.1109\/TNN.2009.2016842","volume":"20","author":"Y.H. Xia","year":"2009","unstructured":"Y.H. Xia, Z.J. Yang, M.A. Han, Lag synchronization of chaotic delayed Yang\u2013Yang type fuzzy neural networks with noise perturbation based on adaptive control and parameter identification. IEEE Trans. Neural Netw. 20(7), 1165\u20131180 (2009)","journal-title":"IEEE Trans. Neural Netw."},{"issue":"3","key":"9523_CR38","doi-asserted-by":"crossref","first-page":"1650","DOI":"10.1016\/j.nonrwa.2009.03.020","volume":"11","author":"Y.Q. Yang","year":"2010","unstructured":"Y.Q. Yang, J.D. Cao, Exponential synchronization of the complex dynamical networks with a coupling delay and impulsive effects. Nonlinear Anal., Real World Appl. 11(3), 1650\u20131659 (2010)","journal-title":"Nonlinear Anal., Real World Appl."},{"key":"9523_CR39","first-page":"521","volume-title":"Proc. IEEE Int. Conf. Intel. Procees. Syst","author":"Y.F. Zhang","year":"1997","unstructured":"Y.F. Zhang, Z.Y. He, A secure communication scheme based on cellular neural network, in Proc. IEEE Int. Conf. Intel. Procees. Syst, vol. 1 (1997), pp. 521\u2013524"},{"issue":"6","key":"9523_CR40","doi-asserted-by":"crossref","first-page":"1573","DOI":"10.1007\/s00034-011-9311-z","volume":"30","author":"X.M. Zhang","year":"2011","unstructured":"X.M. Zhang, G.P. Lu, Y.F. Zhang, Synchronization for time-delay Lur\u2019e systems with sector and slope restricted nonlinearities under communication constraints. Circuits Syst. Signal Process. 30(6), 1573\u20131593 (2011)","journal-title":"Circuits Syst. Signal Process."},{"issue":"14","key":"9523_CR41","doi-asserted-by":"crossref","first-page":"7614","DOI":"10.1016\/j.amc.2012.01.028","volume":"218","author":"Z.Q. Zhang","year":"2012","unstructured":"Z.Q. Zhang, H.Y. Shaom, Z. Wang, Reduced-order observer design for the synchronization of the generalized Lorenz chaotic systems. Appl. Math. Comput. 218(14), 7614\u20137621 (2012)","journal-title":"Appl. Math. Comput."},{"issue":"3","key":"9523_CR42","doi-asserted-by":"crossref","first-page":"1267","DOI":"10.1016\/j.jfranklin.2012.01.011","volume":"349","author":"W.N. Zhou","year":"2012","unstructured":"W.N. Zhou, T.B. Wang, J.P. Mou, J.A. Fang, Mean square exponential synchronization in Lagrange sense for uncertain complex dynamical networks. J. Frank. Inst. 349(3), 1267\u20131282 (2012)","journal-title":"J. Frank. Inst."},{"issue":"12","key":"9523_CR43","doi-asserted-by":"crossref","first-page":"2882","DOI":"10.1109\/TCSI.2011.2161363","volume":"58","author":"J. Zhou","year":"2011","unstructured":"J. Zhou, Q.J. Wu, L. Xiang, Pinning complex delayed dynamical networks by a single impulsive controller. IEEE Trans. Circuits Syst. I 58(12), 2882\u20132893 (2011)","journal-title":"IEEE Trans. Circuits Syst. I"}],"container-title":["Circuits, Systems, and Signal Processing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00034-012-9523-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00034-012-9523-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00034-012-9523-x","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,2]],"date-time":"2024-05-02T01:46:13Z","timestamp":1714614373000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00034-012-9523-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,11,27]]},"references-count":43,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2013,8]]}},"alternative-id":["9523"],"URL":"https:\/\/doi.org\/10.1007\/s00034-012-9523-x","relation":{},"ISSN":["0278-081X","1531-5878"],"issn-type":[{"value":"0278-081X","type":"print"},{"value":"1531-5878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,11,27]]}}}