{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,17]],"date-time":"2025-10-17T13:51:21Z","timestamp":1760709081966},"reference-count":42,"publisher":"Springer Science and Business Media LLC","issue":"S1","license":[{"start":{"date-parts":[[2016,6,8]],"date-time":"2016-06-08T00:00:00Z","timestamp":1465344000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Neural Comput & Applic"],"published-print":{"date-parts":[[2017,12]]},"DOI":"10.1007\/s00521-016-2370-0","type":"journal-article","created":{"date-parts":[[2016,6,7]],"date-time":"2016-06-07T23:28:50Z","timestamp":1465342130000},"page":"765-773","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Delay-dependent exponential stability of recurrent neural networks with Markovian jumping parameters and proportional delays"],"prefix":"10.1007","volume":"28","author":[{"given":"Liqun","family":"Zhou","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2016,6,8]]},"reference":[{"issue":"3","key":"2370_CR1","doi-asserted-by":"crossref","first-page":"545","DOI":"10.1016\/j.nonrwa.2004.11.004","volume":"6","author":"S Guo","year":"2005","unstructured":"Guo S, Huang L (2005) Periodic oscillation for a class of neural networks with variable coefficients. Nonlinear Anal RWA 6(3):545\u2013561","journal-title":"Nonlinear Anal RWA"},{"issue":"9","key":"2370_CR2","first-page":"279","volume":"51","author":"Z Wang","year":"2005","unstructured":"Wang Z, Ho DWC, Liu X (2005) State estimation for delayed neural networks. IEEE Trans Signal Process 51(9):279\u2013284","journal-title":"IEEE Trans Signal Process"},{"issue":"5","key":"2370_CR3","doi-asserted-by":"crossref","first-page":"667","DOI":"10.1016\/j.neunet.2005.03.015","volume":"19","author":"Y Liu","year":"2006","unstructured":"Liu Y, Wang Z, Liu X (2006) Global exponential stability of generalized recurrent neural networks with discrete and distributed delays. Neural Netw 19(5):667\u2013675","journal-title":"Neural Netw"},{"issue":"1\u20132","key":"2370_CR4","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1016\/j.physleta.2007.03.088","volume":"368","author":"Q Song","year":"2007","unstructured":"Song Q, Wang Z (2007) A delay-dependent LMI approach to dynamics analysis of discrete-time recurrent neural networks with time-varying delays. Phys Lett A 368(1\u20132):134\u2013145","journal-title":"Phys Lett A"},{"issue":"13\u201315","key":"2370_CR5","doi-asserted-by":"crossref","first-page":"2823","DOI":"10.1016\/j.neucom.2007.08.024","volume":"71","author":"Q Song","year":"2008","unstructured":"Song Q (2008) Exponential stability of recurrent neural networks with both time-varying delays and general activation functions via LMI approach. Neurocomputing 71(13\u201315):2823\u20132830","journal-title":"Neurocomputing"},{"issue":"3","key":"2370_CR6","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1007\/s00521-007-0121-y","volume":"17","author":"Y Kao","year":"2008","unstructured":"Kao Y, Gao C (2008) Global exponential stability analysis for cellular neural networks with variable coefficients and delays. Neural Comput Appl 17(3):291\u2013296","journal-title":"Neural Comput Appl"},{"issue":"6","key":"2370_CR7","doi-asserted-by":"crossref","first-page":"1248","DOI":"10.1109\/TCSI.2008.2006210","volume":"56","author":"W Chen","year":"2009","unstructured":"Chen W, Zheng W (2009) Global exponential stability of impulsive neural networks with variable delay: an LMI approach. IEEE Trans Circuits Syst I 56(6):1248\u20131259","journal-title":"IEEE Trans Circuits Syst I"},{"issue":"2","key":"2370_CR8","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1007\/s11063-010-9130-4","volume":"31","author":"M Tan","year":"2010","unstructured":"Tan M (2010) Global asympotic stability of fuzzy cellular neural networks with unbounded distributed delays. Neural Process Lett 31(2):147\u2013157","journal-title":"Neural Process Lett"},{"issue":"8","key":"2370_CR9","doi-asserted-by":"crossref","first-page":"1365","DOI":"10.1109\/TNN.2010.2051455","volume":"21","author":"T Li","year":"2010","unstructured":"Li T, Song A, Fei S, Wang T (2010) Delay-derivative-dependent stability for delayed neural networks with unbound distributed delay. IEEE Trans Neural Netw 21(8):1365\u20131371","journal-title":"IEEE Trans Neural Netw"},{"issue":"1","key":"2370_CR10","doi-asserted-by":"crossref","first-page":"677","DOI":"10.1007\/s11071-012-0487-y","volume":"70","author":"P Balasubramaniam","year":"2012","unstructured":"Balasubramaniam P (2012) Synchronization of recurrent neural networks with mixed time-delays via output coupling with delayed feedback. Nonlinear Dyn 70(1):677\u2013691","journal-title":"Nonlinear Dyn"},{"issue":"13","key":"2370_CR11","doi-asserted-by":"crossref","first-page":"1823","DOI":"10.1016\/j.fss.2009.12.016","volume":"161","author":"R Rakkiyappan","year":"2010","unstructured":"Rakkiyappan R, Balasubramaniam P (2010) On exponential stability results for fuzzy impulsive neural networks. Fuzzy Set Syst 161(13):1823\u20131835","journal-title":"Fuzzy Set Syst"},{"key":"2370_CR12","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1016\/j.amc.2009.02.002","volume":"212","author":"R Samidurai","year":"2009","unstructured":"Samidurai R, Sakthivel R, Anthoni SM (2009) Global asymptotic stability of BAM neural networks with mixed delays and impulses. Appl Math Comput 212:113\u2013119","journal-title":"Appl Math Comput"},{"issue":"1","key":"2370_CR13","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/j.nahs.2009.08.004","volume":"4","author":"R Samidurai","year":"2010","unstructured":"Samidurai R (2010) Global exponential stability of neutral-type impulsive neural networks with discrete and distributed delays. Nonlinear Anal Hyb Syst 4(1):103\u2013112","journal-title":"Nonlinear Anal Hyb Syst"},{"issue":"3","key":"2370_CR14","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1093\/imamat\/8.3.271","volume":"8","author":"L Fox","year":"1971","unstructured":"Fox L, Mayers DF (1971) On a functional differential equational. J Inst Math Appl 8(3):271\u2013307","journal-title":"J Inst Math Appl"},{"key":"2370_CR15","first-page":"319","volume":"46","author":"GA Derfel","year":"1990","unstructured":"Derfel GA (1990) Kato problem for functional equational and difference schr $$\\ddot{o}$$ o \u00a8 dinger operators. Oper Theory Adv Appl 46:319\u2013321","journal-title":"Oper Theory Adv Appl"},{"issue":"1\u20133","key":"2370_CR16","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1016\/0898-1221(94)00102-2","volume":"8","author":"A Iserles","year":"1994","unstructured":"Iserles A (1994) The asymptotic behavior of certain difference equation with proportional delays. Comput Math Appl 8(1\u20133):141\u2013152","journal-title":"Comput Math Appl"},{"issue":"1","key":"2370_CR17","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1017\/S0956792500002163","volume":"7","author":"YK Liu","year":"1994","unstructured":"Liu YK (1994) Asymptotic behavior of functional differential equations with proportional time delays. Eur J Appl Math 7(1):11\u201330","journal-title":"Eur J Appl Math"},{"issue":"18","key":"2370_CR18","doi-asserted-by":"crossref","first-page":"3679","DOI":"10.1016\/j.comcom.2006.06.009","volume":"29","author":"J Wei","year":"2006","unstructured":"Wei J, Xu C, Zhou X, Li Q (2006) A robust packet scheduling algorithm for proportional delay differentiation services. Comput Commun 29(18):3679\u20133690","journal-title":"Comput Commun"},{"issue":"3","key":"2370_CR19","doi-asserted-by":"crossref","first-page":"1895","DOI":"10.1007\/s11071-013-0912-x","volume":"73","author":"L Zhou","year":"2013","unstructured":"Zhou L (2013) Dissipativity of a class of cellular neural networks with proportional delays. Nonlinear Dyn 73(3):1895\u20131903","journal-title":"Nonlinear Dyn"},{"issue":"3","key":"2370_CR20","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1007\/s11063-012-9269-2","volume":"38","author":"L Zhou","year":"2013","unstructured":"Zhou L (2013) Delay-dependent exponential stability of cellular neural networks with multi-proportional delays. Neural Process Lett 38(3):321\u2013346","journal-title":"Neural Process Lett"},{"issue":"1","key":"2370_CR21","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1016\/j.amc.2013.12.061","volume":"229","author":"L Zhou","year":"2014","unstructured":"Zhou L, Chen X, Yang Y (2014) Asymptotic stability of cellular neural networks with multi-proportional delays. Appl Math Comput 229(1):457\u2013466","journal-title":"Appl Math Comput"},{"issue":"1","key":"2370_CR22","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1007\/s11071-014-1271-y","volume":"77","author":"L Zhou","year":"2014","unstructured":"Zhou L (2014) Global asymptotic stability of cellular neural networks with proportional delays. Nonlinear Dyn 77(1):41\u201347","journal-title":"Nonlinear Dyn"},{"issue":"4","key":"2370_CR23","doi-asserted-by":"crossref","first-page":"619","DOI":"10.1007\/s11063-014-9377-2","volume":"42","author":"L Zhou","year":"2015","unstructured":"Zhou L (2015) Delay-dependent exponential synchronization of recurrent neural networks with multiple proportional delays. Neural Process Lett 42(4):619\u2013632","journal-title":"Neural Process Lett"},{"key":"2370_CR24","doi-asserted-by":"crossref","first-page":"1149","DOI":"10.1016\/j.neucom.2014.09.016","volume":"149","author":"C Zheng","year":"2015","unstructured":"Zheng C, Li N, Cao J (2015) Matrix measure based stability criteria for high-order networks with proportional delay. Neurcomputing 149:1149\u20131154","journal-title":"Neurcomputing"},{"key":"2370_CR25","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1016\/j.amc.2014.11.044","volume":"14","author":"LV Hiena","year":"2015","unstructured":"Hiena LV, Son DT (2015) Finite-time stability of a class of non-autonomous neural networks with heterogeneous proportional delays. Appl Math Comput 14:14\u201323","journal-title":"Appl Math Comput"},{"issue":"15","key":"2370_CR26","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/j.neucom.2015.02.061","volume":"161","author":"L Zhou","year":"2015","unstructured":"Zhou L (2015) Novel global exponential stability criteria for hybrid BAM neural networks with proportional delays. Neurocomputing 161(15):99\u2013106","journal-title":"Neurocomputing"},{"issue":"6","key":"2370_CR27","doi-asserted-by":"crossref","first-page":"1550071","DOI":"10.1142\/S1793524515500710","volume":"8","author":"L Zhou","year":"2015","unstructured":"Zhou L, Zhang Y (2015) Global exponential stability of cellular neural networks with multi-proportional delays. Int J Biomath 8(6):1550071","journal-title":"Int J Biomath"},{"issue":"1","key":"2370_CR28","first-page":"89","volume":"60","author":"L Zhou","year":"2015","unstructured":"Zhou L, Zhang Y (2016) Global exponential periodicity and stability of recurrent neural networks with multi-proportional delays. ISA Trans 60(1):89\u201395","journal-title":"ISA Trans"},{"issue":"2","key":"2370_CR29","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1016\/j.jfranklin.2015.10.021","volume":"353","author":"L Zhou","year":"2016","unstructured":"Zhou L, Zhang Y (2016) Global exponential stability of a class of impulsive recurrent neural networks with proportional delays via fixed point theory. J Frankl Inst 353(2):561\u2013575","journal-title":"J Frankl Inst"},{"issue":"4\u20135","key":"2370_CR30","doi-asserted-by":"crossref","first-page":"346","DOI":"10.1016\/j.physleta.2006.03.078","volume":"356","author":"Z Wang","year":"2006","unstructured":"Wang Z, Liu Y, Yu L, Liu X (2006) Exponential stability of delayed recurrent neural networks with Markovian jumping parameters. Phys Lett A 356(4\u20135):346\u2013352","journal-title":"Phys Lett A"},{"issue":"18","key":"2370_CR31","doi-asserted-by":"crossref","first-page":"3201","DOI":"10.1016\/j.physleta.2007.07.090","volume":"372","author":"L Wang","year":"2008","unstructured":"Wang L, Zhang Z, Wang Y (2008) Stochastic exponential stability of the delayed reaction-diffusion recurrent neural networks with Markovian jumping parameters. Phys Lett A 372(18):3201\u20133209","journal-title":"Phys Lett A"},{"issue":"7","key":"2370_CR32","doi-asserted-by":"crossref","first-page":"1102","DOI":"10.1109\/TNN.2009.2016210","volume":"20","author":"Y Liu","year":"2009","unstructured":"Liu Y, Wang Z (2009) Stability and synchronization of discrete-time Markovian jumping neural networks with mixed mode-dependent time delays. IEEE Trans Neural Netw 20(7):1102\u20131116","journal-title":"IEEE Trans Neural Netw"},{"issue":"8","key":"2370_CR33","doi-asserted-by":"crossref","first-page":"1489","DOI":"10.1016\/j.jfranklin.2010.07.002","volume":"347","author":"Q Zhu","year":"2010","unstructured":"Zhu Q, Yang X, Wang H (2010) Stochastically asymptotic stability of delayed recurrent neural networks with both Markovian jump parameters and nonlinear disturbances. J Frankl Inst 347(8):1489\u20131510","journal-title":"J Frankl Inst"},{"issue":"1\u20132","key":"2370_CR34","first-page":"181","volume":"19","author":"C Vidhya","year":"2011","unstructured":"Vidhya C, Balasubramaniam P (2011) Robust stability of uncertain Markovian jumping stochastic Cohen\u2013Grossberg type BAM neural networks with time-varying delays and reaction diffusion terms. Neural Parallel Sci Comput 19(1\u20132):181\u2013196","journal-title":"Neural Parallel Sci Comput"},{"issue":"5","key":"2370_CR35","first-page":"892","volume":"88","author":"P Balasubramaniam","year":"2011","unstructured":"Balasubramaniam P, Syed M (2011) Stochastic stability of uncertain fuzzy recurrent neural networks with Markovian jumping parameters. J Comput Math 88(5):892\u2013904","journal-title":"J Comput Math"},{"issue":"3","key":"2370_CR36","doi-asserted-by":"crossref","first-page":"1353","DOI":"10.1016\/j.nonrwa.2011.10.013","volume":"13","author":"Y Wang","year":"2012","unstructured":"Wang Y, Lin P, Wang L (2012) Exponential stability of reaction-diffusion high-order Markovian jump hopfield neural works with time-varying delays. Nonlinear Anal RWA 13(3):1353\u20131361","journal-title":"Nonlinear Anal RWA"},{"key":"2370_CR37","doi-asserted-by":"crossref","first-page":"757","DOI":"10.1016\/j.jmaa.2011.07.002","volume":"385","author":"G Hu","year":"2012","unstructured":"Hu G, Wang K (2012) Stability in distribution of neural stochastic functional differential equations with Markovian switching. J Math Anal Appl 385:757\u2013769","journal-title":"J Math Anal Appl"},{"issue":"1","key":"2370_CR38","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1007\/s00521-011-0685-4","volume":"21","author":"W Han","year":"2012","unstructured":"Han W, Liu Y, Wang LS (2012) Global exponential stability of delayed fuzzy cellular neural networks with Markovian jumping parameters. Neural Comput Appl 21(1):67\u201372","journal-title":"Neural Comput Appl"},{"issue":"9","key":"2370_CR39","doi-asserted-by":"crossref","first-page":"3612","DOI":"10.1016\/j.cnsns.2012.01.003","volume":"17","author":"P Balasubramaniam","year":"2012","unstructured":"Balasubramaniam P, Krishnasamy R, Rakkiyappan R (2012) Delay-dependent stability criterion for a class of non-linear singular Markovian jump systems with mode-dependent interval time-varying delays. Commun Nonlinear Sci 17(9):3612\u20133627","journal-title":"Commun Nonlinear Sci"},{"key":"2370_CR40","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1016\/j.neunet.2013.04.014","volume":"46","author":"H Huang","year":"2013","unstructured":"Huang H, Huang T, Chen X (2013) A mode-dependent approach to state estimation of recurrent neural networks with Markovian jumping parameters and mixed delays. Neural Netw 46:50\u201361","journal-title":"Neural Netw"},{"key":"2370_CR41","doi-asserted-by":"publisher","DOI":"10.1186\/1687-1847","author":"R Rao","year":"2013","unstructured":"Rao R, Zhong S, Wang X (2013) Delay-dependent exponential stability for Markovian jumping stochastic Cohen-Grossberg neural networks with $$p$$ p -Laplace diffusion and partially known transition rates via a differential inequality. Adv Differ Equ. doi: 10.1186\/1687-1847","journal-title":"Adv Differ Equ"},{"key":"2370_CR42","doi-asserted-by":"crossref","first-page":"3217","DOI":"10.1016\/j.jfranklin.2013.08.003","volume":"350","author":"R Raja","year":"2013","unstructured":"Raja R, Karthik Raja U, Samidurai R, Leelamani A (2013) Dissipativity of discrete-time BAM stochastic neural networks with Markovian switching and impulses. J Frankl Inst 350:3217\u20133247","journal-title":"J Frankl Inst"}],"container-title":["Neural Computing and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00521-016-2370-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-016-2370-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-016-2370-0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-016-2370-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,17]],"date-time":"2024-06-17T12:03:23Z","timestamp":1718625803000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00521-016-2370-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,6,8]]},"references-count":42,"journal-issue":{"issue":"S1","published-print":{"date-parts":[[2017,12]]}},"alternative-id":["2370"],"URL":"https:\/\/doi.org\/10.1007\/s00521-016-2370-0","relation":{},"ISSN":["0941-0643","1433-3058"],"issn-type":[{"value":"0941-0643","type":"print"},{"value":"1433-3058","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,6,8]]}}}