메뉴 건너뛰기




Volumn 2013, Issue , 2013, Pages

Existence and global exponential stability of equilibrium for impulsive cellular neural network models with piecewise alternately advanced and retarded argument

Author keywords

[No Author keywords available]

Indexed keywords


EID: 84897772726     PISSN: 10853375     EISSN: 16870409     Source Type: Journal    
DOI: 10.1155/2013/196139     Document Type: Article
Times cited : (18)

References (42)
  • 1
    • 0024088955 scopus 로고
    • Cellular neural networks: Theory
    • 10.1109/31.7600 MR960777 ZBL0663.94022
    • Chua L. O., Yang L., Cellular neural networks: theory. IEEE Transactions on Circuits and Systems 1988 35 10 1257 1272 10.1109/31.7600 MR960777 ZBL0663.94022
    • (1988) IEEE Transactions on Circuits and Systems , vol.35 , Issue.10 , pp. 1257-1272
    • Chua, L.O.1    Yang, L.2
  • 2
    • 0003560321 scopus 로고
    • Singapore World Scientific Advanced Series on Complex Systems MR857608
    • Wolfram S., Theory and Applications of Cellular Automata 1986 1 Singapore World Scientific Advanced Series on Complex Systems MR857608
    • (1986) Theory and Applications of Cellular Automata , vol.1
    • Wolfram, S.1
  • 3
    • 0024092072 scopus 로고
    • Cellular neural networks: Applications
    • 10.1109/31.7601 MR960778
    • Chua L. O., Yang L., Cellular neural networks: applications. IEEE Transactions on Circuits and Systems 1988 35 10 1273 1290 10.1109/31.7601 MR960778
    • (1988) IEEE Transactions on Circuits and Systems , vol.35 , Issue.10 , pp. 1273-1290
    • Chua, L.O.1    Yang, L.2
  • 4
    • 0027569219 scopus 로고
    • On stability of cellular neural networks with delay
    • 10.1109/81.222796 MR1232558 ZBL0792.68115
    • Civalleri P. P., Gilli M., Pandolfi L., On stability of cellular neural networks with delay. IEEE Transactions on Circuits and Systems I 1993 40 3 157 165 10.1109/81.222796 MR1232558 ZBL0792.68115
    • (1993) IEEE Transactions on Circuits and Systems i , vol.40 , Issue.3 , pp. 157-165
    • Civalleri, P.P.1    Gilli, M.2    Pandolfi, L.3
  • 5
    • 0035303488 scopus 로고    scopus 로고
    • A set of stability criteria for delayed cellular neural networks
    • DOI 10.1109/81.917987, PII S1057712201029518
    • Cao J., A set of stability criteria for delayed cellular neural networks. IEEE Transactions on Circuits and Systems I 2001 48 4 494 498 10.1109/81.917987 MR1827297 ZBL0994.82066 (Pubitemid 32471061)
    • (2001) IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications , vol.48 , Issue.4 , pp. 494-498
    • Cao, J.1
  • 6
    • 0025632457 scopus 로고
    • Stability of a class of nonreciprocal cellular neural networks
    • 10.1109/31.101272
    • Chua L. O., Roska T., Stability of a class of nonreciprocal cellular neural networks. IEEE Transactions on Circuits and Systems I 1990 37 12 1520 1527 10.1109/31.101272
    • (1990) IEEE Transactions on Circuits and Systems i , vol.37 , Issue.12 , pp. 1520-1527
    • Chua, L.O.1    Roska, T.2
  • 8
    • 77955773623 scopus 로고    scopus 로고
    • Impulsive Hopfield-type neural network system with piecewise constant argument
    • 10.1016/j.nonrwa.2009.09.003 MR2661925 ZBL1202.92001
    • Akhmet M. U., Yilmaz E., Impulsive Hopfield-type neural network system with piecewise constant argument. Nonlinear Analysis: Real World Applications 2010 11 4 2584 2593 10.1016/j.nonrwa.2009.09.003 MR2661925 ZBL1202.92001
    • (2010) Nonlinear Analysis: Real World Applications , vol.11 , Issue.4 , pp. 2584-2593
    • Akhmet, M.U.1    Yilmaz, E.2
  • 9
    • 84862275340 scopus 로고    scopus 로고
    • Globally exponential stability of periodic solutions to impulsive neural networks with time-varying delays
    • 358362 10.1155/2012/358362 MR2922935 ZBL1242.93104
    • Shao Y. F., Xu C. J., Zhang Q. H., Globally exponential stability of periodic solutions to impulsive neural networks with time-varying delays. Abstract and Applied Analysis 2012 14 358362 10.1155/2012/358362 MR2922935 ZBL1242.93104
    • (2012) Abstract and Applied Analysis , pp. 14
    • Shao, Y.F.1    Xu, C.J.2    Zhang, Q.H.3
  • 10
    • 78649622043 scopus 로고    scopus 로고
    • A new criterion to global exponential stability for impulsive neural networks with continuously distributed delays
    • 10.1002/mma.1322 MR2762322 ZBL1213.34085
    • Sun G., Li X., A new criterion to global exponential stability for impulsive neural networks with continuously distributed delays. Mathematical Methods in the Applied Sciences 2010 33 17 2107 2117 10.1002/mma.1322 MR2762322 ZBL1213.34085
    • (2010) Mathematical Methods in the Applied Sciences , vol.33 , Issue.17 , pp. 2107-2117
    • Sun, G.1    Li, X.2
  • 11
    • 84855201545 scopus 로고    scopus 로고
    • New results on global exponential stability for impulsive cellular neural networks with any bounded time-varying delays
    • 10.1016/j.mcm.2011.09.009 MR2887425 ZBL1255.93103
    • Wu B., Liu Y., Lu J., New results on global exponential stability for impulsive cellular neural networks with any bounded time-varying delays. Mathematical and Computer Modelling 2012 55 3-4 837 843 10.1016/j.mcm.2011.09. 009 MR2887425 ZBL1255.93103
    • (2012) Mathematical and Computer Modelling , vol.55 , Issue.3-4 , pp. 837-843
    • Wu, B.1    Liu, Y.2    Lu, J.3
  • 12
    • 79959695635 scopus 로고    scopus 로고
    • Global exponential stability for a class of generalized delayed neural networks with impulses
    • 10.1002/mma.1451 MR2839383 ZBL1219.92002
    • Xi Q., Global exponential stability for a class of generalized delayed neural networks with impulses. Mathematical Methods in the Applied Sciences 2011 34 11 1414 1420 10.1002/mma.1451 MR2839383 ZBL1219.92002
    • (2011) Mathematical Methods in the Applied Sciences , vol.34 , Issue.11 , pp. 1414-1420
    • Xi, Q.1
  • 13
    • 60649118394 scopus 로고    scopus 로고
    • Global exponential stability of a class of retarded impulsive differential equations with applications
    • 10.1016/j.chaos.2007.04.005 MR2504578 ZBL1197.34146
    • Xia Y., Wong P. J. Y., Global exponential stability of a class of retarded impulsive differential equations with applications. Chaos, Solitons & Fractals 2009 39 1 440 453 10.1016/j.chaos.2007.04.005 MR2504578 ZBL1197.34146
    • (2009) Chaos, Solitons & Fractals , vol.39 , Issue.1 , pp. 440-453
    • Xia, Y.1    Wong, P.J.Y.2
  • 14
    • 84864476160 scopus 로고    scopus 로고
    • Dynamical analysis of impulsive neural networks with time-varying delays
    • 10.1002/mma.2542 MR2957517 ZBL1253.34068
    • Xiang L., Dynamical analysis of impulsive neural networks with time-varying delays. Mathematical Methods in the Applied Sciences 2012 35 13 1564 1569 10.1002/mma.2542 MR2957517 ZBL1253.34068
    • (2012) Mathematical Methods in the Applied Sciences , vol.35 , Issue.13 , pp. 1564-1569
    • Xiang, L.1
  • 15
    • 14844333215 scopus 로고    scopus 로고
    • Impulsive delay differential inequality and stability of neural networks
    • DOI 10.1016/j.jmaa.2004.10.040, PII S0022247X04008807
    • Xu D., Yang Z., Impulsive delay differential inequality and stability of neural networks. Journal of Mathematical Analysis and Applications 2005 305 1 107 120 10.1016/j.jmaa.2004.10.040 MR2128115 ZBL1091.34046 (Pubitemid 40350371)
    • (2005) Journal of Mathematical Analysis and Applications , vol.305 , Issue.1 , pp. 107-120
    • Xu, D.1    Yang, Z.2
  • 16
    • 33744506602 scopus 로고    scopus 로고
    • Impulsive effects on stability of Cohen-Grossberg neural networks with variable delays
    • DOI 10.1016/j.amc.2005.10.032, PII S0096300305008878
    • Yang Z., Xu D., Impulsive effects on stability of Cohen-Grossberg neural networks with variable delays. Applied Mathematics and Computation 2006 177 1 63 78 10.1016/j.amc.2005.10.032 MR2234497 ZBL1103.34067 (Pubitemid 43815511)
    • (2006) Applied Mathematics and Computation , vol.177 , Issue.1 , pp. 63-78
    • Yang, Z.1    Xu, D.2
  • 17
    • 84876674418 scopus 로고    scopus 로고
    • Analysis of stability for impulsive fuzzy Cohen-Grossberg BAM neural networks with delays
    • 10.1002/mma.2624 MR3056935 ZBL1271.34080
    • Zhang Q., Shao Y., Liu J., Analysis of stability for impulsive fuzzy Cohen-Grossberg BAM neural networks with delays. Mathematical Methods in the Applied Sciences 2013 36 7 773 779 10.1002/mma.2624 MR3056935 ZBL1271.34080
    • (2013) Mathematical Methods in the Applied Sciences , vol.36 , Issue.7 , pp. 773-779
    • Zhang, Q.1    Shao, Y.2    Liu, J.3
  • 18
    • 84863201405 scopus 로고    scopus 로고
    • Robust exponential stability of discrete-time uncertain impulsive neural networks with time-varying delay
    • 10.1002/mma.2531 MR2945852 ZBL1250.93099
    • Zhang Y., Robust exponential stability of discrete-time uncertain impulsive neural networks with time-varying delay. Mathematical Methods in the Applied Sciences 2012 35 11 1287 1299 10.1002/mma.2531 MR2945852 ZBL1250.93099
    • (2012) Mathematical Methods in the Applied Sciences , vol.35 , Issue.11 , pp. 1287-1299
    • Zhang, Y.1
  • 19
    • 0034271522 scopus 로고    scopus 로고
    • Stability of equilibria in a neural network model
    • 10.1002/1099-1476(20000910)23:13<1179: AID-MMA158>3.3.CO;2- Y MR1779387 ZBL0959.92002
    • Barone E., Tebaldi C., Stability of equilibria in a neural network model. Mathematical Methods in the Applied Sciences 2000 23 13 1179 1193 10.1002/1099-1476(20000910)23:13<1179::AID-MMA158>3.3.CO;2-Y MR1779387 ZBL0959.92002
    • (2000) Mathematical Methods in the Applied Sciences , vol.23 , Issue.13 , pp. 1179-1193
    • Barone, E.1    Tebaldi, C.2
  • 20
    • 0034309351 scopus 로고    scopus 로고
    • Global asymptotic stability of neural networks with transmission delays
    • DOI 10.1080/00207720050165807
    • Cao J., Global asymptotic stability of neural networks with transmission delays. International Journal of Systems Science 2000 31 10 1313 1316 10.1080/00207720050165807 (Pubitemid 35394827)
    • (2000) International Journal of Systems Science , vol.31 , Issue.10 , pp. 1313-1316
    • Cao, J.-D.1
  • 21
    • 33947139816 scopus 로고    scopus 로고
    • Global asymptotical stability of recurrent neural networks with multiple discrete delays and distributed delays
    • DOI 10.1109/TNN.2006.881488
    • Cao J., Yuan K., Li H. X., Global asymptotical stability of recurrent neural networks with multiple discrete delays and distributed delays. IEEE Transactions on Neural Networks 2006 17 6 1646 1651 10.1109/TNN.2006.881488 (Pubitemid 44824277)
    • (2006) IEEE Transactions on Neural Networks , vol.17 , Issue.6 , pp. 1646-1651
    • Cao, J.1    Yuan, K.2    Li, H.-X.3
  • 22
    • 84872836818 scopus 로고    scopus 로고
    • Stability and bifurcation analysis for a neural network model with discrete and distributed delays
    • 10.1002/mma.2568 MR3008322 ZBL06133216
    • Du Y., Xu R., Liu Q., Stability and bifurcation analysis for a neural network model with discrete and distributed delays. Mathematical Methods in the Applied Sciences 2013 36 1 49 59 10.1002/mma.2568 MR3008322 ZBL06133216
    • (2013) Mathematical Methods in the Applied Sciences , vol.36 , Issue.1 , pp. 49-59
    • Du, Y.1    Xu, R.2    Liu, Q.3
  • 23
    • 33644674010 scopus 로고    scopus 로고
    • Improved global exponential stability criteria of cellular neural networks with time-varying delays
    • DOI 10.1016/j.mcm.2005.11.007, PII S0895717705005662
    • Liu Q. S., Cao J., Improved global exponential stability criteria of cellular neural networks with time-varying delays. Mathematical and Computer Modelling 2006 43 3-4 423 432 10.1016/j.mcm.2005.11.007 MR2214652 ZBL1157.34055 (Pubitemid 43330870)
    • (2006) Mathematical and Computer Modelling , vol.43 , Issue.3-4 , pp. 423-432
    • Liu, Q.1    Cao, J.2
  • 24
    • 0035427259 scopus 로고    scopus 로고
    • Stability analysis of Hopfield neural networks with uncertainty
    • DOI 10.1016/S0895-7177(01)00067-X, PII S089571770100067X
    • Liu X. Z., Dickson R., Stability analysis of Hopfield neural networks with uncertainty. Mathematical and Computer Modelling 2001 34 3-4 353 363 10.1016/S0895-7177(01)00067-X MR1835832 ZBL0999.34052 (Pubitemid 32533317)
    • (2001) Mathematical and Computer Modelling , vol.34 , Issue.3-4 , pp. 353-363
    • Liu, X.1    Dickson, R.2
  • 25
    • 67349211767 scopus 로고    scopus 로고
    • Global asymptotic stability for neural network models with distributed delays
    • 10.1016/j.mcm.2009.02.002 MR2542590 ZBL1185.34107
    • Oliveira J. J., Global asymptotic stability for neural network models with distributed delays. Mathematical and Computer Modelling 2009 50 1-2 81 91 10.1016/j.mcm.2009.02.002 MR2542590 ZBL1185.34107
    • (2009) Mathematical and Computer Modelling , vol.50 , Issue.1-2 , pp. 81-91
    • Oliveira, J.J.1
  • 26
    • 46749117785 scopus 로고    scopus 로고
    • Delay-dependent robust stability of neutral-type neural networks with time delays
    • Qiu J., Cao J., Delay-dependent robust stability of neutral-type neural networks with time delays. Journal of Mathematical Control Science and Applications 2007 1 179 188
    • (2007) Journal of Mathematical Control Science and Applications , vol.1 , pp. 179-188
    • Qiu, J.1    Cao, J.2
  • 27
    • 67349202777 scopus 로고    scopus 로고
    • On asymptotic stability of discrete-time non-autonomous delayed Hopfield neural networks
    • 10.1016/j.camwa.2008.10.031 MR2523361 ZBL1186.39028
    • Wei X., Zhou D., Zhang Q., On asymptotic stability of discrete-time non-autonomous delayed Hopfield neural networks. Computers & Mathematics with Applications 2009 57 11-12 1938 1942 10.1016/j.camwa.2008.10.031 MR2523361 ZBL1186.39028
    • (2009) Computers & Mathematics with Applications , vol.57 , Issue.11-12 , pp. 1938-1942
    • Wei, X.1    Zhou, D.2    Zhang, Q.3
  • 28
    • 84872778115 scopus 로고
    • Advanced differential equations with piecewise constant argument deviations
    • 10.1155/S0161171283000599 MR729389 ZBL0534.34067
    • Shah S. M., Wiener J., Advanced differential equations with piecewise constant argument deviations. International Journal of Mathematics and Mathematical Sciences 1983 6 4 671 703 10.1155/S0161171283000599 MR729389 ZBL0534.34067
    • (1983) International Journal of Mathematics and Mathematical Sciences , vol.6 , Issue.4 , pp. 671-703
    • Shah, S.M.1    Wiener, J.2
  • 29
    • 0008402812 scopus 로고
    • Retarded differential equations with piecewise constant delays
    • 10.1016/0022-247X(84)90248-8 MR732717 ZBL0557.34059
    • Cooke K. L., Wiener J., Retarded differential equations with piecewise constant delays. Journal of Mathematical Analysis and Applications 1984 99 1 265 297 10.1016/0022-247X(84)90248-8 MR732717 ZBL0557.34059
    • (1984) Journal of Mathematical Analysis and Applications , vol.99 , Issue.1 , pp. 265-297
    • Cooke, K.L.1    Wiener, J.2
  • 31
    • 84880109069 scopus 로고    scopus 로고
    • Oscillatory and periodic solutions in alternately advanced and delayed differential equations
    • Chiu K.-S., Pinto M., Oscillatory and periodic solutions in alternately advanced and delayed differential equations. Carpathian Journal of Mathematics 2013 29 2 149 158
    • (2013) Carpathian Journal of Mathematics , vol.29 , Issue.2 , pp. 149-158
    • Chiu, K.-S.1    Pinto, M.2
  • 32
    • 85084771702 scopus 로고    scopus 로고
    • Stability of oscillatory solutions of differential equations with a general piecewise constant argument
    • MR2854027
    • Chiu K.-S., Stability of oscillatory solutions of differential equations with a general piecewise constant argument. Electronic Journal of Qualitative Theory of Differential Equations 2011 88 1 15 MR2854027
    • (2011) Electronic Journal of Qualitative Theory of Differential Equations , vol.88 , pp. 1-15
    • Chiu, K.-S.1
  • 33
    • 80052440805 scopus 로고    scopus 로고
    • Variation of parameters formula and Gronwall inequality for differential equations with a general piecewise constant argument
    • 10.1007/s10255-011-0107-5 MR2835931 ZBL1270.34169
    • Chiu K.-S., Pinto M., Variation of parameters formula and Gronwall inequality for differential equations with a general piecewise constant argument. Acta Mathematicae Applicatae Sinica (English Series) 2011 27 4 561 568 10.1007/s10255-011-0107-5 MR2835931 ZBL1270.34169
    • (2011) Acta Mathematicae Applicatae Sinica (English Series) , vol.27 , Issue.4 , pp. 561-568
    • Chiu, K.-S.1    Pinto, M.2
  • 34
    • 77956946076 scopus 로고    scopus 로고
    • Periodic solutions of differential equations with a general piecewise constant argument and applications
    • MR2678388 ZBL1211.34082
    • Chiu K.-S., Pinto M., Periodic solutions of differential equations with a general piecewise constant argument and applications. Electronic Journal of Qualitative Theory of Differential Equations 2010 46 1 19 MR2678388 ZBL1211.34082
    • (2010) Electronic Journal of Qualitative Theory of Differential Equations , vol.46 , pp. 1-19
    • Chiu, K.-S.1    Pinto, M.2
  • 37
    • 63449115192 scopus 로고    scopus 로고
    • Asymptotic equivalence of nonlinear and quasi linear differential equations with piecewise constant arguments
    • 10.1016/j.mcm.2008.10.001 MR2532088 ZBL1171.34321
    • Pinto M., Asymptotic equivalence of nonlinear and quasi linear differential equations with piecewise constant arguments. Mathematical and Computer Modelling 2009 49 9-10 1750 1758 10.1016/j.mcm.2008.10.001 MR2532088 ZBL1171.34321
    • (2009) Mathematical and Computer Modelling , vol.49 , Issue.9-10 , pp. 1750-1758
    • Pinto, M.1
  • 38
    • 0000153927 scopus 로고
    • Models of vertically transmitted diseases with sequential-continuous dynamics
    • New York, NY, USA Academic Press
    • Busenberg S., Cooke K., Lakshmikantham V., Models of vertically transmitted diseases with sequential-continuous dynamics. Nonlinear Phenomena in Mathematical Sciences 1982 New York, NY, USA Academic Press 179 187
    • (1982) Nonlinear Phenomena in Mathematical Sciences , pp. 179-187
    • Busenberg, S.1    Cooke, K.2    Lakshmikantham, V.3
  • 39
    • 77952920140 scopus 로고    scopus 로고
    • Advanced impulsive differential equations with piecewise constant arguments
    • 10.3846/1392-6292.2010.15.175-187 MR2604207 ZBL1218.34095
    • Bereketoglu H., Seyhan G., Ogun A., Advanced impulsive differential equations with piecewise constant arguments. Mathematical Modelling and Analysis 2010 15 2 175 187 10.3846/1392-6292.2010.15.175-187 MR2604207 ZBL1218.34095
    • (2010) Mathematical Modelling and Analysis , vol.15 , Issue.2 , pp. 175-187
    • Bereketoglu, H.1    Seyhan, G.2    Ogun, A.3
  • 40
    • 77952097381 scopus 로고    scopus 로고
    • Oscillatory and periodic solutions of impulsive differential equations with piecewise constant argument
    • 10.1007/s10440-009-9458-9 MR2601669 ZBL1196.34104
    • Karakoc F., Bereketoglu H., Seyhan G., Oscillatory and periodic solutions of impulsive differential equations with piecewise constant argument. Acta Applicandae Mathematicae 2010 110 1 499 510 10.1007/s10440-009-9458-9 MR2601669 ZBL1196.34104
    • (2010) Acta Applicandae Mathematicae , vol.110 , Issue.1 , pp. 499-510
    • Karakoc, F.1    Bereketoglu, H.2    Seyhan, G.3
  • 41
    • 30944452132 scopus 로고    scopus 로고
    • The existence and global attractivity of almost periodic sequence solution of discrete-time neural networks
    • DOI 10.1016/j.physleta.2005.10.022, PII S0375960105015811
    • Huang Z. K., Wang X. H., Gao F., The existence and global attractivity of almost periodic sequence solution of discrete-time neural networks. Physics Letters A 2006 350 3-4 182 191 10.1016/j.physleta.2005.10.022 (Pubitemid 43112255)
    • (2006) Physics Letters, Section A: General, Atomic and Solid State Physics , vol.350 , Issue.3-4 , pp. 182-191
    • Huang, Z.1    Wang, X.2    Gao, F.3
  • 42
    • 84968468793 scopus 로고
    • An equation alternately of retarded and advanced type
    • 10.2307/2046483 MR877047 ZBL0628.34074
    • Cooke K. L., Wiener J., An equation alternately of retarded and advanced type. Proceedings of the American Mathematical Society 1987 99 4 726 732 10.2307/2046483 MR877047 ZBL0628.34074
    • (1987) Proceedings of the American Mathematical Society , vol.99 , Issue.4 , pp. 726-732
    • Cooke, K.L.1    Wiener, J.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.