Improved Stability Estimates for Impulsive Delay Reaction-Diffusion Cohen-Grossberg Neural Networks Via Hardy-Poincaré Inequality

[1] ADIMURTHI: Hardy-Sobolev inequality in H1(Ω) and its applications, Commun. Contemp. Math. 4 (2002), 409-434.10.1142/S0219199702000713Search in Google Scholar

[2] AKÇA, H.-ALASSAR, R.-COVACHEV, V.-COVACHEVA, Z.-AL-ZAHRANI, E.: Continuous-time additive Hopfield-type neural networks with impulses, J. Math. Anal. Appl. 290 (2004), 436-451.10.1016/j.jmaa.2003.10.005Search in Google Scholar

[3] AKÇA, H.-COVACHEV, V.: Impulsive Cohen-Grossberg neural networks with S-typedistributed delays, Tatra Mt. Math. Publ. 48 (2011), 1-13.Search in Google Scholar

[4] AKÇA, H.-ALASSAR, R.-COVACHEV, V.-COVACHEVA, Z.: Impulsive Cohen--Grossberg neural networks with S-type distributed delays and reaction-diffusion terms, Int. J. Math. Comput. 10 (2011), 1-12.Search in Google Scholar

[5] BAO, S.: Global exponential robust stability of static reaction-diffusion neural networkswith S-type distributed delays, in: 6th Internat. Symp. on Neural Networks (H. Wang et al., eds.), Wuhan, PRC, 2009, Adv. Intell. Soft Comput., Vol. 56, Springer-Verlag, Berlin, 2009, pp. 69-79.10.1007/978-3-642-01216-7_8Search in Google Scholar

[6] BERMAN, A.-PLEMMONS, R. J.: Nonnegative Matrices in Mathematical Sciences. Academic Press, New York, 1979.10.1016/B978-0-12-092250-5.50009-6Search in Google Scholar

[7] BREZIS, H.- VÁSQUEZ, J. L.: Blow-up solutions of some nonlinear elliptic problems, Rev. Mat. Univ. Complut. Madrid 10 (1997), 443-469.Search in Google Scholar

[8] COHEN, M. A.-GROSSBERG, S.: Absolute stability of global pattern formation andparallel memory storage by competitive neural networks, IEEE Trans. Syst. Man Cybern. 13 (1983), 815-826.10.1109/TSMC.1983.6313075Search in Google Scholar

[9] FIEDLER, M.: Special Matrices and Their Applications in Numerical Mathematics. Martinus Nijhoff, Dordrecht, 1986.10.1007/978-94-009-4335-3Search in Google Scholar

[10] GUAN, Z.-H.-CHEN, G.: On delayed impulsive Hopfield neural networks, Neural Netw. 12 (1999), 273-280.10.1016/S0893-6080(98)00133-6Search in Google Scholar

[11] GUO, D. J.-SUN, J. X.-LIN, Z. I.: Functional Methods of Nonlinear Ordinary DifferentialEquations. Shandong Science Press, Jinan, 1995.Search in Google Scholar

[12] HORN, R. A.-JOHNSON, C. R.: Topics in Matrix Analysis. Cambridge University Press, Cambridge, 1991.10.1017/CBO9780511840371Search in Google Scholar

[13] KAO, Y.-BAO, S.: Exponential stability of reaction-diffusion Cohen-Grossberg neuralnetworks with S-type distributed delays, in: 6th Internat. Symp. on Neural Networks (H. Wang et al., eds.), Wuhan, PRC, 2009, Adv. Intell. Soft Comput., Vol. 56, Springer- -Verlag, Berlin, 2009, pp. 59-68.10.1007/978-3-642-01216-7_7Search in Google Scholar

[14] LI, Z.-LI, K.: Stability analysis of impulsive Cohen-Grossberg neural networks with distributeddelays and reaction-diffusion terms, Appl.Math. Modelling 33 (2009), 1337-1348.10.1016/j.apm.2008.01.016Search in Google Scholar

[15] LI, K.-SONG, Q.: Exponential stability of impulsive Cohen-Grossberg neural networkswith time-varying delays and reaction-diffusion terms, Neurocomputing 72 (2008), 231-240.10.1016/j.neucom.2008.01.009Search in Google Scholar

[16] LIAO, X. X.-YANG, S. Z.-CHEN, S. J.-FU, Y. L.: Stability of general neural networkswith reaction-diffusion, Sci. China Ser. F 44 (2001), 389-395.10.1007/BF02714741Search in Google Scholar

[17] MOHAMAD, S.-GOPALSAMY, K.-AKÇA, H.: Exponential stability of artificial neuralnetworks with distributed delays and large impulses, Nonlinear Anal. RealWorld Appl. 9 (2008), 872-888.10.1016/j.nonrwa.2007.01.011Search in Google Scholar

[18] PAN, J.-LIU, X.-ZHONG, S.: Stability criteria for impulsive reaction-diffusion Cohen--Grossberg neural networks with time-varying delays, Math. Comput. Modelling 51 (2010), 1037-1050.10.1016/j.mcm.2009.12.004Search in Google Scholar

[19] SONG, Q.-CAO, J.: Exponential stability for impulsive BAM neural networks with timevaryingdelays and reaction-diffusion terms, Adv. Differ. Equ. 2007 (2007), 18 pp.10.1155/2007/78160Search in Google Scholar

[20] SONG, Q.-CAO, J.: Stability analysis of Cohen-Grossberg neural network with bothtime-varying delays and continuously distributed delays, J. Comp. Appl. Math. 197 (2006), 188-203.10.1016/j.cam.2005.10.029Search in Google Scholar

[21] WANG, M.-WANG, L.: Global asymptotic robust stability of static neural network modelswith S-type distributed delays, Math. Comput. Modelling 44 (2006), 218-222.10.1016/j.mcm.2006.01.013Search in Google Scholar

[22] ZHANG, Y.: Asymptotic stability of impulsive reaction-diffusion cellular neural networkswith time-varying delays, J. Appl. Math. 2012 (2012), 17 pp.10.1155/2012/501891Search in Google Scholar

[23] ZHANG, Y.-LUO, Q.: Global exponential stability of impulsive delayed reaction--diffusion neural networks via Hardy-Poincaré inequality, Neurocomputing 83 (2012), 198-204.10.1016/j.neucom.2011.12.024Search in Google Scholar