Zhang, Qianhong; Xiang, Riguang Global asymptotic stability of fuzzy cellular neural networks with time-varying delays. (English) Zbl 1220.34098 Phys. Lett., A 372, No. 22, 3971-3977 (2008). Summary: In this Letter fuzzy cellular neural networks with time-varying delays are studied. Sufficient conditions for the existence, uniqueness and global asymptotic stability of equilibrium point are established by using the theory of topological degree and applying the properties of nonsingular M-matrix. The activation functions are not required to be differentiable, bounded or monotone nondecreasing. The results of this Letter are new and they complement previously known results. Cited in 29 Documents MSC: 34K20 Stability theory of functional-differential equations 34K13 Periodic solutions to functional-differential equations 92B20 Neural networks for/in biological studies, artificial life and related topics 37B25 Stability of topological dynamical systems Keywords:fuzzy cellular neural networks; global asymptotic stability; topological degree theory; Lyapunov functional; equilibrium point PDFBibTeX XMLCite \textit{Q. Zhang} and \textit{R. Xiang}, Phys. Lett., A 372, No. 22, 3971--3977 (2008; Zbl 1220.34098) Full Text: DOI References: [1] Chua, L. O.; Yang, L., IEEE Trans. Circuits Syst. I, 35, 1257 (1988) [2] Chua, L. O.; Yang, L., IEEE Trans. Circuits Syst. I, 35, 1273 (1988) [3] Cao, J., Phys. Rev. E, 59, 5940 (1999) [4] Cao, J.; Zhou, D., Neural Networks, 11, 1601 (1998) [5] Li, X.; Huang, L.; Zhu, H., Nonlinear Anal., 53, 319 (2003) [6] Huang, H.; Cao, J.; Wang, J., Phys. Lett. A, 298, 393 (2002) [7] Zhao, H.; Cao, J., Neural Networks, 18, 1332 (2005) · Zbl 1083.68108 [8] Zhang, J., Comput. Math. Appl., 45, 1707 (2003) [9] Zhang, J., Comput. Math. Appl., 47, 183 (2004) [10] Jiang, H.; Teng, Z., Neural Networks, 17, 1415 (2004) · Zbl 1068.68121 [11] Huang, T.; Cao, J.; Li, C., Phys. Lett. A, 352, 94 (2006) [12] Arik, S.; Tavanoglu, V., IEEE Trans. Circuits Syst. I, 45, 168 (1998) [13] Arik, S.; Tavanoglu, V., IEEE Trans. Circuits Syst. I, 47, 571 (2000) [14] Cao, J.; Wang, J., IEEE Trans. Circuits Syst. I, 50, 34 (2003) [15] Yang, T.; Yang, L., IEEE Trans. Circuits Syst. I, 43, 880 (1996) [16] T. Yang, L.B. Yang, C.W. Wu, L.O. Chua, Fuzzy cellular neural networks: Theory, in: Proceedings of IEEE International Workshop on Cellular Neural Networks and Applications, 1996, pp. 181-186; T. Yang, L.B. Yang, C.W. Wu, L.O. Chua, Fuzzy cellular neural networks: Theory, in: Proceedings of IEEE International Workshop on Cellular Neural Networks and Applications, 1996, pp. 181-186 [17] Huang, T., Phys. Lett. A, 351, 48 (2006) [18] Liu, Y.; Tang, W., Phys. Lett. A, 323, 224 (2004) [19] Yuan, K.; Cao, J.; Deng, J., Neurocomputing, 69, 1619 (2006) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.