Li, Yongkun; Li, Youqin Exponential stability of BAM fuzzy cellular neural networks with time-varying delays in leakage terms and impulses. (English) Zbl 1474.34499 Abstr. Appl. Anal. 2014, Article ID 634394, 12 p. (2014). Summary: BAM fuzzy cellular neural networks with time-varying delays in leakage terms and impulses are considered. Some sufficient conditions for the exponential stability of the networks are established by using differential inequality techniques. The results of this paper are completely new and complementary to the previously known results. Finally, an example is given to demonstrate the effectiveness and conservativeness of our theoretical results. Cited in 2 Documents MSC: 34K20 Stability theory of functional-differential equations 34K36 Fuzzy functional-differential equations 92B20 Neural networks for/in biological studies, artificial life and related topics × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Kosko, B., Bidirectional associative memories, IEEE Transactions on Systems, Man, and Cybernetics, 18, 1, 49-60 (1988) · doi:10.1109/21.87054 [2] Kosko, B., Adaptive bi-directional associative memories, Applied Optics, 26, 4947-4960 (1987) [3] Kosko, B., A dynamical system approach machine intelligence, Neural Networks and Fuzzy Systems, 38-108 (1992) · Zbl 0755.94024 [4] Liao, X.; Wong, K.-W.; Yang, S., Convergence dynamics of hybrid bidirectional associative memory neural networks with distributed delays, Physics Letters A, 316, 1-2, 55-64 (2003) · Zbl 1038.92001 · doi:10.1016/S0375-9601(03)01113-7 [5] Liao, X. F.; Yu, J. B., Qualitative analysis of bi-directional associative memory with time delay, International Journal of Circuit Theory and Applications, 26, 219-229 (1988) · Zbl 0915.94012 [6] Chen, A.; Huang, L.; Liu, Z.; Cao, J., Periodic bidirectional associative memory neural networks with distributed delays, Journal of Mathematical Analysis and Applications, 317, 1, 80-102 (2006) · Zbl 1086.68111 · doi:10.1016/j.jmaa.2005.09.092 [7] Zhang, Z.; Liu, W.; Zhou, D., Global asymptotic stability to a generalized Cohen-Grossberg BAM neural networks of neutral type delays, Neural Networks, 25, 94-105 (2012) · Zbl 1266.34124 [8] Samidurai, R.; Sakthivel, R.; Anthoni, S. M., Global asymptotic stability of BAM neural networks with mixed delays and impulses, Applied Mathematics and Computation, 212, 1, 113-119 (2009) · Zbl 1173.34346 · doi:10.1016/j.amc.2009.02.002 [9] Zhang, L.; Si, L., Existence and exponential stability of almost periodic solution for BAM neural networks with variable coefficients and delays, Applied Mathematics and Computation, 194, 1, 215-223 (2007) · Zbl 1193.34158 · doi:10.1016/j.amc.2007.04.044 [10] Liu, Y.; Tang, W., Existence and exponential stability of periodic solution for BAM neural networks with periodic coefficients and delays, Neurocomputing, 69, 2152-2160 (2006) [11] Hu, L.; Liu, H.; Zhao, Y., New stability criteria for BAM neural networks with time-varying delays, Neurocomputing, 72, 3245-3252 (2009) [12] Li, Y.; Liu, P., Existence and stability of positive periodic solution for BAM neural networks with delays, Mathematical and Computer Modelling, 40, 7-8, 757-770 (2004) · Zbl 1197.34125 · doi:10.1016/j.mcm.2004.10.007 [13] Li, C.; Li, C.; Liao, X.; Huang, T., Impulsive effects on stability of high-order BAM neural networks with time delays, Neurocomputing, 74, 1541-1550 (2011) [14] Balasubramaniam, P.; Rakkiyappan, R.; Sathy, R., Delay dependent stability results for fuzzy BAM neural networks with Markovian jumping parameters, Expert Systems With Applications, 38, 121-130 (2011) [15] Li, Y.; Chen, X.; Zhao, L., Stability and existence of periodic solutions to delayed CohenCGrossberg BAM neural networks with impulses on time scales, Neurocomputing, 72, 1621-1630 (2009) [16] Yang, T.; Yang, L.-B., The global stability of fuzzy cellular neural network, IEEE Transactions on Circuits and Systems, 43, 10, 880-883 (1996) · doi:10.1109/81.538999 [17] Yang, T.; Yang, L.; Wu, C.; Chua, L., Fuzzy cellular neural networks: theory, Proceedings of the IEEE International Workshop on Cellular Neural Networks Application [18] Arunkumar, A.; Sakthivel, R.; Mathiyalagan, K.; Anthoni, S. M., State estimation for switched discrete-time stochastic BAM neural networks with time varying delay, Nonlinear Dynamics, 73, 3, 1565-1585 (2013) · Zbl 1281.93096 · doi:10.1007/s11071-013-0886-8 [19] Vadivel, P.; Sakthivel, R.; Mathiyalagan, K.; Arunkumar, A., Robust state estimation for uncertain fuzzy bidirectional associative memory networks with time-varying delays, Physica Scripta, 88, 3 (2013) · Zbl 1279.92013 [20] Mathiyalagan, K.; Sakthivel, R.; Anthoni, S. M., New robust passivity criteria for stochastic fuzzy BAM neural networks with time-varying delays, Communications in Nonlinear Science and Numerical Simulation, 17, 3, 1392-1407 (2012) · Zbl 1239.93112 · doi:10.1016/j.cnsns.2011.07.032 [21] Vadivel, P.; Sakthivel, R.; Mathiyalagan, K.; Thangaraj, P., New passivity criteria for fuzzy BAM neural networks with Markovian jumping parameters and time-varying delays, Reports on Mathematical Physics, 71, 1, 69-91 (2013) · Zbl 1270.93101 · doi:10.1016/S0034-4877(13)60022-1 [22] Balasubramaniam, P.; Nagamani, G.; Rakkiyappan, R., Passivity analysis for neural networks of neutral type with Markovian jumping parameters and time delay in the leakage term, Communications in Nonlinear Science and Numerical Simulation, 16, 11, 4422-4437 (2011) · Zbl 1219.92001 · doi:10.1016/j.cnsns.2011.03.028 [23] Li, X.; Cao, J., Delay-dependent stability of neural networks of neutral type with time delay in the leakage term, Nonlinearity, 23, 7, 1709-1726 (2010) · Zbl 1196.82102 · doi:10.1088/0951-7715/23/7/010 [24] Liu, B., Global exponential stability for BAM neural networks with time-varying delays in the leakage terms, Nonlinear Analysis: Real World Applications, 14, 1, 559-566 (2013) · Zbl 1260.34138 · doi:10.1016/j.nonrwa.2012.07.016 [25] Balasubramaniam, P.; Kalpana, M.; Rakkiyappan, R., Existence and global asymptotic stability of fuzzy cellular neural networks with time delay in the leakage term and unbounded distributed delays, Circuits, Systems, and Signal Processing, 30, 6, 1595-1616 (2011) · Zbl 1238.93085 · doi:10.1007/s00034-011-9288-7 [26] Li, X.; Rakkiyappan, R.; Balasubramaniam, P., Existence and global stability analysis of equilibrium of fuzzy cellular neural networks with time delay in the leakage term under impulsive perturbations, Journal of the Franklin Institute, 348, 2, 135-155 (2011) · Zbl 1241.92006 · doi:10.1016/j.jfranklin.2010.10.009 [27] Lakshmanan, S.; Park, J. H.; Jung, H. Y.; Balasubramaniam, P., Design of state estimator for neural networks with leakage, discrete and distributed delays, Applied Mathematics and Computation, 218, 22, 11297-11310 (2012) · Zbl 1277.93078 · doi:10.1016/j.amc.2012.05.022 [28] Li, X.; Fu, X.; Balasubramaniam, P.; Rakkiyappan, R., Existence, uniqueness and stability analysis of recurrent neural networks with time delay in the leakage term under impulsive perturbations, Nonlinear Analysis: Real World Applications, 11, 5, 4092-4108 (2010) · Zbl 1205.34108 · doi:10.1016/j.nonrwa.2010.03.014 [29] Gopalsamy, K., Leakage delays in BAM, Journal of Mathematical Analysis and Applications, 325, 2, 1117-1132 (2007) · Zbl 1116.34058 · doi:10.1016/j.jmaa.2006.02.039 [30] Li, C.; Huang, T., On the stability of nonlinear systems with leakage delay, Journal of the Franklin Institute, 346, 4, 366-377 (2009) · Zbl 1166.93367 · doi:10.1016/j.jfranklin.2008.12.001 [31] Balasubramaniam, P.; Kalpana, M.; Rakkiyappan, R., Global asymptotic stability of BAM fuzzy cellular neural networks with time delay in the leakage term, discrete and unbounded distributed delays, Mathematical and Computer Modelling, 53, 5-6, 839-853 (2011) · Zbl 1217.34116 · doi:10.1016/j.mcm.2010.10.021 [32] Li, Y. K.; Yang, L.; Sun, L. J., Existence and exponential stability of an equilibrium point for fuzzy BAM neural networks with time-varying delays in leakage terms on time scales, Advances in Difference Equations, 2013, article 218 (2013) · Zbl 1379.34087 · doi:10.1186/1687-1847-2013-218 [33] Lakshmikantham, V.; Bainov, D. D.; Simeonov, D., Theory of Impilsive Differential Equations (1989), Singaore: World Scientific, Singaore · Zbl 0719.34002 [34] Li, Y., Global exponential stability of BAM neural networks with delays and impulses, Chaos, Solitons and Fractals, 24, 1, 279-285 (2005) · Zbl 1099.68085 · doi:10.1016/j.chaos.2004.09.027 [35] Liu, X.; Ballinger, G., Existence and continuability of solutions for differential equations with delays and state-dependent impulses, Nonlinear Analysis: Theory, Methods & Applications, 51, 4, 633-647 (2002) · Zbl 1015.34069 · doi:10.1016/S0362-546X(01)00847-1 [36] Yang, T.; Yang, L.; Wu, C.; Chua, L., Fuzzy cellular neural networks: applications, Proceedings of the IEEE International Workshop on Cellular Neural Networks Application 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. 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