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Periodic bidirectional associative memory neural networks with distributed delays. (English) Zbl 1086.68111

Summary: Some sufficient conditions are obtained for the existence and global exponential stability of a periodic solution to the general Bidirectional Associative Memory (BAM) neural networks with distributed delays by using the continuation theorem of Mawhin’s coincidence degree theory and the Lyapunov functional method and the Young’s inequality technique. These results are helpful for designing a globally exponentially stable and periodic oscillatory BAM neural network, and the conditions can be easily verified and be applied in practice. An example is also given to illustrate our results.

MSC:

68T05 Learning and adaptive systems in artificial intelligence
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[1] Cao, J., New results concerning exponential stability and periodic solutions of delayed cellular neural networks, Phys. Lett. A, 307, 136-147 (2003) · Zbl 1006.68107
[2] Cao, J.; Wang, J., Global asymptotic stability of a general class of recurrent neural networks with time-varying delays, IEEE Trans. Circuits Syst. I Regul. Pap., 50, 34-44 (2003) · Zbl 1368.34084
[3] Cao, J.; Dong, M., Exponential stability of delayed bi-directional associative memory networks, Appl. Math. Comput., 135, 105-112 (2003) · Zbl 1030.34073
[4] Cao, J.; Wang, L., Exponential stability and periodic oscillatory solution in BAM networks with delays, IEEE Trans. Neural Networks, 13, 457-463 (2002)
[5] Cao, J.; Wang, L., Periodic oscillatory solution of bidirectional associative memory networks with delays, Phys. Rev. E, 61, 1825-1828 (2000)
[6] Chen, A.; Cao, J.; Huang, L., Exponential stability of BAM neural networks with transmission delays, Neurocomputing, 57, 435-454 (2004)
[7] Chen, A.; Huang, L.; Cao, J., Existence and stability of almost periodic solution for BAM neural networks with delays, Appl. Math. Comput., 137, 177-193 (2003) · Zbl 1034.34087
[8] Chen, J.; Chen, X., Special Matrices (2001), Tsinghua Univ. Press: Tsinghua Univ. Press Beijing
[9] Chapeau-Blondeau, F.; Chauvet, G., Stable, oscillatory, and chaotic regimes in the dynamics of small neural networks with delay, Neural Networks, 5, 735-744 (1992)
[10] Feng, C.; Plamondon, R., On the stability analysis of delayed neural network systems, Neural Networks, 14, 1181-1188 (2001)
[11] Freeman, W. J., The physiology of perception, Sci. Amer., 34-41 (1991)
[12] Gaines, D. R.E.; Mawhin, J. L., Coincidence Degree and Non-Linear Differential Equations (1977), Springer: Springer Berlin
[13] Gopalsamy, K.; Mohamad, S., Time delays and stimulus-dependent pattern formation in periodic environments in isolated neurons, IEEE Trans. Neural Networks, 13, 551-563 (2002) · Zbl 1017.34073
[14] Gopalsamy, K.; He, X., Delay-independent stability in bi-directional associative memory networks, IEEE Trans. Neural Networks, 7, 998-1002 (1994)
[15] Hardy, G. H.; Littlewood, J. E.; Pólya, G., A Theorem of W.H. Young. Section 8.3, (Inequalities (1988), Cambridge Univ. Press: Cambridge Univ. Press Cambridge, UK), 198-200
[16] Hjelmfelt, A.; Ross, J., Pattern recognition, chaos, and multiplicity in neural networks of excitable systems, Proc. Nat. Acad. Sci., 91, 63-67 (1994)
[17] Kosko, B., Adaptive bi-directional associative memories, Appl. Optim., 26, 4947-4960 (1987)
[18] Kosko, B., Bidirectional associative memories, IEEE Trans. Man Cybernet., 18, 49-60 (1988)
[19] Kosko, B., Neural Networks and Fuzzy Systems—A Dynamical System Approach to Machine Intelligence (1992), Prentice Hall: Prentice Hall Englewood Cliffs, NJ, pp. 38-108
[20] Li, Y. K., Existence and stability of periodic solutions for Cohen-Grossberg neural networks with multiple delays, Chaos Solitons Fractals, 20, 459-466 (2004) · Zbl 1048.34118
[21] Mohamad, S., Global exponential stability in continuous-time and discrete-time delayed bidirectional neural networks, Phys. D, 159, 233-251 (2001) · Zbl 0984.92502
[22] Ott, E.; Grebogi, C.; Yorke, J. A., Controlling chaos, Phys. Rev. Lett., 46, 1196-1199 (1990) · Zbl 0964.37501
[23] Skarda, C. A.; Freeman, W. J., How brains make chaos in order to make sense of the world, Behavioral Brain Sci., 10, 161-195 (1987)
[24] Sree Hari Rao, V.; Nagaraj, R., Global exponential convergence analysis of activations in bi-directional associative memory neural networks, Differential Equations Dynam. Systems, 12, 3-21 (2004) · Zbl 1131.34325
[25] Sree Hari Rao, V.; Phaneendra, Bh. R.M.; Prameela, V., Global dynamics of bidirectional associative memory networks with transmission delays, Differential Equations Dynam. Systems, 4, 453-471 (1996) · Zbl 0871.34043
[26] Sree Hari Rao, V.; Phaneendra, Bh. R.M.; Prameela, V., Global dynamics of bidirectional associative memory neural networks involving transmission delays and dead zones, Neural Networks, 12, 455-465 (1999)
[27] Townley, S.; Πchmann, A.; Weiß, M. G.; Mcclements, W.; Ruiz, A. C.; Owens, D. H.; Präzel-Wolters, D., Existence and learning of oscillations in recurrent neural networks, IEEE Trans. Neural Networks, 11, 205-214 (2000)
[28] van Den Driessche, P.; Zou, X., Global attractivity in delayed Hopfield neural networks models, SIAM J. Appl. Math., 58, 1878-1890 (1998) · Zbl 0917.34036
[29] Wang, L.; Zou, X., Hopf bifurcation in bidirectional associative memory neural networks with delays: Analysis and computation, J. Comput. Appl. Math., 167, 73-90 (2004) · Zbl 1054.65076
[30] Wu, J., Introduction to Neural Dynamics and Signal Transmission Delay (2001), de Gruyter: de Gruyter New York · Zbl 0977.34069
[31] Yao, Y.; Freeman, W. J.; Burke, B.; Yang, Q., Pattern recognition by a distributed neural network: An industrial application, Neural Networks, 4, 103-121 (1991)
[32] Yi, Z.; Heng, P. A.; Vadakkepat, P., Absolute periodicity and absolute stability of delayed neural networks, IEEE Trans. Circuits Systems I, 49, 256-261 (2002) · Zbl 1368.93616
[33] Yi, Z., Global exponential stability and periodic solutions of delay Hopfield neural networks, Internat. J. Systems Sci., 27, 227-232 (1996) · Zbl 0845.93071
[34] Yi, Z.; Zhong, S. M.; Li, Z. L., Periodic solutions and stability of Hopfield neural networks with variable delays, Internat. J. Systems Sci., 27, 895-902 (1996) · Zbl 0863.34038
[35] Zheng, Y.; Chen, T., Global exponential stability of delayed periodic dynamical systems, Phys. Lett. A, 322, 344-355 (2004) · Zbl 1118.81479
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