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Impulsive hybrid discrete-time Hopfield neural networks with delays and multistability analysis. (English) Zbl 1225.93073

Summary: We investigate multistability of discrete-time Hopfield-type neural networks with distributed delays and impulses, by using Lyapunov functionals, stability theory and control by impulses. Examples and simulation results are given to illustrate the effectiveness of the results.

MSC:

93C55 Discrete-time control/observation systems
92B20 Neural networks for/in biological studies, artificial life and related topics
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[1] Akça, H.; Alassar, R.; Covachev, V.; Covacheva, Z., Discrete counterparts of continuous-time additive Hopfield-type neural networks with impulses, Dynamic systems and applications, 13, 1, 77-92, (2004) · Zbl 1058.34007
[2] Akça, H.; Alassar, R.; Covachev, V.; Yurtsever, H.A., Discrete-time impulsive Hopfield neural networks with finite distributed delays, Computer assisted mechanics and engineering sciences, 14, 2, 145-158, (2007) · Zbl 1122.92001
[3] Campbell, S.A.; Ncube, I.; Wu, J., Multistability and stable asynchronous periodic oscillations in a multiple-delayed neural system, Physica D: nonlinear phenomena, 214, 2, 101-119, (2006) · Zbl 1100.34054
[4] Cao, J.; Feng, G.; Wang, Y., Multistability and multiperiodicity of delayed cohen – grossberg neural networks with a general class of activation functions, Physica D: nonlinear phenomena, 237, 13, 1734-1749, (2008) · Zbl 1161.34044
[5] Cheng, C.-Y.; Lin, K.-H.; Shih, C.-W., Multistability in recurrent neural networks, SIAM journal on applied mathematics, 66, 4, 1301-1320, (2006) · Zbl 1106.34048
[6] Cheng, C.-Y.; Lin, K.-H.; Shih, C.-W., Multistability and convergence in delayed neural networks, Physica D: nonlinear phenomena, 225, 1, 61-74, (2007) · Zbl 1132.34058
[7] Chua, Leon O.; Yang, Lin, Cellular neural networks: theory, IEEE transactions on circuits and systems, 35, 10, 1257-1272, (1988) · Zbl 0663.94022
[8] Cohen, M.A.; Grossberg, S., Absolute stability of global pattern formation and parallel memory storage by competitive neural networks, IEEE transactions on systems, man, and cybernetics, 13, 5, 815-826, (1983) · Zbl 0553.92009
[9] Hopfield, J.J., Neural networks and physical systems with emergent collective computational abilities, Proceedings of the national Academy of sciences, 79, 2554-2558, (1982) · Zbl 1369.92007
[10] Huang, G.; Cao, J., Multistability in bidirectional associative memory neural networks, Physics letters, section A: general, atomic and solid state physics, 372, 16, 2842-2854, (2008) · Zbl 1220.92002
[11] Huang, G.; Cao, J., Multistability of neural networks with discontinuous activation function, Communications in nonlinear science and numerical simulation, 13, 10, 2279-2289, (2008) · Zbl 1221.34131
[12] Huang, Z.-T.; Luo, X.-S.; Yang, Q.-G., Global asymptotic stability analysis of bidirectional associative memory neural networks with distributed delays and impulse, Chaos, solitons and fractals, 34, 3, 878-885, (2007) · Zbl 1154.34380
[13] Huang, Z.; Mohamad, S.; Bin, H., Multistability of HNNs with almost periodic stimuli and continuously distributed delays, International journal of systems science, 40, 6, 615-625, (2009) · Zbl 1291.93266
[14] Huang, Z.; Wang, X.; Xia, Y., Exponential stability of impulsive cohen – grossberg networks with distributed delays, International journal of circuit theory and applications, 36, 3, 345-365, (2008) · Zbl 1179.92003
[15] Huo, H.-F.; Li, W.-T., Dynamics of continuous-time bidirectional associative memory neural networks with impulses and their discrete counterparts, Chaos, solitons and fractals, 42, 4, 2218-2229, (2009) · Zbl 1198.34152
[16] Kaslik, E.; Balint, St., Configurations of steady states for Hopfield-type neural networks, Applied mathematics and computation, 182, 1, 934-946, (2006) · Zbl 1115.93062
[17] Kaslik, E., & Sivasundaram, S. Multistability in impulsive hybrid hopfield neural networks with distributed delays. Nonlinear Analysis: Real World Applications, in press (doi:10.1016/j.nonrwa.2010.10.018). · Zbl 1221.34219
[18] Kelin, L.; Zuoan, L.; Qiankun, S., Behavior of impulsive fuzzy cellular neural networks with distributed delays, Electronic journal of differential equations, 1-16, (2007) · Zbl 1274.92006
[19] Kosko, Bart, Bidirectional associative memories, IEEE transactions on systems, man and cybernetics, 18, 1, 49-60, (1988)
[20] Li, K., Stability analysis for impulsive cohen – grossberg neural networks with time-varying delays and distributed delays, Nonlinear analysis: real world applications, 10, 5, 2784-2798, (2009) · Zbl 1162.92002
[21] Li, Y.; Hua, Y.; Fei, Y., Global exponential stability of delayed cohen – grossberg BAM neural networks with impulses on time scales, Journal of inequalities and applications, 2009, (2009) · Zbl 1180.34081
[22] Li, Y.; Yang, C., Global exponential stability analysis on impulsive BAM neural networks with distributed delays, Journal of mathematical analysis and applications, 324, 2, 1125-1139, (2006) · Zbl 1102.68117
[23] Li, K.; Zhang, X.; Li, Z., Global exponential stability of impulsive cellular neural networks with time-varying and distributed delay, Chaos, solitons and fractals, 41, 3, 1427-1434, (2009) · Zbl 1198.34154
[24] Liu, B.; Huang, L., Global exponential stability of BAM neural networks with recent-history distributed delays and impulses, Neurocomputing, 69, 16-18, 2090-2096, (2006)
[25] Mohamad, S., Global exponential stability in continuous-time and discrete-time delayed bidirectional neural networks, Physica D: nonlinear phenomena, 159, 3-4, 233-251, (2001) · Zbl 0984.92502
[26] Mohamad, S., Global exponential stability in discrete-time analogues of delayed cellular neural networks, Journal of difference equations and applications, 9, 6, 559-575, (2003) · Zbl 1045.65067
[27] Mohamad, S., Exponential stability preservation in discrete-time analogues of artificial neural networks with distributed delays, Journal of computational and applied mathematics, 215, 1, 270-287, (2008) · Zbl 1154.39011
[28] Mohamad, S.; Gopalsamy, K., Dynamics of a class of discrete-time neural networks and their continuous-time counterparts, Mathematics and computers in simulation, 53, 1-2, 1-39, (2000)
[29] Mohamad, S.; Gopalsamy, K.; Akça, H., Exponential stability of artificial neural networks with distributed delays and large impulses, Nonlinear analysis: real world applications, 9, 3, 872-888, (2008) · Zbl 1154.34042
[30] Morita, M., Memory and learning of sequential patterns by nonmonotone neural networks, Neural networks, 9, 8, 1477-1489, (1996)
[31] Nie, X.; Cao, J., Multistability of competitive neural networks with time-varying and distributed delays, Nonlinear analysis: real world applications, 10, 2, 928-942, (2009) · Zbl 1167.34383
[32] Ping, Z.W.; Lu, J.G., Global exponential stability of impulsive cohen – grossberg neural networks with continuously distributed delays, Chaos, solitons and fractals, 41, 1, 164-174, (2009) · Zbl 1198.34159
[33] Qu, H.; Yi, Z., Convergence and periodicity of solutions for a class of discrete-time recurrent neural network with two neurons, (), 291-296
[34] Shih, C.-W.; Tseng, J.-P., Convergent dynamics for multistable delayed neural networks, Nonlinearity, 21, 10, 2361-2389, (2008) · Zbl 1162.34002
[35] Song, Q.; Cao, J., Dynamical behaviors of discrete-time fuzzy cellular neural networks with variable delays and impulses, Journal of the franklin institute, 345, 1, 39-59, (2008) · Zbl 1167.93369
[36] Wang, X.; Jiang, M.; Fang, S., Stability analysis in Lagrange sense for a non-autonomous cohen – grossberg neural network with mixed delays, Nonlinear analysis, theory, methods and applications, 70, 12, 4294-4306, (2009) · Zbl 1162.34338
[37] Wang, L.; Lu, W.; Chen, T., Multistability of neural networks with a class of activation functions, (), 323-332, (PART 1)
[38] Wang, Y.; Xiong, W.; Zhou, Q.; Xiao, B.; Yu, Y., Global exponential stability of cellular neural networks with continuously distributed delays and impulses, Physics letters, section A: general, atomic and solid state physics, 350, 1-2, 89-95, (2006) · Zbl 1195.34064
[39] Xia, Y.; Huang, Z.; Han, M., Exponential \(p\)-stability of delayed cohen – grossberg-type BAM neural networks with impulses, Chaos, solitons and fractals, 38, 3, 806-818, (2008) · Zbl 1146.34329
[40] Yi, Z.; Tan, K.K.; Lee, T.H., Multistability analysis for recurrent neural networks with unsaturating piecewise linear transfer functions, Neural computation, 15, 3, 639-662, (2003) · Zbl 1085.68142
[41] Yi, Z.; Tan, K.K., Multistability of discrete-time recurrent neural networks with unsaturating piecewise linear activation functions, IEEE transactions on neural networks, 15, 2, 329-336, (2004)
[42] Yin, L.; Li, X., Impulsive stabilization for a class of neural networks with both time-varying and distributed delays, Advances in difference equations, 2009, (2009) · Zbl 1398.34104
[43] Zhang, H.; Chen, L., Asymptotic behavior of discrete solutions to delayed neural networks with impulses, Neurocomputing, 71, 4-6, 1032-1038, (2008)
[44] Zhang, L.; Yi, Z.; Yu, J.; Heng, P.A., Some multistability properties of bidirectional associative memory recurrent neural networks with unsaturating piecewise linear transfer functions, Neurocomputing, 72, 16-18, 3809-3817, (2009)
[45] Zhao, X., Qualitative analysis of general discrete-time recurrent neural networks with impulses, (), 128-137, (PART 1)
[46] Zhou, Q., Global exponential stability of BAM neural networks with distributed delays and impulses, Nonlinear analysis: real world applications, 10, 1, 144-153, (2009) · Zbl 1154.34391
[47] Zhou, J.; Li, S., Global exponential stability of impulsive BAM neural networks with distributed delays, Neurocomputing, 72, 7-9, 1688-1693, (2009)
[48] Zhou, L.; Li, C.-D.; Wan, J., Global stability of discrete-time recurrent neural networks with impulse effects, International journal of nonlinear sciences and numerical simulation, 10, 1, 93-97, (2009)
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