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New results for global robust stability of bidirectional associative memory neural networks with multiple time delays. (English) Zbl 1198.34163
Summary: This paper presents some new sufficient conditions for the global robust asymptotic stability of the equilibrium point for bidirectional associative memory (BAM) neural networks with multiple time delays. The results we obtain impose constraint conditions on the network parameters of neural system independently of the delay parameter, and they are applicable to all bounded continuous non-monotonic neuron activation functions. We also give some numerical examples to demonstrate the applicability and effectiveness of our results, and compare the results with the previous robust stability results derived in the literature. Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

MSC:
34K20Stability theory of functional-differential equations
92B20General theory of neural networks (mathematical biology)
93D09Robust stability of control systems
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References:
[1] Arik, S.; Tavsanoglu, V.: On the global asymptotic stability of delayed cellular neural networks, IEEE trans circ syst I 47, 571-574 (2000) · Zbl 0997.90095 · doi:10.1109/81.841859
[2] Yi, Z.; Tan, K. K.: Dynamic stability conditions for Lotka -- Volterra recurrent neural networks with delays, Phys rev E 66, 011910 (2002)
[3] Song, Q.; Wang, Z.: Neural networks with discrete and distributed time-varying delays: a general stability analysis, Chaos, solitons & fractals 37, No. 5, 1538-1547 (2008) · Zbl 1142.34380
[4] Zhang, H.; Xia, Y.: Existence and exponential stability of almost periodic solution for Hopfield-type neural networks with impulse, Chaos, solitons & fractals 37, No. 4, 1076-1082 (2008) · Zbl 1155.34323
[5] Park, H. J.: On global stability criterion of neural networks with continuously distributed delays, Chaos, solitons & fractals 37, No. 2, 444-449 (2008) · Zbl 1141.93054
[6] Yu, K. -W.; Lien, C. -H.: Global exponential stability conditions for generalized state-space systems with time-varying delays, Chaos, solitons & fractals 36, No. 4, 920-927 (2008) · Zbl 1139.93354 · doi:10.1016/j.chaos.2006.07.008
[7] Zhang, Q.; Wei, X.; Xu, J.: Delay-dependent exponential stability criteria for non-autonomous cellular neural networks with time-varying delays, Chaos, solitons & fractals 36, No. 4, 985-990 (2008) · Zbl 1139.93031 · doi:10.1016/j.chaos.2006.07.034
[8] Song, Q.; Zhang, J.: Global exponential stability of impulsive Cohen Grossberg neural network with time-varying delays, Nonlinear anal: real world appl 9, No. 2, 500-510 (2008) · Zbl 1142.34046 · doi:10.1016/j.nonrwa.2006.11.015
[9] Liu, Y.; Wang, Z.; Liu, X.: An LMI approach to stability analysis of stochastic high-order Markovian jumping neural networks with mixed time delays, Nonlinear anal: hybrid syst 2, No. 1, 110-120 (2008) · Zbl 1157.93039 · doi:10.1016/j.nahs.2007.06.001
[10] Mohamad, S.; Gopalsamy, K.; Akca, H.: Exponential stability of artificial neural networks with distributed delays and large impulses, Nonlinear anal: real world appl 9, No. 3, 872-888 (2008) · Zbl 1154.34042 · doi:10.1016/j.nonrwa.2007.01.011
[11] Chen, B.; Wang, J.: Global exponential periodicity and global exponential stability of a class of recurrent neural networks with various activation functions and time-varying delays, Neural networks 20, No. 10, 1067-1080 (2007) · Zbl 1254.34114
[12] Arik, S.: Global asymptotic stability analysis of bidirectional associative memory neural networks with time delays, IEEE trans neural networks 16, No. 3, 580-586 (2005)
[13] Zhang, J.; Yang, Y.: Global stability analysis of bidirectional associative memory neural networks with time delay, Int J circ theor appl 29, 185-196 (2001) · Zbl 1001.34066
[14] Liao, X. F.; Yu, J.; Chen, G.: Novel stability criteria for bidirectional associative memory neural networks with time delays, Int J circ theor appl 30, 519-546 (2002) · Zbl 1014.93036
[15] Zhao, H.: Global stability of bidirectional associative memory neural networks with distributed delays, Phys lett A 30, 519-524 (2002)
[16] Mohamad, S.: Global exponential stability in continuous-time and discrete-time delayed bidirectional neural networks, Phys D 159, 233-251 (2001) · Zbl 0984.92502 · doi:10.1016/S0167-2789(01)00344-X
[17] Lou, X.; Cui, B.; Wu, W.: On global exponential stability and existence of periodic solutions for BAM neural networks with distributed delays and reaction diffusion terms, Chaos, solitons & fractals 36, No. 4, 1044-1054 (2008) · Zbl 1139.93030 · doi:10.1016/j.chaos.2006.08.005
[18] Jiang, H.; Cao, J.: BAM-type Cohen Grossberg neural networks with time delays, Math comput model 47, No. 1-2, 92-103 (2008) · Zbl 1143.34048 · doi:10.1016/j.mcm.2007.02.020
[19] Wang, B.; Jian, J.; Guo, C.: Global exponential stability of a class of BAM networks with time-varying delays and continuously distributed delays, Neurocomputing 71, No. 4-6, 495-501 (2008)
[20] Gu, H.; Jiang, H.; Teng, Z.: Existence and globally exponential stability of periodic solution of BAM neural networks with impulses and recent-history distributed delays, Neurocomputing 71, No. 4-6, 813-822 (2008)
[21] Jiang, M.; Shen, Y.: Stability of non-autonomous bidirectional associative memory neural networks with delay, Neurocomputing 71, No. 4 -- 6, 863-874 (2008)
[22] Wan, L.; Zhou, Q.: Convergence analysis of stochastic hybrid bidirectional associative memory neural networks with delays, Phys lett A 370, No. 5-6, 423-432 (2007)
[23] Zhang, L.; Si, L.: Existence and exponential stability of almost periodic solution for BAM neural networks with variable coefficients and delays, Appl math comput 194, No. 1, 215-223 (2007) · Zbl 1193.34158 · doi:10.1016/j.amc.2007.04.044
[24] Wan, L.; Zhou, Q.: Global exponential stability of BAM neural networks with time-varying delays and diffusion terms, Phys lett A 371, No. 1-2, 83-89 (2007) · Zbl 1209.93107 · doi:10.1016/j.physleta.2007.06.008
[25] 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 & fractals 34, No. 3, 878-885 (2007) · Zbl 1154.34380 · doi:10.1016/j.chaos.2006.03.112
[26] Chen, W. -H.; Lu, X.: Mean square exponential stability of uncertain stochastic delayed neural networks, Phys lett A 372, No. 7, 1061-1069 (2008) · Zbl 1217.92005 · doi:10.1016/j.physleta.2007.09.009
[27] Sun, C.; Feng, C. B.: On robust exponential periodicity of interval neural networks with delays, Neural process lett 20, 53-61 (2004)
[28] Cao, J.; Huang, D. -S.; Qu, Y.: Global robust stability of delayed recurrent neural networks, Chaos, solitons & fractals 23, No. 1, 221-229 (2005) · Zbl 1075.68070 · doi:10.1016/j.chaos.2004.04.002
[29] Cao, J.; Ho, D. W. C.; Huang, X.: LMI-based criteria for global robust stability of bidirectional associative memory networks with time delay, Nonlinear anal, ser A 66, No. 7, 1558-1572 (2007) · Zbl 1120.34055 · doi:10.1016/j.na.2006.02.009
[30] Qiu, J.; Zhang, J.; Wang, J.; Xia, Y.; Shi, P.: A new global robust stability criteria for uncertain neural networks with fast time-varying delays, Chaos, solitons & fractals 37, No. 2, 360-368 (2008) · Zbl 1141.93046 · doi:10.1016/j.chaos.2007.10.040
[31] Liao, X. F.; Wong, K.: Global exponential stability of hybrid bidirectional associative memory neural networks with discrete delays, Phys rev E 67, 0402901 (2003)
[32] Liao, X. F.; Wong, K.: Robust stability of interval bidirectional associative memory neural network with time delays, IEEE trans syst man cybernet 34, 1142-1154 (2004)
[33] Senan, S.; Arik, S.: Global robust stability of bidirectional associative memory neural networks with multiple time delays, IEEE trans syst man cybernet B 37, No. 5, 1375-1381 (2007) · Zbl 1198.34163
[34] Horn, R. A.; Johnson, C. R.: Topics in matrix analysis, (1991) · Zbl 0729.15001