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Asymptotic stability of BAM neural networks of neutral-type with impulsive effects and time delay in the leakage term. (English) Zbl 1247.34122
A class of bi-directional associatative memory (BAM) neural networks of neutral type with discrete interval and distributed time varying delays and time delay in the leakage term under impulsive perturbation is studied. The authors first prove existence and uniqueness of the equilibrium point of such nets by means of topological degree theory, Lyapunov method and linear matrix inequality approach. Then sufficient conditions for global asymptotic stability of the equilibrium point are derived. Numerical examples are provided in order to illustrate the obtained theoretical results.

MSC:
34K20 Stability theory of functional-differential equations
92B20 Neural networks for/in biological studies, artificial life and related topics
34K40 Neutral functional-differential equations
34K25 Asymptotic theory of functional-differential equations
34K45 Functional-differential equations with impulses
34K21 Stationary solutions of functional-differential equations
47N20 Applications of operator theory to differential and integral equations
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References:
[1] DOI: 10.1109/TNN.2005.844910
[2] DOI: 10.1016/j.neucom.2004.12.002 · Zbl 05011764
[3] DOI: 10.1080/00207160802588544 · Zbl 1205.34091
[4] Boyd S., Linear Matrix Inequalities in Systems and Control Theory (1994)
[5] DOI: 10.1088/0951-7715/19/7/008 · Zbl 1118.37038
[6] Chan C. S.L.L.W., IEEE Trans. Automat. Control 8 pp 267– (1997)
[7] Chen D., Int. J. Comput. Sci. Netw. Secur. 6 pp 94– (2006)
[8] DOI: 10.1016/j.chaos.2007.01.042 · Zbl 1152.34386
[9] DOI: 10.1007/s00521-010-0415-3
[10] Gopalsamy K., Stability and Oscillations in Delay Differential Equations of Population Dynamics (1992) · Zbl 0752.34039
[11] DOI: 10.1016/j.jmaa.2006.02.039 · Zbl 1116.34058
[12] DOI: 10.1007/978-1-4612-0039-0
[13] Guo D., Nonlinear Functional Analysis (1985)
[14] DOI: 10.1109/72.557697
[15] DOI: 10.1109/21.87054
[16] Lakshmikantham V., Theory of Impulsive Differential Equations (1989) · Zbl 0718.34011
[17] Li Y. K., Chaos Solitons Fractals 24 pp 279– (2005)
[18] DOI: 10.1080/00207720903042921 · Zbl 1292.93108
[19] DOI: 10.1016/j.jmaa.2006.01.016 · Zbl 1102.68117
[20] DOI: 10.1016/j.jfranklin.2008.12.001 · Zbl 1166.93367
[21] DOI: 10.1088/0951-7715/23/7/010 · Zbl 1196.82102
[22] DOI: 10.1016/j.nonrwa.2010.03.014 · Zbl 1205.34108
[23] DOI: 10.1016/j.neucom.2005.09.014 · Zbl 05184753
[24] DOI: 10.1016/j.neucom.2008.11.006 · Zbl 05719060
[25] DOI: 10.1080/00207160701636436 · Zbl 1173.34045
[26] DOI: 10.1016/j.neucom.2006.02.020 · Zbl 05184828
[27] DOI: 10.1016/j.chaos.2005.08.018 · Zbl 1121.92006
[28] DOI: 10.1016/j.physleta.2005.09.067
[29] DOI: 10.1016/j.chaos.2009.03.024 · Zbl 1198.93182
[30] DOI: 10.1016/j.amc.2007.10.032 · Zbl 1149.34345
[31] DOI: 10.1016/j.nonrwa.2009.06.004 · Zbl 1239.34081
[32] DOI: 10.1080/00207160801923072 · Zbl 1178.34092
[33] DOI: 10.1016/j.nonrwa.2008.10.050 · Zbl 1186.34101
[34] DOI: 10.1080/00207160902736944 · Zbl 1214.34076
[35] DOI: 10.1080/00207160802166507 · Zbl 1186.68392
[36] DOI: 10.1016/j.physleta.2004.12.007 · Zbl 1123.68347
[37] DOI: 10.1109/3477.537315
[38] DOI: 10.1016/j.neucom.2007.07.015 · Zbl 05718487
[39] DOI: 10.1016/j.chaos.2006.08.045 · Zbl 1144.34347
[40] DOI: 10.1016/j.neucom.2010.03.007 · Zbl 05849753
[41] DOI: 10.1080/00207160701670336 · Zbl 1153.34349
[42] DOI: 10.1007/11538059_73
[43] DOI: 10.1016/j.neucom.2008.07.001 · Zbl 05718982
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