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Stochastic stability of impulsive BAM neural networks with time delays. (English) Zbl 1219.93090
Summary: The problem of stability analysis of stochastic BAM neural networks with time delays and impulse effects is investigated in this paper. Using the Lyapunov technique and the generalized Hanalay inequality, we characterize theoretically the aggregated effects of impulse and stability properties of the impulse-free version. The present approaches allow us to estimate the feasible upper bounds of impulse strengths and can also extend to the more general impulsive nonlinear systems with delays.

93D05Lyapunov and other classical stabilities of control systems
34K20Stability theory of functional-differential equations
34F05ODE with randomness
34K45Functional-differential equations with impulses
60H10Stochastic ordinary differential equations
92B20General theory of neural networks (mathematical biology)
Full Text: DOI
[1] Kosko, B.: Adaptive bi-directional associative memories, Applied optimization 26, 4947-4960 (1987)
[2] Kosko, B.: Bidirectional associative memories, IEEE transactions on systems, man and cybernetics 18, 49-60 (1988)
[3] Cao, J.: Global exponential stability of Hopfield neural networks, International journal of systems science 32, 233-236 (2001) · Zbl 1011.93091
[4] Xu, Z. B.: Global convergence and asymptotic stability of asymmetric Hopfield neural networks, Journal of mathematical analysis and application 191, 405-427 (1995) · Zbl 0819.68101 · doi:10.1006/jmaa.1995.1138
[5] Li, C. D.; Liao, X. F.: Delay-dependent exponential stability analysis of bi-directional associative memory neural networks: an LMI approach, Chaos, solitons and fractals 24, No. 4, 1119-1134 (2005) · Zbl 1101.68771 · doi:10.1016/j.chaos.2004.09.052
[6] Guan, Z. H.; James, L.; Chen, G. R.: On impulsive auto-associative neural networks, Neural networks 13, 63-69 (2000)
[7] Zidong, Wang; Shu, Huisheng; Fang, Jian’an; Liua, Xiaohui: Robust stability for stochastic Hopfield neural networks with time delays, Nonlinear analysis: real world applications 7, 1119-1128 (2006) · Zbl 1122.34065 · doi:10.1016/j.nonrwa.2005.10.004
[8] Huang, He; Cao, Jinde: Exponential stability analysis of uncertain stochastic neural networks with multiple delays, Nonlinear analysis: real world applications 8, 646-653 (2007) · Zbl 1152.34387 · doi:10.1016/j.nonrwa.2006.02.003
[9] Huang, He; Ho, Daniel W. C.; Qu, Yuzhong: Robust stability of stochastic delayed additive neural networks with Markovian switching, Neural networks 20, 799-809 (2007) · Zbl 1125.68096 · doi:10.1016/j.neunet.2007.07.003
[10] Wang, Zidong; Liu, Yurong; Li, Maozhen; Liu, Xiaohui: Stability analysis for stochastic Cohen--Grossberg neural networks with mixed time delays, IEEE transactions on neural networks 17, No. 3, 814-820 (2006)
[11] Zhang, Huaguang; Wang, Yingchun: Stability analysis of Markovian jumping stochastic Cohen--Grossberg neural networks with mixed time delays, IEEE transactions on neural networks 19, No. 2, 366-370 (2008)
[12] Lou, Xuyang; Cui, Baotong: Stochastic exponential stability for Markovian jumping BAM neural networks with time-varying delays, IEEE transactions on systems, man and cybernetics, part B (Cybernetics) 37, No. 3, 713-719 (2007) · Zbl 1156.68540