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$p$th moment stability analysis of stochastic recurrent neural networks with time-varying delays. (English) Zbl 1144.93030
Summary: This paper addresses, in great detail, the issue of $p$th moment exponential stability of stochastic recurrent neural networks with time-varying delays. With the help of the Dini-derivative of the expectation of $V\left(t,X\left(t\right)\right)$ “along” the solution $X\left(t\right)$ of the model and the technique of Halanay-type inequality, some novel sufficient conditions on $p$th moment exponential stability of the trivial solution has been established. Results of the development as presented in this paper are more general than those reported in some previously published papers. An example is also given to illustrate that our results are correct and effectiveness.
##### MSC:
 93E15 Stochastic stability 92B20 General theory of neural networks (mathematical biology)
##### Keywords:
stochastic neural networks; stability
##### References:
 [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 · doi:10.1016/S0375-9601(02)01720-6 [2] Cao, J.; Wang, J.: Absolute exponential stability of recurrent neural networks with Lipschitz-continuous activation functions and time delays, Neural networks 17, 379-390 (2004) · Zbl 1074.68049 · doi:10.1016/j.neunet.2003.08.007 [3] Cao, J.; Wang, Z.; Sun, Y.: Synchronization in an array of linearly stochastically coupled networks with time delays, Physica A 385, 718-728 (2007) [4] Chen, H.; Hung, Y.; Chen, C.; Liao, T.; Chen, C. K.: Image-processing algorithms realized by discrete-time cellular neural networks and their circuit implementations, Chaos soliton fract. 29, 1100-1108 (2006) · Zbl 1142.68575 · doi:10.1016/j.chaos.2005.08.067 [5] Haykin, S.: Neural networks, (1994) [6] Hu, J.; Zhong, S.; Liang, L.: Exponential stability analysis of stochastic delayed cellular neural network, Chaos soliton fract. 27, 1006-1010 (2006) · Zbl 1084.68099 · doi:10.1016/j.chaos.2005.04.067 [7] Huang, C.; Huang, L.: Existence and global exponential stability of periodic solutions of two-neuron networks with time-varying delays, Appl. math. Lett. 19, 126-134 (2006) · Zbl 1096.34051 · doi:10.1016/j.aml.2005.04.001 [8] Huang, H.; Cao, J.: Exponential stability analysis of uncertain stochastic neural networks with multiple delays, Nonlinear anal.: RWA 8, No. 2, 646-653 (2007) · Zbl 1152.34387 · doi:10.1016/j.nonrwa.2006.02.003 [9] Huang, L.; Huang, C.; Liu, B.: Dynamics of a class of cellular neural networks with time-varying delays, Phys. lett. A 345, 330-344 (2005) [10] Li, X.; Cao, J.: Exponential stability of stochastic Cohen – Grossberg neural networks with time-varying delays, Lncs 3496, 162-167 (2005) · Zbl 1082.68654 · doi:10.1007/b136476 [11] Li, X.; Cao, J.: Exponential stability of stochastic interval Hopfield neural networks with time-varying delays, Neural network world 16, No. 1, 31-40 (2007) [12] Liao, X.; Mao, X.: Exponential stability and instability of stochastic neural networks, Stochast. anal. Appl. 14, 165-185 (1996) · Zbl 0848.60058 · doi:10.1080/07362999608809432 [13] Liao, X.; Mao, X.: Stability of stochastic neural networks, Neural parallel sci. Comput. 14, 205-224 (1996) · Zbl 1060.92502 [14] Liu, D.; Michel, A.: Cellular neural networks for associative memories, IEEE trans. Circuits syst. 40, 119-121 (1993) · Zbl 0800.92046 · doi:10.1109/82.219843 [15] Lu, Z.; Shieh, L.; Chen, G.; Coleman, N.: Adaptive feedback linearization control of chaotic systems via recurrent high-order neural networks, Inform. sci. 176, No. 16, 2337-2354 (2006) · Zbl 1116.93035 · doi:10.1016/j.ins.2005.08.002 [16] Mao, X.: Stochastic differential equation and application, (1997) [17] Oh, S.; Pedrycz, W.; Roh, S.: Genetically optimized fuzzy polynomial neural networks with fuzzy set-based polynomial neurons, Inform. sci. 176, No. 23, 3490-3519 (2006) · Zbl 1119.68159 · doi:10.1016/j.ins.2005.11.009 [18] Sun, Y.; Cao, J.: Pth moment exponential stability of stochastic recurrent neural networks with time-varying delays, Nonlinear anal.: RWA 8, 1171-1185 (2007) · Zbl 1196.60125 · doi:10.1016/j.nonrwa.2006.06.009 [19] Sun, Y.; Cao, J.; Wang, Z.: Exponential synchronization of stochastic perturbed chaotic delayed neural networks, Neurocomputing 70, No. 13 – 15, 2477-2485 (2007) [20] Venetianer, P.; Roska, T.: Image compression by delayed cnns, IEEE trans. Circuits syst. I 45, 205-215 (1998) [21] Wan, L.; Sun, J.: Mean square exponential stability of delayed Hopfield neural networks, Phys. lett. A 343, 306-318 (2005) · Zbl 1194.37186 · doi:10.1016/j.physleta.2005.06.024 [22] Wongseree, W.; Chaiyaratana, N.; Vichittumaros, K.; Winichagoon, P.; Fucharoen, S.: Thalassaemia classification by neural networks and genetic programming, Inform. sci. 177, No. 3, 771-786 (2007) [23] Yuan, Z.; Yuan, L.; Huang, L.: Dynamics of periodic Cohen – Grossberg neural networks with varying delays, Neurocomputing 70, 164-172 (2006) [24] Zhao, H.; Cao, J.: New conditions for global exponential stability of cellular neural networks with delays, Neural networks 18, 1332-1340 (2005) · Zbl 1083.68108 · doi:10.1016/j.neunet.2004.11.010 [25] Zhao, H.; Ding, N.: Dynamic analysis of stochastic Cohen – Grossberg neural networks with time delays, Appl. math. Comput. 183, No. 1, 464-470 (2006) · Zbl 1117.34080 · doi:10.1016/j.amc.2006.05.087