×

Mean square exponential stability of stochastic recurrent neural networks with time-varying delays. (English) Zbl 1152.60346

Summary: The stability of a class of stochastic Recurrent Neural Networks with time-varying delays is investigated in this paper. With the help of the Lyapunov function and the Dini derivative of the expectation of \(V(t,X(t))\) “along” the solution \(X(t)\) of the model, a set of novel sufficient conditions on mean square exponential stability has been established. An example is also given to illustrate the effectiveness of our results.

MSC:

60K20 Applications of Markov renewal processes (reliability, queueing networks, etc.)
62M45 Neural nets and related approaches to inference from stochastic processes
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Roska, T.; Chua, L. O., Cellular neural networks with nonlinear and delay-type template, Int. J. Circuit Theory Appl., 20, 469-481 (1992) · Zbl 0775.92011
[2] Venetianer, P.; Roska, T., Image compression by delayed CNNs, IEEE Trans. Circuits Syst. I, 45, 205-215 (1998)
[3] Chen, T., Global exponential stability of delayed Hopfield neural networks, Neural Netw., 14, 977-980 (2001)
[4] Cao, J.; Wang, L., Exponential stability and periodic oscillatory solution in BAM networks with delays, IEEE Trans. Neural Netw., 13, 457-463 (2002)
[5] Chen, A.; Cao, J., Periodic bi-directional Cohen-Grossberg neural networks with distributed delays, Nonlinear Anal., 66, 2947-2961 (2007) · Zbl 1122.34055
[6] Liu, Z.; Chen, A.; Cao, J.; Huang, L., Existence and global exponential stability of periodic solution for BAM neural networks with periodic coefficients and time-varying delays, IEEE Trans. Circuits Syst.-I, 50, 1162-1173 (2003) · Zbl 1368.93471
[7] Cao, J.; Chen, T., Globally exponentially robust stability and periodicity of delayed neural networks, Chaos, Solitons Fractals, 4, 957-963 (2004) · Zbl 1061.94552
[8] Wei, J.; Yuan, Y., Synchronized Hopf bifurcation analysis in a neural network model with delays, J. Math. Anal. Appl., 312, 205-229 (2005) · Zbl 1085.34058
[9] Liao, X.; Liu, Q.; Zhang, W., Delay-dependent asymptotic stability for neural networks with distributed delays, Nonlinear Anal.: RWA, 7, 1178-1192 (2006) · Zbl 1194.34140
[10] Huang, C.; Huang, L.; Yuan, Z., Dynamics of a class of Cohen-Grossberg neural networks with time-varying delays, Nonlinear Anal.: RWA, 8, 40-52 (2007) · Zbl 1123.34053
[11] Haykin, S., Neural Networks (1994), Prentice-Hall: Prentice-Hall NJ · Zbl 0828.68103
[12] Liao, X.; Mao, X., Exponential stability and instability of stochastic neural networks, Stoch. Anal. Appl, 14, 165-185 (1996) · Zbl 0848.60058
[13] Liao, X.; Mao, X., Stability of stochastic neural networks, Neural. Parallel Sci. Comput, 14, 205-224 (1996) · Zbl 1060.92502
[14] Wan, L.; Sun, J., Mean square exponential stability of delayed Hopfield neural networks, Phys. Lett. A, 343, 306-318 (2005) · Zbl 1194.37186
[15] Hu, J.; Zhong, S.; Liang, L., Exponential stability analysis of stochastic delayed cellular neural network, Chaos, Solitions Fractals, 27, 1006-1010 (2006) · Zbl 1084.68099
[16] Zhao, H.; Ding, N., Dynamic analysis of stochastic Cohen-Grossberg neural networks with time delays, Appl. Math. Comput., 183, 464-470 (2006) · Zbl 1117.34080
[17] Mao, X., Stochastic Differential Equation and Application (1997), Horwood Publishing: Horwood Publishing Chichester · Zbl 0874.60050
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.