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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.

60K20Applications of Markov renewal processes
62M45Neural nets and related approaches (inference from stochastic processes)
Full Text: DOI
[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 · doi:10.1002/cta.4490200504
[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 · doi:10.1016/j.na.2006.04.016
[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)
[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 · doi:10.1016/j.chaos.2004.03.019
[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 · doi:10.1016/j.jmaa.2005.03.049
[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 · doi:10.1016/j.nonrwa.2005.11.001
[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 · doi:10.1016/j.nonrwa.2005.04.008
[11] Haykin, S.: Neural networks, (1994) · 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 · 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] 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
[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 · doi:10.1016/j.chaos.2005.04.067
[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 · doi:10.1016/j.amc.2006.05.087
[17] Mao, X.: Stochastic differential equation and application, (1997) · Zbl 0892.60057