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Dynamics of Cohen-Grossberg neural networks with mixed delays and impulses. (English) Zbl 1160.37431

Summary: Impulsive Cohen-Grossberg neural networks with bounded and unbounded delays (i.e., mixed delays) are investigated. By using the Leray-Schauder fixed point theorem, differential inequality techniques, and constructing suitable Lyapunov functional, several new sufficient conditions on the existence and global exponential stability of periodic solution for the system are obtained, which improves some of the known results. An example and its numerical simulations are employed to illustrate our feasible results.

MSC:

37N20 Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics)
34K13 Periodic solutions to functional-differential equations
92B20 Neural networks for/in biological studies, artificial life and related topics
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References:

[1] M. A. Cohen and S. Grossberg, “Absolute stability of global pattern formation and parallel memory storage by competitive neural networks,” IEEE Transactions on Systems, Man, and Cybernetics, vol. 13, no. 5, pp. 815-826, 1983. · Zbl 0553.92009 · doi:10.1109/TSMC.1983.6313075
[2] C. Huang and L. Huang, “Dynamics of a class of Cohen-Grossberg neural networks with time-varying delays,” Nonlinear Analysis: Real World Applications, vol. 8, no. 1, pp. 40-52, 2007. · Zbl 1123.34053 · doi:10.1016/j.nonrwa.2005.04.008
[3] T. Chen and L. Rong, “Robust global exponential stability of Cohen-Grossberg neural networks with time delays,” IEEE Transactions on Neural Networks, vol. 15, no. 1, pp. 203-206, 2004. · doi:10.1109/TNN.2003.822974
[4] J. Cao and J. Liang, “Boundedness and stability for Cohen-Grossberg neural network with time-varying delays,” Journal of Mathematical Analysis and Applications, vol. 296, no. 2, pp. 665-685, 2004. · Zbl 1044.92001 · doi:10.1016/j.jmaa.2004.04.039
[5] W. Zhao, “Global exponential stability analysis of Cohen-Grossberg neural network with delays,” Communications in Nonlinear Science and Numerical Simulation, vol. 13, no. 5, pp. 847-856, 2008. · Zbl 1221.93207 · doi:10.1016/j.cnsns.2006.09.004
[6] K. Yuan and J. Cao, “An analysis of global asymptotic stability of delayed Cohen-Grossberg neural networks via nonsmooth analysis,” IEEE Transactions on Circuits and Systems I, vol. 52, no. 9, pp. 1854-1861, 2005. · Zbl 1374.34291 · doi:10.1109/TCSI.2005.852210
[7] L. Huang, C. Huang, and B. Liu, “Dynamics of a class of cellular neural networks with time-varying delays,” Physics Letters A, vol. 345, no. 4-6, pp. 330-344, 2005. · Zbl 1345.92014 · doi:10.1016/j.physleta.2005.07.039
[8] J. Zhang, Y. Suda, and H. Komine, “Global exponential stability of Cohen-Grossberg neural networks with variable delays,” Physics Letters A, vol. 338, no. 1, pp. 44-50, 2005. · Zbl 1136.34347 · doi:10.1016/j.physleta.2005.02.005
[9] W. Lu and T. Chen, “New conditions on global stability of Cohen-Grossberg neural networks,” Neural Computation, vol. 15, no. 5, pp. 1173-1189, 2003. · Zbl 1086.68573 · doi:10.1162/089976603765202703
[10] T. Chen and L. Rong, “Delay-independent stability analysis of Cohen-Grossberg neural networks,” Physics Letters A, vol. 317, no. 5-6, pp. 436-449, 2003. · Zbl 1030.92002 · doi:10.1016/j.physleta.2003.08.066
[11] L. Wang and X. Zou, “Exponential stability of Cohen-Grossberg neural networks,” Neural Networks, vol. 15, no. 3, pp. 415-422, 2002. · doi:10.1016/S0893-6080(02)00025-4
[12] L. Wan and J. Sun, “Global asymptotic stability of Cohen-Grossberg neural network with continuously distributed delays,” Physics Letters A, vol. 342, no. 4, pp. 331-340, 2005. · Zbl 1222.93200 · doi:10.1016/j.physleta.2005.05.026
[13] Z. Chen and J. Ruan, “Global stability analysis of impulsive Cohen-Grossberg neural networks with delay,” Physics Letters A, vol. 345, no. 1-3, pp. 101-111, 2005. · Zbl 1345.92012 · doi:10.1016/j.physleta.2005.06.104
[14] Q. Song and J. Zhang, “Global exponential stability of impulsive Cohen-Grossberg neural network with time-varying delays,” Nonlinear Analysis: Real World Applications, vol. 9, no. 2, pp. 500-510, 2008. · Zbl 1142.34046 · doi:10.1016/j.nonrwa.2006.11.015
[15] Q. Song and J. Cao, “Impulsive effects on stability of fuzzy Cohen-Grossberg neural networks with time-varying delays,” IEEE Transactions on Systems, Man, and Cybernetics, Part B, vol. 37, no. 3, pp. 733-741, 2007. · doi:10.1109/TSMCB.2006.887951
[16] Q. Song and Z. Wang, “Stability analysis of impulsive stochastic Cohen-Grossberg neural networks with mixed time delays,” Physica A, vol. 387, no. 13, pp. 3314-3326, 2008. · doi:10.1016/j.physa.2008.01.079
[17] C. Bai, “Stability analysis of Cohen-Grossberg BAM neural networks with delays and impulses,” Chaos, Solitons & Fractals, vol. 35, no. 2, pp. 263-267, 2008. · Zbl 1166.34328 · doi:10.1016/j.chaos.2006.05.043
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