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Robust synchronization of coupled delayed neural networks under general impulsive control. (English) Zbl 1198.34129
Summary: This paper investigates the robust synchronization model of coupled delayed neural networks under general impulsive control. The uncertain coupling function can be linear or nonlinear in the network. By using Lyapunov functions and analysis technique, we get a result to ensure the general robust impulsive synchronization of coupled delayed networks.
Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

MSC:
34H15 Stabilization of solutions to ordinary differential equations
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37N35 Dynamical systems in control
92B20 Neural networks for/in biological studies, artificial life and related topics
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[1] Pecora, L.M.; Carroll, T.L., Synchronization in chaotic system, Phys rev lett, 64, 821-824, (1990) · Zbl 0938.37019
[2] Wu, C.W.; Chua, L.O., Synchronization in an array of linearly coupled dynamical systems, IEEE trans circuits syst I, 42, 430-447, (1995) · Zbl 0867.93042
[3] Pecora, L.M.; Carroll, T.L.; Johnson, G.; Mar, D.; Fink, K.S., Synchronization stability in coupled oscillator arrays: solution for arbitrary congfiurations, Int J bifur chaos, 10, 273-290, (2000) · Zbl 1090.34542
[4] Pogromsky, A.; Santoboni, G.; Nijmeijer, H., Partial synchronization from symmetry toward stability, Physica D, 172, 65-87, (2002) · Zbl 1008.37012
[5] Dogaru, R., Universality and emergent computation in cellular neural networks, (2003), World Scientific Singapore · Zbl 1058.68076
[6] Wang, X.; Chen, G., Complex networks: small-world, free-scale, and beyond, IEEE circuits syst mag, 3, 6-20, (2003)
[7] Zhou, J.; Chen, T.P.; Xiang, L., Robust synchronization of delayed neural networks based on adaptive control and parameters identification, Chaos, solitons & fractals, 27, 905-913, (2006) · Zbl 1091.93032
[8] Millerioux, G.; Daafouz, J., Input independent chaos synchronization of switched systems, IEEE trans automat contr, 49, 1182-1186, (2004) · Zbl 1365.93266
[9] Song, Q.K.; Cao, J.D., Synchronization and anti-synchronization for chaotic systems, Chaos, solitons & fractals, 33, 929-939, (2007) · Zbl 1133.37313
[10] Cao, J.D.; Lu, J.Q., Adaptive synchronization of neural networks with or without time-varying delays, Chaos, 16, 1, 013133, (2006) · Zbl 1144.37331
[11] Chen, G.R.; Zhou, J.; Liu, Z.R., Global synchronization of coupled delayed neural networks and applications to chaotic CNN model, Int J bifur chaos, 17, 2229-2240, (2004) · Zbl 1077.37506
[12] Lu, W.L.; Chen, T.P., Synchronization of coupled connected neural networks with delays, IEEE trans circuits syst I, 51, 2491-2503, (2004) · Zbl 1371.34118
[13] Lu, J.Q.; Daniel, WCHo, Local and global synchronization in general complex dynamical networks with delay coupling, Chaos, solitons & fractals, 37, 5, 1497-1510, (2008) · Zbl 1142.93426
[14] Cui BT, Lou XY. Synchronization of chaotic recurrent neural networks with time-varying delays using nonlinear feedback control. Chaos, Solitons & Fractals, in press, doi:10.1016/j.chaos.2007.01.100.
[15] Lu, H.T.; Chen, G.R., Global synchronization in an array of linearly coupled delayed neural networks with an arbitrary coupling matrix, Int J bifur chaos, 16, 3357-3368, (2006) · Zbl 1127.34046
[16] Lakshmikantham, V.; Bainov, D.; Simeonov, P.S., Theory of impulsive differential equations, (1989), World Scientific Singapore · Zbl 0719.34002
[17] Yang, T., Impulsive systems and control: theory and applications, (2001), Nova Science Publishers New York
[18] Sun, J.T.; Zhang, Y.P.; Wu, Q., Less conservative conditions for asymptotic stability of impulsive control systems, IEEE trans auto contr, 48, 829-831, (2003) · Zbl 1364.93691
[19] Zhang, Y.; Sun, J.T., Stability of impulsive neural networks with time delays, Phys lett A, 348, 44-50, (2005) · Zbl 1195.93122
[20] Xia, Y.H.; Cao, J.D.; Cheng, S.S., Global exponential stability of delayed cellular neural networks with impulses, Neurocomputing, 70, 2495-2501, (2007)
[21] Wu, H.J.; Sun, J.T., p-moment stability of stochastic differential equations with impulsive jump and Markovian switching, Automatica, 42, 1753-1759, (2006) · Zbl 1114.93092
[22] Itoh, M.; Yang, T.; Chua, L.O., Experimental study of impulsive synchronization of chaotic and hyperchaotic circuits, Int J bifur chaos, 9, 1393-1424, (1999) · Zbl 0963.34029
[23] Sun, J.T.; Zhang, Y.P.; Qiao, F.; Wu, Q.D., Some impulsive synchronization criterions for coupled chaotic systems via unidirectional linear error feedback approach, Chaos, solitons & fractals, 19, 1049-1055, (2004) · Zbl 1069.37029
[24] Liu, B.; Liu, X.Z.; Chen, G.R., Robust impulsive synchronization of uncertain dynamical networks, IEEE trans circuits syst I, 52, 1431-1441, (2005) · Zbl 1374.82016
[25] Guan, Z.H.; Hill, D.; Shen, X., On hybrid impulsive and switching systems and application to nonlinear control, IEEE trans auto contr, 50, 1058-1062, (2005) · Zbl 1365.93347
[26] Chen, D.L.; Sun, J.T.; Huang, C.S., Impulsive control and synchronization of general chaotic system, Chaos, solitons & fractals, 28, 213-218, (2006) · Zbl 1091.93023
[27] Li, C.D.; Liao, X.F.; Yang, X.F.; Huang, T.W., Impulsive stabilization and synchronization of a class of chaotic delay systems, Chaos, 15, 4, 043103, (2005) · Zbl 1144.37371
[28] Zhang, R.; Xu, Z.Y.; Yang, S.X.; He, X.M., Generalized synchronization via impulsive control, Chaos, solitons & fractals, 38, 1, 97-105, (2008) · Zbl 1142.34355
[29] Li, P.; Cao, J.D.; Wang, Z.D., Robust impulsive synchronization of coupled delayed neural networks with uncertainties, Physica A, 373, 261-272, (2007)
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