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Stability and periodicity in delayed cellular neural networks with impulsive effects. (English) Zbl 1115.34072

Global exponential stability and periodicity are investigated for delayed cellular neural networks with impulsive effects. Some sufficient conditions are derived for checking the global exponential stability. The existence of a periodic solution for this system is based on the Halanay inequality and a fixed point theorem. The criteria given are easily verifiable, possess many adjustable parameters, and depend on the impulses.

MSC:

34K20 Stability theory of functional-differential equations
34K45 Functional-differential equations with impulses
34K13 Periodic solutions to functional-differential equations
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[1] Akca, H.; Alassar, R.; Covachev, V.; Covachev, Z.; Zahrani, E.A., Continuous-time additive Hopfield-type neural networks with impulses, J. math. anal. appl., 290, 436-451, (2004) · Zbl 1057.68083
[2] Beckenbach, E.F.; Bellman, R., Inequalities, (1965), Springer Berlin, Germany · Zbl 0128.27401
[3] 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
[4] Cao, J.; Wang, J., Global asymptotic stability of a general class of recurrent neural networks with time-varying delays, IEEE trans. circuits syst.-I, 50, 34-44, (2003) · Zbl 1368.34084
[5] Chua, L.O.; Yang, L., Cellular neural networks: theory and applications, IEEE trans. circuits and syst., 35, 1257-1290, (1988) · Zbl 0663.94022
[6] Gopalsamy, K., Stability of artificial neural networks with impulses, Appl. math. comput., 154, 783-813, (2004) · Zbl 1058.34008
[7] Guan, Z.; Chen, G., On delayed impulsive Hopfield neural networks, Neural networks, 12, 273-280, (1999)
[8] Guan, Z.; Lam, J.; Chen, G., On impulsive autoassociative neural networks, Neural networks, 13, 63-69, (2000)
[9] Guo, S.; Huang, L., Periodic oscillation for a class of neural networks with variable coefficients, Nonlinear anal., 6, 545-561, (2005) · Zbl 1080.34051
[10] Lakshmikanthan, V.; Bainov, D.D.; Simeonov, P.S., Theory of impulsive differential equations, (1989), World Scientific Singapore
[11] Liao, X.; Wang, J., Algebraic criteria for global exponential stability of cellular neural networks with multiple time delays, IEEE trans. circuits syst.-I, 50, 268-275, (2003) · Zbl 1368.93504
[12] Liu, X.; Ballinger, G., Uniform asymptotic stability of impulsive delay differential equations, Comput. math. appl., 41, 903-915, (2001) · Zbl 0989.34061
[13] Nieto, J.J., Basic theory for nonresonance impulsive periodic problems of first order, J. math. anal. appl., 205, 423-433, (1997) · Zbl 0870.34009
[14] T. Roska, T. Boros, P. Thirn, L.O. Chua, Detecting simple motion using cellular neural networks, in: Proceedings of the 1990 IEEE International Workshop on Cellular Neural Networks and Their Applications, 127-138.
[15] Venetianer, P.L.; Roska, T., Image compression by cellular neural networks, IEEE trans. circuits syst.-I, 45, 205-215, (1998)
[16] Xu, D.; Yang, Z., Impulsive delay differential inequality and stability of neural networks, J. math. anal. appl., 305, 107-120, (2005) · Zbl 1091.34046
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