×

Impulsive generalized synchronization for a class of nonlinear discrete chaotic systems. (English) Zbl 1221.93171

Summary: The problem of impulsive generalized synchronization for a class of nonlinear discrete chaotic systems is investigated in this paper. Firstly the response system is constructed based on the impulsive control theory. Then by the asymptotic stability criteria of discrete systems with impulsive effects, some sufficient conditions for asymptotic \(H\)-synchronization between the drive system and response system are obtained. Numerical simulations are given to show the effectiveness of the proposed method.

MSC:

93C55 Discrete-time control/observation systems
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37N35 Dynamical systems in control
39A28 Bifurcation theory for difference equations
93D15 Stabilization of systems by feedback
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Pecoral, L. M.; Carroll, T. L., Synchronization in chaotic systems, Phys Rev Lett, 64, 821-824 (1990) · Zbl 0938.37019
[2] Chen, G. R.; Yu, X. H., On time-delay feedback control of chaotic systems, IEEE T Circuits Syst I, 64, 767-772 (1999) · Zbl 0951.93034
[3] Yang, X. S.; Chen, G., Some observer-based criteria for discrete-time generalized chaos synchronization, Chaos Soliton Fract, 13, 1303-1308 (2002) · Zbl 1006.93580
[4] Lu, J. G.; Xi, Y. G., Line generalized synchronization of continuous-time chaotic systems, Chaos Soliton Fract, 17, 825-831 (2003) · Zbl 1043.93518
[5] Wang, Y. W.; Guan, Z. H., Generalized synchronization of continuous chaotic system, Chaos Soliton Fract, 27, 97-101 (2006) · Zbl 1083.37515
[6] Meng, J.; Wang, X. Y., Generalized projective synchronization of a class of delayed neural networks, Mod Phys Lett B, 22, 181-190 (2008) · Zbl 1158.93026
[7] Lu, J. F., Generalized (complete, lag, anticipated) synchronization of discrete-time chaotic systems, Commun Nonlinear Sci Numer Simul, 13, 1851-1859 (2008) · Zbl 1221.37216
[8] Huang, Y. H.; Wang, Y. W.; Xiao, J. W., Generalized lag-synchronization of continuous chaotic system, Chaos Soliton Fract, 40, 766-770 (2009) · Zbl 1197.37030
[9] Ma, Z. J.; Liu, Z. R.; Zhang, G., Generalized synchronization of discrete systems, Appl Math Mech, 28, 609-614 (2007) · Zbl 1231.37021
[10] Li, G. H., Generalized synchronization of chaos based on suitable separation, Chaos Soliton Fract, 39, 2056-2062 (2009) · Zbl 1197.37035
[11] Zhang, G.; Liu, Z. R.; Ma, Z. J., Generalized synchronization of different dimensional chaotic dynamical systems, Chaos Soliton Fract, 32, 773-779 (2009) · Zbl 1138.37316
[12] Zheng, S.; Dong, G. G.; Bi, Q. S., Adaptive modified function projective synchronization of hyperchaotic systems with unknown parameters, Commun Nonlinear Sci Numer Simul, 15, 3547-3556 (2010) · Zbl 1222.93205
[13] Bainov, D. D.; Simeonov, P. S., Systems with impulse effect: stability, theory and applications (1989), Halsted Press: Halsted Press New York · Zbl 0676.34035
[14] Lakshmikantham, V.; Bainov, D. D.; Simeonov, P. S., Theory of impulsive differential equations (1989), World Scientific: World Scientific Singapore · Zbl 0719.34002
[15] Yang, T., Impulsive control theory (2001), Springer: Springer Berlin
[16] Jiang, H. B.; Yu, J. J.; Zhou, C. G., Robust fuzzy control of nonlinear fuzzy impulsive systems with time-varying delay, IEE Control Theory Appl, 2, 654-661 (2008)
[17] Yang, T.; Yang, L. B.; Yang, C. M., Impulsive synchronization of Lorenz systems, Phys Lett A, 226, 349-354 (1997)
[18] Sun, J. T.; Zhang, Y. P.; Wu, Q. D., Impulsive control for the stabilization and synchronization of Lorenz systems, Phys Lett A, 298, 153-160 (2002) · Zbl 0995.37021
[19] Zhang, X. H.; Liao, X. F.; Li, C. D., Impulsive control, complete and lag synchronization of unified chaotic system with continuous periodic switch, Chaos Soliton Fract, 26, 845-854 (2005) · Zbl 1093.93025
[20] Jiang, H. B., Hybrid adaptive and impulsive synchronization of uncertain complex dynamical networks by the generalized Barbalat’s lemma, IET Control Theory Appl, 3, 1330-1340 (2009)
[21] Zheng, S.; Dong, G. G.; Bi, Q. S., Impulsive synchronization of complex networks with non-delayed and delayed coupling, Phys Lett A, 373, 4255-4259 (2009) · Zbl 1234.05220
[22] Zhang, L. P.; Jiang, H. B.; Bi, Q. S., Reliable impulsive synchronization for a class of nonlinear chaotic systems, Chinese Phys B, 19 (2010), 010507-5
[23] Jiang, H. B.; Bi, Q. S., Impulsive synchronization of networked nonlinear dynamical systems, Phys Lett A, 374, 2723-2729 (2010) · Zbl 1237.34101
[24] Liu, B.; Liu, X. Z., Robust stability of uncertain discrete impulsive systems, IEEE T Circuits Syst II, 54, 455-459 (2007)
[25] Zhang, Y. P.; Sun, J. T.; Feng, G., Impulsive control of discrete systems with time delay, IEEE T Automat Contr, 54, 830-834 (2009)
[26] Zheng, Y. A.; Nian, Y. B.; Liu, Z. R., Impulsive control for the stabilization of discrete chaotic system, Chinese Phys Lett, 19, 1251-1253 (2002)
[27] Xu, H. L.; Teo, K. L., Stabilizability of discrete chaotic systems via unified impulsive control, Phys Lett A, 374, 235-240 (2009) · Zbl 1235.70138
[28] Zheng, Y. A.; Nian, Y. B.; Liu, Z. R., Impulsive synchronization of discrete chaotic systems, Chinese Phys Lett, 20, 199-201 (2003)
[29] Zhang, L. P.; Jiang, H. B.; Bi, Q. S., Reliable impulsive lag synchronization for a class of nonlinear discrete chaotic systems, Nonlinear Dynam, 59, 529-534 (2010) · Zbl 1189.93085
[30] Zhang, R.; Xu, Z. Y.; He, X. M., Impulsive generalized synchronization of chaotic system, Chinese Phys, 16, 1912-1917 (2007)
[31] Zhang, R.; Xu, Z. Y.; Yang, S. X.; He, X. M., Generalized synchronization via impulsive control, Chaos Soliton Fract, 38, 97-105 (2008) · Zbl 1142.34355
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.