Complete and lag synchronization of hyperchaotic systems using small impulses. (English) Zbl 1129.93508

Summary: The complete synchronization and lag synchronization of the hyperchaotic systems are restated as the impulsive control issues. Some simple and easy-to-be-verified stability criteria for impulsive control systems are derived, and then applied to synchronize and lag-synchronize the hyperchaotic Chua’s oscillators. Moreover, the boundaries of the stable regions are also estimated. Some computer simulations illustrate the effectiveness of our results.


93D15 Stabilization of systems by feedback
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37N35 Dynamical systems in control
Full Text: DOI


[1] Pecora, L. M.; Carroll, T. L., Synchronization in chaotic systems, Phys. Rev. Lett., 64, 821-824 (1990) · Zbl 0938.37019
[2] Jiang, G.-P.; Zheng, W. X.; Chen, G., Global chaos synchronization with channel time-delay, Chaos, Solitons & Fractals, 20, 267-275 (2004) · Zbl 1045.34021
[3] Sun, J., Some global synchronization criteria for coupled delay-systems via unidirectional linear error feedback approach, Chaos, Solitons & Fractals, 19, 789-794 (2004) · Zbl 1135.34341
[4] Grassi, G.; Mascolo, S., Nonlinear observer design to synchronize hyperchaotic systems via a scalar signal, IEEE Trans. CAS, 44, 10, 1143-1147 (1997)
[5] Grassi, G.; Mascolo, S., Synchronizing hyperchaotic systems by observer design, IEEE Trans. CAS, 46, 4 (1999) · Zbl 1159.94361
[6] Wang, C.-C.; Su, J.-P., A new adaptive variable structure control for chaotic synchronization and secure communication, Chaos, Solitons & Fractals, 20, 967-977 (2004) · Zbl 1050.93036
[7] Wang, Y.; Guan, Z.-H.; Wen, X., Adaptive synchronization for Chen chaotic system with fully unknown parameters, Chaos, Solitons & Fractals, 19, 899-903 (2004) · Zbl 1053.37528
[8] Duan, C. K.; Yang, S. S., Synchronizing hyperchaos with a scalar signal by parameter controlling, Phys. Lett. A, 229, 151-155 (1997) · Zbl 1043.37502
[9] Chen, S.; Yang, Q.; Wang, C., Impulsive control and synchronization of unified chaotic system, Chaos, Solitons & Fractals, 20, 751-758 (2004) · Zbl 1050.93051
[10] Sun, J.; Zhang, Y.; Qiao, F.; Wu, Q., Some impulsive synchronization criterions for coupled chaotic systems via unidirectional linear error feedback approach, Chaos, Solitons & Fractals, 19, 1049-1055 (2004) · Zbl 1069.37029
[11] Bu, S.; Wang, S.; Ye, H., An algorithm based on variable feedback to synchronize chaotic and hyperchaotic systems, Physica D, 164, 45-52 (2002) · Zbl 1008.37016
[12] Shahverdiev, E. M.; Sivaprakasam, S.; Shore, K. A., Lag times and parameter mismatches in synchronization of unidirectionally coupled chaotic external cavity semiconductor lasers, Phys. Rev. E, 66, 037202 (2002)
[13] Taherion1, S.; Lai, Y.-C., Observability of lag synchronization of coupled chaotic oscillators, Phys. Rev. E, 59, R6247-R6250 (1999)
[14] Barsella, A.; Lepers, C., Chaotic lag synchronization and pulse-induced transient chaos in lasers coupled by saturable absorber, Opt. Commun., 205, 397-403 (2002)
[15] Huang, X.; Xu, J.; huang, W.; Zhu, F., Error analysis for delay synchronization of chaotic system, Acta Phys. Sin., 50, 2296-2302 (2001)
[16] Shahverdiev, E. M.; Sivaprakasam, S.; Shore, K. A., Lag synchronization in time-delayed systems, Phys. Lett. A, 292, 320-324 (2002) · Zbl 0979.37022
[17] Yang, T., Impulsive control theory (2001), Springer-Verlag: Springer-Verlag Berlin · Zbl 0996.93003
[18] Li, Z. G.; Wen, C. Y.; Soh, Y. C., Analysis and design of impulsive control systems, IEEE Trans. Autom. Control, 46, 6, 894-903 (2001) · Zbl 1001.93068
[19] Yang, T.; Leon, O.; Chua, Impulsive stability for control and synchronization of chaotic systems: theory and Application to secure communication, IEEE Trans. CAS-1, 44, 10, 976-988 (1997)
[20] Yang, T., Impulsive control, IEEE Trans. Autom. Control, 44, 5, 1081-1083 (1999) · Zbl 0954.49022
[21] Chua, L. O.; Yang, T., Cellular neural networks: theory, IEEE Trans. Circ. Syst., 35, 1257-1272 (1998) · Zbl 0663.94022
[22] Kapitaniak, T.; Chua, L. O.; Zhong, G. Q., Experimental hyperchaos in coupled Chua’s circuits, IEEE Trans. CAS-1, 41, 499-503 (1994)
[23] Cafagna, D.; Grassi, G., Synchronizing hyperchaos using a scalar signal: a unified framework for systems with one or several non-linearities, Circ. Syst., 28-31, 575-580 (2002), APCCAS ’02. 2002, Asia-Pacific Conference
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.