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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.

MSC:
93D15 Stabilization of systems by feedback
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37N35 Dynamical systems in control
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[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 Berlin
[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
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