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The function cascade synchronization method and applications. (English) Zbl 1221.93124
Summary: A new function cascade synchronization method of chaos system is proposed to achieve generalized projective synchronization for chaotic systems. Based on Laypunov stability, the proposed synchronization technique is applied to three famous chaotic systems: the unified chaotic system, Liu system and Rössler system, which can make the states of two identical chaotic systems asymptotically synchronized by choosing different special suitable error functions. Numerical simulations are presented to show the effectiveness.
93C40Adaptive control systems
37D45Strange attractors, chaotic dynamics
34H10Chaos control (ODE)
37N35Dynamical systems in control
[1]Pecora, L. M.; Carroll, T. L.: Synchronization in chaotic systems, Phys rev lett 64, 821-824 (1990)
[2]Ott, E.; Grebogi, C.; Yorke, J. A.: Controlling chaos, Phys rev lett 64, 1196-1199 (1990) · Zbl 0964.37501 · doi:10.1103/PhysRevLett.64.1196
[3]Park, J. H.: Adaptive synchronization of a unified chaotic systems with an uncertain parameter, Int J nonlin sci numer simu 6, 201-206 (2005)
[4]Carroll, T. L.; Pecora, L. M.: Synchronizing chaotic circuits, IEEE trans circ syst 38, 453 (1991)
[5]Wang, Y. W.; Guan, Z. H.; Wang, H. O.: Feedback an adaptive control for the synchronization of Chen system via a single variable, Phys lett A 312, 34-40 (2003) · Zbl 1024.37053 · doi:10.1016/S0375-9601(03)00573-5
[6]Lu, J. A.; Wu, X. Q.; Han, X.; Lü, J. H.: Adaptive feedback synchronization of a unified chaotic system, Phys lett A 329, 327-333 (2004) · Zbl 1209.93119 · doi:10.1016/j.physleta.2004.07.024
[7]Elabbasy, E. M.; Agiza, H. N.; El-Dessoky, M. M.: Adaptive synchronization of Lü system with uncertain parameters, Chaos solit fract 21, 657-667 (2004) · Zbl 1062.34039 · doi:10.1016/j.chaos.2003.12.028
[8]Bowong, S.: Adaptive synchronization between two different chaotic dynamical systems, Commun nonlinear sci numer simul 12, No. 6, 976-985 (2007) · Zbl 1115.37030 · doi:10.1016/j.cnsns.2005.10.003
[9]Yan, J. P.; Li, C. P.: Generalized projective synchronization of a unified chaotic system, Chaos solit fract 26, 1119-1124 (2005) · Zbl 1073.65147 · doi:10.1016/j.chaos.2005.02.034
[10]Lu, J. A.; Wu, X. Q.; Han, X.; Lü, J. H.: Synchronization of a unified chaotic system and the application in secure communication, Phys lett A 305, 365-370 (2002) · Zbl 1005.37012 · doi:10.1016/S0375-9601(02)01497-4
[11]Wen, G. L.; Xu, D.: Nonlinear observer control for full – state projective synchronization in chaotic continuous – time systems, Chaos solit fract 26, 71-77 (2005) · Zbl 1122.93311 · doi:10.1016/j.chaos.2004.09.117
[12]Hu, M. F.; Xu, Z. Y.; Zhang, R.: Full state hybrid projective synchronization in continuous-time chaotic (hyperchaotic) systems, Commun nonlinear sci numer simul (2006)
[13]Ruan, J.; Li, L. J.: An improved method in synchronization of chaotic systems, Commun nonlinear sci numer simul 3, No. 3, 140-143 (1998) · Zbl 1122.37309 · doi:10.1016/S1007-5704(98)90002-8
[14]Zeng, X. P.; Ruan, J.; Li, L. J.: Synchronization of chaotic systems by feedback, Commun nonlinear sci numer simul 4, No. 2, 162-165 (1999) · Zbl 1044.37558 · doi:10.1016/S1007-5704(99)90032-1 · doi:http://ns.nlspku.ac.cn/journal/abs14/17.html
[15]Carroll, T. L.; Pecora, L. M.: Cascading synchronized chaotic, Physica D 67, 126 (1993) · Zbl 0800.94100 · doi:10.1016/0167-2789(93)90201-B
[16]Abarbanel, H. D. I.; Rulkov, N. F.; Sushchik, M. M.: Generalized synchronization of chaos: the auxiliary system approach, Phys rev E 53, 4528-4535 (1996)
[17]Güémez, J.; Matías, M. A.: Modified method for synchronizing and cascading chaotic systems, Phys rev E 52, R2145-R2148 (1995)
[18]Wang, G. R.; Yu, X. L.; Chen, S. G.: Chaos, synchronization and application of chaos, (2001)
[19]Chen, Y.; Li, X.: Function projective synchronization between two identical chaotic systems, Int J mod phys C 18, No. 5, 560-570 (2007) · Zbl 1139.37301 · doi:10.1142/S0129183107010607
[20]Lü, J. H.; Chen, G. R.: A new chaotic attractor coined, Int J bifurcat chaos 12, No. 3, 659-661 (2002) · Zbl 1063.34510 · doi:10.1142/S0218127402004620
[21]Lü, J. H.; Chen, G. R.; Cheng, D. Z.; Celikovsky, S.: Bridge the gap between the Lorenz system and the Chen system, Int J bifurcat chaos 12, No. 12, 2917-2926 (2002) · Zbl 1043.37026 · doi:10.1142/S021812740200631X
[22]Lü, J. H.; Zhou, T. S.; Zhang, S. C.: Chaos synchronization between linearly coupled chaotic systems, Chaos solit fract 14, No. 4, 529-541 (2002) · Zbl 1067.37043 · doi:10.1016/S0960-0779(02)00005-X
[23]Rössler, O. E.: An equation for continuous chaos, Phys lett A 57, 397-398 (1976)
[24]Liu, C. X.; Liu, T.; Liu, L.; Liu, K.: A new chaotic attractor, Chaos solit fract 22, 1031-1038 (2004)
[25]Lorenz, E. N.: Deterministic non-periods flows, J atmos sci 20, 130-141 (1963)
[26]Chen, G. R.; Ueta, T.: Yet another chaotic attractor, Int J bifurcat chaos 9, 1465-1466 (1999) · Zbl 0962.37013 · doi:10.1142/S0218127499001024
[27]Sparrow, C.: The Lorenz equations: bifurcations, chaos, and strange attractors, (1982)