×

Chaos synchronization between two different chaotic systems using active control. (English) Zbl 1091.93520

Summary: This work presents chaos synchronization between two different chaotic systems by using active control. This technique is applied to achieve chaos synchronization for each pair of the dynamical systems Lorenz, Lü and Chen. Numerical simulations are shown to verify the results.

MSC:

93C10 Nonlinear systems in control theory
37N35 Dynamical systems in control
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
Full Text: DOI

References:

[1] Pecora, L. M.; Carroll, T. L., Synchronization in chaotic systems, Phys. Rev. Lett., 64, 8, 821 (1990) · Zbl 0938.37019
[2] Chen, S.; Lü, J., Parameters identification and synchronization of chaotic systems based upon adaptive control, Phys. Lett. A, 299, 353 (2002) · Zbl 0996.93016
[3] Agiza, H. N.; Yassen, M. T., Synchronization of Rossler and Chen chaotic dynamical systems using active control, Phys. Lett. A, 278, 191 (2001) · Zbl 0972.37019
[4] Ho, M.-C; Hung, Y.-C, Synchronization of two different systems by using generalized active control, Phys. Lett. A, 301, 424 (2002) · Zbl 0997.93081
[5] Huang, L.; Feng, R.; Wang, M., Synchronization of chaotic systems via nonlinear control, Phys. Lett. A, 320, 271 (2004) · Zbl 1065.93028
[6] Liao, T.-L, Adaptive synchronization of two Lorenz systems, Chaos, Solitons & Fractals, 9, 1555 (1998) · Zbl 1047.37502
[7] Liao, T.-L; Lin, S.-H, Adaptive control and synchronization of Lorenz systems, J. Franklin Inst., 336, 925 (1999) · Zbl 1051.93514
[8] Yassen, M. T., Adaptive control and synchronization of a modified Chua’s circuit system, Appl. Math. Comput., 135, 1, 113 (2001) · Zbl 1038.34041
[9] Lorenz, E. N., Deterministic non-periodic flows, J. Atmos. Sci., 20, 130 (1963) · Zbl 1417.37129
[10] Stewart, I., The Lorenz attractor exists, Nature, 406, 948 (2000)
[11] Chen, G.; Ueta, T., Yet another chaotic attractor, Int. J. Bifurcat. Chaos, 9, 1465 (1999) · Zbl 0962.37013
[12] Vanêĉek, A.; Ĉelikovskŷ, S., Control systems: from linear analysis to synthesis of chaos (1996), Prentice-Hall: Prentice-Hall London · Zbl 0874.93006
[13] Lü, J.; Chen, G., A new chaotic attractor coined, Int. J. Bifurcat. Chaos, 12, 659 (2002) · Zbl 1063.34510
[14] Lü, J.; Chen, G.; Zhang, S., Dynamical analysis of a new chaotic attractor, Int. J. Bifurcat. Chaos, 12, 1001 (2002) · Zbl 1044.37021
[15] Lü, J.; Chen, G.; Zhang, S., The compound structure of a new chaotic attractor, Chaos, Solitons & Fractals, 14, 669 (2002) · Zbl 1067.37042
[16] Richter, H., Controlling the Lorenz system: combining global and local schemes, Chaos, Solitons & Fractals, 12, 2375 (2001) · Zbl 1073.93537
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.