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Synchronization of the unified chaotic systems via active control. (English) Zbl 1091.93030

Summary: This paper investigates the synchronization of coupled unified chaotic systems via active control. The synchronization is given in the slave-master scheme and the controller ensures that the states of the controlled chaotic slave system exponentially synchronize with the state of the master system. Numerical simulations are provided for illustration and verification of the proposed method.

MSC:

93D15 Stabilization of systems by feedback
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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[1] Lorenz, E., Deterministic nonperiodic flows, J Atmos Sci, 20, 130-141 (1963) · Zbl 1417.37129
[2] Sparrow, C., The Lorenz equations: bifurcations, chaos, and strange attractors, Appl Math Sci, 41 (1982) · Zbl 0504.58001
[3] Stewart, H. B., Visualization of the Lorenz system, Physica D: Nonlinear Phenom, 18, 479-480 (1986) · Zbl 0594.58049
[4] Chen, C. C.; Tsai, C. H.; Fu, C. C., Rich dynamics in self-interacting Lorenz systems, Phys Lett A, 194, 265-271 (1994) · Zbl 0959.37509
[5] Abdelkader, M. A., Generalized Lorenz-type systems, J Math Anal Appl, 199, 1-13 (1996) · Zbl 0857.34001
[6] Bai, E. W.; Lonngren, K. E., Synchronization of two Lorenz systems using active control, Chaos, Solitons & Fractals, 8, 51-58 (1997) · Zbl 1079.37515
[7] Liao, T. L., Adaptive synchronization of two Lorenz systems, Chaos, Solitons & Fractals, 9, 1555-1561 (1998) · Zbl 1047.37502
[8] Li, D.; Lu, J.; Wu, X., Linearly coupled synchronization of the unified chaotic systems and the Lorenz systems, Chaos, Solitons & Fractals, 23, 79-85 (2005) · Zbl 1063.37030
[9] Chen, G. R.; Ueta, T., Yet another chaotic attractor, Int J Bifurcat Chaos, 9, 146-156 (1999) · Zbl 0962.37013
[10] Lü, J.; Chen, G.; Cheng, D., A new chaotic system and beyond: the generalized Lorenz-like system, Int J Bifurcat Chaos, 14, 1507-1537 (2004) · Zbl 1129.37323
[11] Lü, J.; Chen, G.; Cheng, D., Bridge the gap between the Lorenz system and the Chen system, Int J Bifurcat Chaos, 12, 2917-2926 (2002) · Zbl 1043.37026
[12] Bai, E. W.; Lonngren, K. E., Sequential synchronization of two Lorenz systems using active control, Chaos, Solitons & Fractals, 11, 1041-1044 (2000) · Zbl 0985.37106
[13] Lü, J., Chaos synchronization between linearly coupled chaotic systems, Chaos, Solitons & Fractals, 14, 529-541 (2002) · Zbl 1067.37043
[14] Chen HK. Synchronization of two different chaotic systems: a new system and each of the dynamical systems Lorenz, Chen and Lü. Chaos, Solitons & Fractals. Available online at www.sciencedirect.com; Chen HK. Synchronization of two different chaotic systems: a new system and each of the dynamical systems Lorenz, Chen and Lü. Chaos, Solitons & Fractals. Available online at www.sciencedirect.com
[15] Lonngren, K. E.; Bai, E. W.; Uçar, A., Dynamics and synchronization of the Hastings-Powell model of the food chain, Chaos, Solitons & Fractals, 20, 387-393 (2004) · Zbl 1045.37061
[16] Uçar, A.; Lonngren, K. E.; Bai, E. W., Synchronization of chaotic behavior in nonlinear Bloch equations, Phys Lett A, 314, 96-101 (2004) · Zbl 1035.34037
[17] Lonngren, K. E.; Bai, E. W., On the Uçar prototype model, Int J Eng Sci, 40, 1855-1857 (2002) · Zbl 1211.34089
[18] Goodwin, G. C.; Graebe, S. F.; Salgado, M. E., Control system design (2001), Prentice Hall: Prentice Hall New Jersey
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