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Full state hybrid projective synchronization of a general class of chaotic maps. (English) Zbl 1221.34121

Summary: A systematic and concrete scheme is proposed to study the full state hybrid projective synchronization (FSHPS) of a general class of chaotic maps based on the active control idea. The scheme is accessible to the FSHPS of two identical or different chaotic maps. The 3D generalized Hénon map and 3D discrete-time Grassi-Miller map are chosen to illustrate the proposed scheme, and numerical simulations are given to show the effectiveness of the proposed chaos synchronization method.

MSC:

34C28 Complex behavior and chaotic systems of ordinary differential equations
37N35 Dynamical systems in control
34D06 Synchronization of solutions to ordinary differential equations
39A10 Additive difference equations
93C55 Discrete-time control/observation systems
Full Text: DOI

References:

[1] Fujisaka, H.; Yamada, T., Stability theory of synchronized motion in coupled-oscillator systems, Prog Theor Phys, 69, 32-47 (1983) · Zbl 1171.70306
[2] Perora, L. M.; Carroll, T. L., Synchronization in chaotic systems, Phys Rev Lett, 64, 821-824 (1990) · Zbl 0938.37019
[3] Boccaletti, S.; Kurths, J.; Osipov, G.; Valladares, D. L.; Zhou, C. S., The synchronization of chaotic systems, Phys Rep, 366, 1-101 (2002) · Zbl 0995.37022
[4] Park, E. H.; Zaks, M. A.; Kurths, J., Phase synchronization in the forced Lorenz system, Phys Rev E, 60, 6627-6638 (1999) · Zbl 1062.37502
[5] Hu, J.; Chen, S. H.; Chen, L., Adaptive control for anti-synchronization of Chua’s chaotic system, Phys Lett A, 339, 455-460 (2005) · Zbl 1145.93366
[6] Mainieri, R.; Rehacek, J., Projective synchronization in three-dimensional chaotic systems, Phys Rev Lett, 82, 3042-3045 (1999)
[7] Xu, D., Control of projective synchronization in chaotic systems, Phys Rev E, 63, 2, 027201 (2001)
[8] Xu, D.; Li, Z.; Bishop, S. R., Manipulating the scaling factor of projective synchronization in three-dimensional chaotic systems, Chaos, 11, 3, 439-442 (2001) · Zbl 0996.37075
[9] Xu, D.; Chee, C. Y., Controlling the ultimate state of projective synchronization in chaotic systems of arbitrary dimension, Phys Rev E, 66, 4, 046218 (2002)
[10] Wen, G. L.; Xu, D., Observer-based control for full-state projective synchronization of a general class of chaotic maps in any dimension, Phys Lett A, 333, 420-425 (2004) · Zbl 1123.37326
[11] Kocarev, L.; Parlitz, U., Generalized synchronization, predictability and equivalence of unidirectionally coupled dynamical systems, Phys Rev Lett, 76, 1816-1819 (1996)
[12] Yang, X. S., Concepts of synchronization in dynamical systems, Phys Lett A, 260, 340-344 (1999) · Zbl 0939.34041
[13] Yan, Z. Y., \(Q-S\) synchronization in 3D Henon-Like map and generalized Henon map via a scalar controller, Phys Lett A, 342, 309-317 (2005) · Zbl 1222.37093
[14] Hu MF, Xu ZY, Zhang R. Full state hybrid projective synchronization in continuous-time chaotic (hyperchaotic) systems. Commun Nonlinear Sci Numer Simul, in press, doi:10.1016/j.cnsns.2006.05.003; Hu MF, Xu ZY, Zhang R. Full state hybrid projective synchronization in continuous-time chaotic (hyperchaotic) systems. Commun Nonlinear Sci Numer Simul, in press, doi:10.1016/j.cnsns.2006.05.003 · Zbl 1123.37013
[15] Chee, C. Y.; Xu, D., Secure digital communication using controlled projective synchronization of chaos, Chaos, Solitons Fract, 23, 3, 1063-1070 (2005) · Zbl 1068.94010
[16] Yan, Z. Y., A nonlinear control scheme to anticipated and complete synchronization in discrete-time chaotic(hyperchaotic) systems, Phys Lett A, 343, 423-431 (2005) · Zbl 1194.37065
[17] Bai, E. W.; Lonngren, K. E., Synchronization of two Lorenz systems using active control, Chaos, Solitons Fract, 8, 51-58 (1997) · Zbl 1079.37515
[18] Yassen, M. T., Chaos synchronization between two different chaotic systems using active control, Chaos, Solitons Fract, 23, 131-140 (2005) · Zbl 1091.93520
[19] Stefanski, K., Modelling chaos and hyperchaos with 3D maps, Chaos, Solitons Fract, 9, 83-93 (1998) · Zbl 0934.37033
[20] Grassi, G.; Miller, D. A., Theory and experimental realization of observer-based discrete-time hyperchaos synchronization, IEEE Trans Circ Syst I, 49, 373-378 (2002)
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