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Projective synchronization of a new hyperchaotic Lorenz system. (English) Zbl 1209.93105
Summary: This Letter mainly concerns projective synchronization (PS) of a new hyperchaotic Lorenz system. PS with both identical and different scaling factors between two hyperchaotic Lorenz systems are realized. A general sufficient condition for PS in a certain class of chaotic (hyperchaotic) system with uncertainties is obtained by using adaptive control. Numerical simulations are performed to verify and illustrate the analytical results.

MSC:
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
34H10 Chaos control for problems involving ordinary differential equations
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References:
[1] Pecora, L.M.; Carroll, T.L., Phys. rev. lett., 64, 821, (1990)
[2] Kocarev, L.; Parlitz, U., Phys. rev. lett., 76, 1816, (1996)
[3] Rosenblum, M.G.; Pikovsky, A.S.; Kurths, J., Phys. rev. lett., 76, 1804, (1996)
[4] Cao, L.; Lai, Y., Phys. rev. E, 58, 382, (1998)
[5] Rosenblum, M.G.; Pikovsky, A.S.; Kurths, J., Phys. rev. lett., 78, 4193, (1997)
[6] Mainieri, R.; Rehacek, J., Phys. rev. lett., 12, 3042, (1999)
[7] Xu, D.; Ong, W.L.; Li, Z., Phys. lett. A, 305, 167, (2002)
[8] Xu, D.; Chee, C.Y.; Li, C., Chaos solitons fractals, 22, 175, (2004)
[9] Wen, G.; Xu, D., Chaos solitons fractals, 26, 71, (2005)
[10] Li, G.-H., Chaos solitons fractals, 32, 1786, (2007)
[11] Park, J.H., Chaos solitons fractals, 34, 1552, (2007)
[12] Park, J.H., Chaos solitons fractals, 34, 1154, (2007)
[13] Park, J.H., J. comput. appl. math., (2007)
[14] Hu, M.; Yang, Y.; Xu, Z., Physica A, 381, 457, (2007)
[15] Li, Z.; Xu, D., Chaos solitons fractals, 22, 477, (2004)
[16] Jia, Q., Phys. lett. A, 366, 217, (2007)
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