Adaptive added-order anti-synchronization of chaotic systems with fully unknown parameters. (English) Zbl 1179.65158

Summary: The authors investigate the chaos anti-synchronization between two different dimensional chaotic systems with fully unknown parameters via added-order. Based on the Lyapunov stability theory, the adaptive controllers with corresponding parameter update laws are designed such that the two different chaotic systems with different dimensions can be synchronized asymptotically. Finally, two illustrative numerical simulations are given to demonstrate the effectiveness of the proposed scheme.


65P20 Numerical chaos
Full Text: DOI


[1] Pecora, L. M.; Carroll, T. L., Synchronization in chaotic systems, Phys. Rev. Lett., 64, 821-824 (1990) · Zbl 0938.37019
[2] Ghosh, D., Nonlinear-observer-based synchronization scheme for multiparameter estimation, Europhys. Lett., 84, 40012 (2008)
[3] Ma, J.; Ying, H. P.; Pu, Z. S., An anti-control scheme for spiral under Lorenz chaotic signal, Chin. Phys. Lett., 22, 1065-1068 (2005)
[4] Ghosh, D.; Banerjee, S., Adaptive scheme for synchronization-based multiparameter estimation from a single chaotic time series and its applications, Phys. Rev. E, 78, 056211 (2008)
[5] Ghosh, D.; Chowdhury, A. R.; Saha, P., On the various kinds of synchronization in delayed Duffing-Van der Pol system, Comm. Nonlinear Sci. Numer. Simul., 13, 4, 790-803 (2008) · Zbl 1221.34196
[6] Ma, J.; Wang, Q. Y.; Jin, W. Y.; Ya-Feng, Xia, Control chaos in the Hindmarsh-Rose neuron by using intermittent feedback with one variable, Chin. Phys. Lett., 25, 10, 3582-3585 (2008)
[7] Bowong, S., A new adaptive chaos synchronization principle for a class of chaotic systems, Int. J. Nonlinear Sci. Numer. Simul., 6, 4, 399-409 (2005)
[8] 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
[9] Voss, H. U., Anticipating chaotic synchronization, Phys. Rev. E, 61, 5114-5115 (2000)
[10] Kocarev, L.; Parlitz, U., Generalized synchronization predictability and equivalence of unidirectionally coupled dynamical systems, Phys. Rev. Lett., 76, 1816-1819 (1996)
[11] Ghosh, D., Generalized projective synchronization in time-delayed systems: nonlinear observer approach, Chaos, 19, 013102 (2009) · Zbl 1311.34111
[12] Zhang, Y. P.; Sun, J. T., Chaotic synchronization and anti-synchronization based on suitable separation, Phys. Lett. A, 330, 442-447 (2004) · Zbl 1209.37039
[13] 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
[14] Wang, Z. L., Anti-synchronization in two non-identical hyperchaotic systems with known or unknown parameters, Comm. Nonlinear Sci. Numer. Simulat., 14, 2366-2372 (2009)
[15] Al-Sawalha, M. M.; Noorani, M. S.M., Anti-synchronization of two hyperchaotic systems via nonlinear control, Comm. Nonlinear. Sci. Numer. Simul. (2008) · Zbl 1188.70060
[16] Bazhenov, M.; Huerta, R.; Rabinovich, M. I.; Sejnowski, T., Cooperative behavior of a chain of synaptically coupled chaotic neurons, Phys. D, 116, 392-400 (1998) · Zbl 0917.92004
[17] Kotani, K.; Takamasu, K.; Ashkenazy, Y.; Stanley, H. E.; Yamamoto, Y., Model for cardio respiratory synchronization in humans, Phys. Rev. E, 65, 051923-051929 (2002)
[18] Ho, M. C.; Hung, Y.; Liua, Z.; Jiang, I., Reduced-order synchronization of chaotic systems with parameters unknown, Phys. Lett. A, 348, 251-259 (2006)
[19] Femat, R.; Perales, G., Synchronization of chaotic systems with different order, Phys. Rev. E, 65, 036226-036233 (2002)
[20] Jia, Q., Projective synchronization of a new hyperchaotic Lorenz system, Phys. Lett. A, 370, 40-45 (2007) · Zbl 1209.93105
[21] Lü, C.; Lü, T.; Lü, L. LüandK., A new chaotic attractor, Chaos Soliton Fract., 22, 1031-1038 (2004) · Zbl 1060.37027
[22] Chen, G.; Ueta, T., A new chaotic attractor coined, Int. J. Bifurcat. Chaos, 12, 659-661 (2002) · Zbl 1063.34510
[23] Lorenz, E. N., Deterministic nonperiodic flow, J. Atmos. Sci., 20, 2, 130-141 (1963) · Zbl 1417.37129
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