Robust adaptive modified function projective synchronization of different hyperchaotic systems subject to external disturbance. (English) Zbl 1248.93089

Summary: Robust adaptive modified function projective synchronization between two different hyperchaotic systems is investigated where external uncertainties are considered and the scale factors are different from each other. A synchronization criterion is presented, which can be realized by adaptive feedback controller with compensator to eliminate the influence of uncertainties effectively. The update laws of the unknown parameters are given and the sufficient conditions are deduced based on stability theory and adaptive control. Some mistakes in previous works are pointed out and revised. Finally, the hyperchaotic Lü and new hyperchaotic Lorenz systems are taken for example and numerical simulations are presented to verify the effectiveness and robustness of the proposed control scheme.


93C40 Adaptive control/observation systems
93C73 Perturbations in control/observation systems
93C15 Control/observation systems governed by ordinary differential equations
34D06 Synchronization of solutions to ordinary differential equations
37N35 Dynamical systems in control
Full Text: DOI


[1] Yang, T.; Chua, L.O., Secure communication via chaotic parameter modulation, IEEE trans circuits syst I, 43, 817-819, (1996)
[2] Feki, M., An adaptive chaos synchronization scheme applied to secure communication, Chaos soliton fract, 3, 959-964, (2003)
[3] Li, C.; Liao, X.; Wong, K., Chaotic lag synchronization of coupled time-delayed systems and its application in secure communication, Physica D, 194, 187-202, (2004) · Zbl 1059.93118
[4] Chang, W.D., Digital secure communication via chaotic systems, Digital signal process, 19, 693-699, (2009)
[5] Nana, B.; Woafo, P.; Domngang, S., Chaotic synchronization with experimental application to secure communications, Commun nonlinear sci numer simul, 14, 2266-2276, (2009)
[6] Carroll, T.L.; Heagy, J.F.; Pecora, L.M., Transforming signals with chaotic synchronization, Phys rev E, 54, 4676-4680, (1996)
[7] Zhang, Y.; Sun, J., Chaotic synchronization and anti-synchronization based on suitable separation, Phys lett A, 330, 442-447, (2004) · Zbl 1209.37039
[8] Rosenblum, M.G.; Pikovsky, A.S.; Kurths, J., Phase synchronization of chaotic oscillators, Phys rev lett, 76, 1804-1807, (1996)
[9] Rosenblum, M.G.; Pikovsky, A.S.; Kurths, J., From phase to lag synchronization in coupled chaotic oscillators, Phys rev lett, 78, 4193-4196, (1997)
[10] Boccaletti, S.; Valladares, D.L., Characterization of intermittent lag synchronization, Phys rev E, 62, 7497-7500, (2000)
[11] Rulkov, N.F.; Sushchik, M.M.; Tsimring, L.S., Generalized synchronization of chaos in directionally coupled chaotic systems, Phys rev E, 51, 980-994, (1995)
[12] Hramov, A.E.; Koronovskii, A.A.; Moskalenko, O.I., Generalized synchronization onset, Europhys lett, 72, 901-910, (2005)
[13] Hramov, A.E.; Koronovskii, A.A., An approach to chaotic synchronization, Chaos, 14, 603-610, (2004) · Zbl 1080.37029
[14] Mainieri, R.; Rehacek, J., Projective synchronization in three-dimensional chaotic systems, Phys rev lett, 82, 3042-3045, (1999)
[15] Du, H.; Zeng, Q.; Wang, C., Function projective synchronization of different chaotic systems with uncertain parameters, Phys lett A, 372, 5402-5410, (2008) · Zbl 1223.34077
[16] Du, H.; Zeng, Q.; Wang, C.; Ling, M., Function projective synchronization in coupled chaotic systems, Nonlinear anal – real, 11, 705-712, (2010) · Zbl 1181.37039
[17] Wu, Z.Y.; Fu, X.C., Adaptive function projective synchronization of discrete chaotic systems with unknown parameters, Chin phys lett, 27, 050502, (2010)
[18] Sudheer, K.S.; Sabir, M., Function projective synchronization in chaotic and hyperchaotic systems through open-plus-closed-loop coupling, Chaos, 20, 013115, (2010) · Zbl 1311.34100
[19] Du, H.; Zeng, Q.; Wang, C., Modified function projective synchronization of chaotic system, Chaos soliton fract, 42, 2399-2404, (2009) · Zbl 1198.93011
[20] Sudheer, K.S.; Sabir, M., Adaptive modified function projective synchronization between hyperchaotic Lorenz system and hyperchaotic Lü system with uncertain parameters, Phys lett A, 373, 3743-3748, (2009) · Zbl 1233.93060
[21] Wang, J.A.; Liu, H.P., Adaptive modified function projective synchronization of different hyperchaotic systems, Acta phys sin, 59, 2265-2271, (2010) · Zbl 1224.93075
[22] Chen, A.; Lu, J.; Lü, J.; Yu, S., Generating hyperchaotic Lü attractor via state feedback control, Physica A, 364, 103-110, (2006)
[23] Wang, X.; Wang, M., A hyperchaos generated from Lorenz system, Physica A, 387, 3751-3758, (2008)
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