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Adaptive synchronization of a hyperchaotic system with uncertain parameter. (English) Zbl 1142.37325
Summary: This paper addresses the synchronization problem of two Lü hyperchaotic dynamical systems in the presence of unknown system parameters. Based on Lyapunov stability theory an adaptive control law is derived to make the states of two identical Lü hyperchaotic systems with unknown system parameters asymptotically synchronized. Numerical simulations are presented to show the effectiveness of the proposed chaos synchronization schemes.

37D45Strange attractors, chaotic dynamics
93D15Stabilization of systems by feedback
Full Text: DOI
[1] Rossler, O. E.: An equation for hyperchaos. Phys lett A 71, No. 2 -- 3, 155-157 (1979) · Zbl 0996.37502
[2] Liao, T. L.; Huang, N. S.: An observer-based approach for chaotic synchronization with applications to secure communications. IEEE trans circ syst I 46, No. 9, 1144-1150 (1999) · Zbl 0963.94003
[3] Matsumot, T.; Chua, L. O.; Kobayashi, K.: Hyperchaos: laboratory experiment and numerical confirmation. IEEE trans circ syst I 33, No. 11, 1143-1147 (1986)
[4] Tsubone, T.; Saito, T.: Hyperchaos from a 4-D manifold piecewise-linear system. IEEE trans circ syst I 45, No. 9, 889-894 (1998)
[5] Pecora, L. M.; Carroll, T. L.: Synchronization of chaotic systems. Phys rev lett 64, No. 8, 821-830 (1990) · Zbl 0938.37019
[6] Carroll, T. L.; Pecora, L. M.: Synchronizing a chaotic systems. IEEE trans circ syst 38, 453-456 (1991)
[7] Chen, G.; Xie, Q.: Synchronization stability analysis of the chaotic Rössler system. Int J bifurcat chaos 6, No. 11, 2153-2161 (1996) · Zbl 1298.34096
[8] Bai, E. W.; Lonngren, K. E.: Synchronization and control of chaotic systems. Chaos, solitons & fractals 10, 1571-1576 (1997) · Zbl 0958.93513
[9] Cuomo, K. M.; Oppenheim, A. V.: Circuit implementation of synchronized chaos with applications to communications. Phys rev lett 71, 65 (1993)
[10] Wu, C.; Yang, T.; Chua, L. O.: On adaptive synchronization and control of nonlinear dynamical systems. Int J bifurcat chaos 6, No. 3, 455-472 (1996) · Zbl 0875.93182
[11] Zeng, Y.; Singh, S. N.: Adaptive control of chaos in Lorenz systems. Dyn control 7, 143-154 (1996) · Zbl 0875.93191
[12] Elabbasy, E. M.; Agiza, H. N.; E1-Dessoky, M. M.: Adaptive synchronization of Lü system with uncertain parameters. Chaos, solitons & fractals 21, 657-667 (2004) · Zbl 1062.34039
[13] Bai, E. W.; Lonngren, K. E.: Sequential synchronization of two Lorenz system using active control. Chaos, solitons & fractals 11, 1041-1044 (2000) · Zbl 0985.37106
[14] Agiza, H. N.; Yassen, M. T.: Synchronization of Rössler and Chen chaotic dynamical systems using active control. Phys lett A 278, 191-197 (2001) · Zbl 0972.37019
[15] Li, Z.; Han, C.; Shi, S.: Modification for synchronization of Rössler and Chen chaotic systems. Phys lett A 301, 224-230 (2002) · Zbl 0997.37014
[16] Kocarev, L.; Parlitz, U.: General approach for chaotic synchronization with applications to communications. Phys rev lett 74, No. 25, 5028-5031 (1995)
[17] Murali, K.; Lakshmanan, M.: Secure communication using a compound signal from generalized synchronizable chaotic systems. Phys lett A 241, 303-310 (1998) · Zbl 0933.94023
[18] Bernardo, M. D.: An adaptive approach to the control and synchronization of continuous-time chaotic systems. Int J bifurcat chaos 6, No. 3, 557-568 (1996) · Zbl 0900.70413
[19] Chen, G.; Dong, X.: Form chaos to order: methodologies, perspectives and applications. (1998) · Zbl 0908.93005
[20] Chen, S.; Lü, J.: Synchronization of an uncertain unified chaotic system via adaptive control. Chaos, solitons & fractals 14, No. 4, 643-647 (2002) · Zbl 1005.93020
[21] Chen, S.; Lü, J.: Parameter identification and synchronization of chaotic systems based on adaptive control. Phys lett A 299, No. 4, 353-358 (2002) · Zbl 0996.93016
[22] Pecora, L. M.; Carroll, T. L.; Johnson, G. A.; Mar, D. J.; Heagy, J. F.: Fundamentals of synchronization in chaotic systems, concepts, and applications. Chaos 7, No. 4, 520-543 (1997) · Zbl 0933.37030
[23] Mascolo S, Grassi G. Observers for hyperchaos synchronization with application to secure communications. In: Proceedings of the 1998 IEEE int conf on control applications, Trieste, Italy, 1 -- 4 September 1998, p. 1016 -- 20.
[24] Makoto, I.; Chua, L. O.: Reconstruction and synchronization of hyperchaotic circuits via one state variable. Int J bifurcat chaos 12, No. 10, 2069-2085 (2002) · Zbl 1046.94019