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Zhu, Congxu

Adaptive synchronization of two novel different hyperchaotic systems with partly uncertain parameters. (English) Zbl 1182.37028

Appl. Math. Comput. 215, No. 2, 557-561 (2009).
Chaos synchronization plays an important role for understanding the cooperative behavior in coupled chaotic oscillators.
A variety of approaches have been proposed for the synchronization of chaotic and hyperchaotic systems such as linear and nonlinear feedback synchronization methods, adaptive synchronization methods, backstepping design methods, and sliding mode control methods etc. However, most of the methods mentioned above and many other existing synchronization methods mainly concern the synchronization of two identical chaotic or hyperchaotic systems, the methods of synchronization of two different chaotic or hyperchaotic systems are far from being straight-forward because of their different structures and parameter mismatch.
This paper addresses the problem of adaptive synchronization of two different new hyperchaotic systems with some uncertain parameters. On the basis of the Lyapunov stability theory and the adaptive control theory, a new adaptive synchronization control law and a novel parameter estimation update law are proposed to achieve synchronization between the two novel different hyperchaotic systems with uncertain parameters. Numerical simulations are given to demonstrate the effectiveness of the proposed synchronization scheme and verify the theoretical results.
Reviewer: George S. Stavrakakis (Chania)

Cited in 18 Documents

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
93C40 Adaptive control/observation systems
37B25 Stability of topological dynamical systems

Keywords:

hyperchaotic system; adaptive control; chaos synchronization; Lyapunov stability theorem; hyper chaotic systems
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\textit{C. Zhu}, Appl. Math. Comput. 215, No. 2, 557--561 (2009; Zbl 1182.37028)
Full Text: DOI

References:

[1] Rösler, O. E., An equation for hyperchaos, Phys. Lett. A, 71, 155-157 (1979) · Zbl 0996.37502
[2] Li, Y.; Tang, W. K.S.; Chen, G., Hyperchaos evolved from the generalized Lorenz equation, Int. J. Circuit Theory Appl., 33, 235-251 (2005) · Zbl 1079.34032
[3] Li, Y.; Tang, W. K.S.; Chen, G., Generating hyperchaos via state feedback control, Int. J. Bifur. Chaos, 15, 3367-3375 (2005)
[4] Chen, A.; Lu, J.; Lü, J.; Yu, S., Generating hyperchaotic Lü attractor via state feedback control, Physica A: Stat. Mech. Appl., 364, 103-110 (2006)
[5] Pikovsky, A.; Rosenblum, M.; Kurths, J., Synchronization: A Universal Concept in Nonlinear Sciences (2001), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0993.37002
[6] Pecora, L. M.; Carroll, T. L., Synchronization in chaotic systems, Phys. Rev. Lett., 64, 821-824 (1990) · Zbl 0938.37019
[7] Yan, Z., Controlling hyperchaos in the new hyperchaotic Chen system, Appl. Math. Comput., 168, 1239-1250 (2005) · Zbl 1160.93384
[8] Wang, F.; Liu, C., A new criterion for chaos and hyperchaos synchronization using linear feedback control, Phys. Lett. A, 360, 274-278 (2006) · Zbl 1236.93131
[9] Jia, Q., Adaptive control and synchronization of a new hyperchaotic system with unknown parameters, Phys. Lett. A, 362, 424-429 (2007) · Zbl 1197.34107
[10] Zhou, X.; Wu, Y.; Li, Y.; Xue, H., Adaptive control and synchronization of a novel hyperchaotic system with uncertain parameters, Appl. Math. Comput., 203, 80-85 (2008) · Zbl 1155.37026
[11] Zhang, H.; Ma, X.; Li, M.; Zou, J., Controlling and tracking hyperchaotic Rösler system via active backstepping design, Chaos Soliton Fract., 26, 353-361 (2005) · Zbl 1153.93381
[12] Li, G. H.; Zhou, S. P.; Yang, K., Generalized projective synchronization between two different chaotic systems using active backstepping control, Phys. Lett. A, 355, 326-330 (2006)
[13] Jang, M.-J.; Chen, C.-L.; Chen, C.-K., Sliding mode control of hyperchaos in Rösler systems, Chaos Soliton Fract., 14, 1465-1476 (2002) · Zbl 1037.93507
[14] Yassen, M. T., Synchronization hyperchaos of hyperchaotic systems, Chaos Soliton Fract., 37, 465-475 (2008) · Zbl 1360.34118
[15] Huang, J., Adaptive synchronization between different hyperchaotic systems with fully uncertain parameters, Phys. Lett. A, 372, 4799-4804 (2008) · Zbl 1221.93127
[16] Vincent, U. E., Synchronization of identical and non-identical 4-D chaotic systems using active control, Chaos Soliton Fract., 37, 1065-1075 (2008) · Zbl 1153.37359
[17] Chen, Z.; Yang, Y.; Qi, G.; Yuan, Z., A novel hyperchaos system only with one equilibrium, Phys. Lett. A, 360, 696-701 (2007) · Zbl 1236.37022
[18] Qi, G.; Chen, G.; Du, S.; Chen, Z.; Yuan, Z., Analysis of a new chaotic system, Physica A: Stat. Mech. Appl., 352, 295-308 (2005)
[19] Wang, X.; Wang, M., A hyperchaos generated from Lorenz system, Physica A: Stat. Mech. Appl., 387, 3751-3758 (2008)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.