Synchronization of a Class of Chaotic and Hyperchaotic Systems via a Simple Universal Control Method

Article Preview

Abstract:

This paper investigates the synchronization of chaotic and hyperchaotic systems, and proposes a simple and universal method for chaos synchronization through investigating the dynamical behavior of the chaotic error system. In comparison with previous methods, the present controllers are simpler than the existing results. Especially, for some class of three dimensional chaotic systems, the obtained controllers in this paper contain single state feedback. Numerical simulations verify the effectiveness and correctness of the proposed method.

You might also be interested in these eBooks

Info:

Periodical:

Pages:

798-801

Citation:

Online since:

June 2012

Authors:

Export:

Price:

Permissions CCC:

Permissions PLS:

Сopyright:

© 2012 Trans Tech Publications Ltd. All Rights Reserved

Share:

Citation:

[1] L. Pecora and T. Carroll, Synchronization in chaotic systems. Phys. Rev. Lett., 64: (1990) 821–824, 1990.

DOI: 10.1103/physrevlett.64.821

Google Scholar

[2] S.  Boccaletti, J.  Kurths, G.  Osipov, D.  Valladares, et al, The synchronization of chaotic systems. Phys. Rep., 366: 1–101, 2002.

DOI: 10.1016/s0370-1573(02)00137-0

Google Scholar

[3] J.  Ojalvo and R.  Roy, Spatiotemporal communication with synchronized optical chaos. Phys. Rev. Lett., 86: 5204–5207, 2001.

DOI: 10.1103/physrevlett.86.5204

Google Scholar

[4] K.  Murali and M.  Lakshmanan, Drive-response scenario of chaos synchronization in identical nonlinear systems. Phys. Rev. E, 49: 4882–4887, 1994.

DOI: 10.1103/physreve.49.4882

Google Scholar

[5] J. Heagl, T.  Carroll and L.  Pecora, Desynchronization by periodic orbits. Phys. Rev. E, 52: R1253–1256, 1995. .

DOI: 10.1103/physreve.52.r1253

Google Scholar

[6] D.  Huang and R.  Guo, Identifying parameter by identical synchronization between different systems. Chaos, 14: 152–159, 2004.

DOI: 10.1063/1.1635095

Google Scholar

[7] R.  Guo, A simple adaptive controller for chaos and hyperchaos synchronization. Phys. Lett. A, 372: 5593–5597, 2008.

DOI: 10.1016/j.physleta.2008.07.016

Google Scholar

[8] R.  Guo, D.  Huang and L. Zhang, Chaotic synchronization based on Lie derivative method. Chaos, Solitons & Frac., 25: 1255–1259, 2005.

DOI: 10.1016/j.chaos.2004.11.067

Google Scholar

[9] W.  Lin, Adaptive chaos control and synchronization in only locally Lipschitz systems. Phys. Lett. A, 372: 3195–3200, 2008.

DOI: 10.1016/j.physleta.2008.01.038

Google Scholar

[10] W. Yu, Stabilization of three-dimensional chaotic systems via single state feedback controller. Phys. Lett. A, 374: 1488–1492, 2010.

DOI: 10.1016/j.physleta.2010.01.048

Google Scholar

[11] K.  Ito, Chaos in the Rikitake two-disc dynamo system. Earth Planet. Sci. Lett., 51: 451-456, 1980.

DOI: 10.1016/0012-821x(80)90224-1

Google Scholar