Time-varying synchronization of chaotic systems in the presence of system mismatch

Henry Leung; Zhiwen Zhu

doi:10.1103/PhysRevE.69.026201

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Time-varying synchronization of chaotic systems in the presence of system mismatch

Henry Leung^*

Zhiwen Zhu^†

Department of Electrical and Computer Engineering, University of Calgary, Calgary, Alberta, Canada T2N 1N4

Communications Research Centre Canada, Ottawa, Ontario, Canada K2H 8S2

^*Electronic address: leungh@enel.ucalgary.ca
^†Electronic address: zhiwen.zhu@crc.ca

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Phys. Rev. E 69, 026201 – Published 17 February, 2004

DOI: https://doi.org/10.1103/PhysRevE.69.026201

Abstract

The problem of synchronization of two identical chaotic systems in the presence of system mismatch is investigated in this article. The instantaneous mean square error (E) of the unidirectionally coupled synchronization scheme is analyzed based on the Jacobian equation of the response system. It is shown that synchronization based on a constant coupling parameter does not produce satisfactory performance. A synchronization scheme is proposed here, and the time-varying coupling parameter sequence used in this new scheme is obtained by minimizing the instantaneous E. Numerical simulations show that the proposed time-varying synchronization method has smaller mean square synchronization error than the conventional approach based on using a constant coupling parameter.

References (16)

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[c1] H. Fujisaka and T. Yamada, Prog. Theor. Phys. 69, 32 (1983).

[c2] L. M. Pecora and T. L. Carroll, Phys. Rev. Lett. 64, 821 (1990).

[c3] J. H. Peng, E. J. Ding, M. Ding, and W. Yang, Phys. Rev. Lett. 76, 904 (1996).

[c4] N. Sharma and P. G. Poonacha, Phys. Rev. E 56, 1242 (1997).

[c5] L. M. Pecora, T. L. Carroll, G. A. Johnson, and D. J. Mar, Chaos 7, 520 (1997).

[c6] D. J. Gauthier and J. C. Bienfang, Phys. Rev. Lett. 77, 1751 (1996).

[c7] P. Ashwin, J. Buescu, and I. Stewart, Phys. Lett. A 193, 126 (1994).

[c8] N. F. Rulkov and M. M. Sushchik, Int. J. Bifurcation Chaos Appl. Sci. Eng. 7, 625 (1997).

[c9] M. M. Sushchik, Jr., N. F. Rulkov, and H. D. I. Abarbanel, IEEE Trans. Circuits Syst., I: Fundam. Theory Appl. 44, 867 (1997).

[c10] G. A. Johnson, D. J. Mar, T. L. Carroll, and L. M. Pecora, Phys. Rev. Lett. 80, 3956 (1998).

[c11] Y. M. Liaw and P. C. Tung, Phys. Rev. E 56, 5265 (1997).

[c12] H. D. I. Abarbanel, R. Brown, J. J. Sidorowich, and L. S. Tsmring, Rev. Mod. Phys. 65, 1331 (1993).

[c13] H. D. I. Abarbanel, R. Brown, and M. B. Kennel, Int. J. Mod. Phys. B 5, 1347 (1991).

[c14] Z. Zhu, H. Leung, and Z. Ding, IEEE Trans. Circuits Syst., I: Fundam. Theory Appl. 46, 1320 (1999).

[c15] H. Leung and Z. Zhu, IEEE Trans. Circuits Syst., I: Fundam. Theory Appl. 48, 1118 (2001).

[c16] H. Leung, Z. Zhu, and Z. Ding, IEEE Trans. Signal Process. 48, 1807 (2001).

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Time-varying synchronization of chaotic systems in the presence of system mismatch

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