LettersNo Access

STUDY OF GLOBALLY EXPONENTIAL SYNCHRONIZATION FOR THE FAMILY OF RÖSSLER SYSTEMS

Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan, Hubei 430074, P. R. China

Currently, the author is also with the School of Automatics, Wuhan, University of Science and Technology, Wuhan, Hubei 430070, P. R. China.

Search for more papers by this author

and

PEI YU

Department of Applied Mathematics, The University of Western Ontario, London, Ontario N6A 5B7, Canada

Author for correspondence.

Search for more papers by this author

https://doi.org/10.1142/S0218127406016148Cited by:22 (Source: Crossref)

Abstract

This paper considers the globally exponential synchronization (GES) of the family of Rössler chaotic systems. One pair of the six transmitter-receiver systems is specifically studied, and algebraic criterion for the GES is obtained via proper nonlinear feedback controls. Based on the study of the systems' structures, appropriate Lyapunov functions are constructed for error systems. The method presented in this paper provides a convenient tool in the practical use of chaos control and synchronization. Numerical simulations are provided to demonstrate the theoretical results.

Keywords:

References

G. Chen , Controlling Chaos and Bifurcations in Engineering Systems ( CRC Press , Boca Raton, FL , 2000 ) . Google Scholar
G. R. Chen and X. Dong, Int. J. Bifurcation and Chaos 3, 1363 (1993), DOI: 10.1142/S0218127493001112. Link, Web of Science, Google Scholar
G. R. Chen and J. H. Lü , Dynamical Analysis, Control and Synchronization of Lorenz Families ( Chinese Science Press , Beijing , 2003 ) . Google Scholar
K. M. Cuomo and A. V. Oppenheim, Phys. Rev. Lett. 71, 65 (1993), DOI: 10.1103/PhysRevLett.71.65. Crossref, Web of Science, Google Scholar
P. E. Curran and L. O. Chua, Int. J. Bifurcation and Chaos 7, 1375 (1997), DOI: 10.1142/S0218127497001096. Link, Web of Science, Google Scholar
J. Q. Fang, Prog. Phys. 16, 1 (1996). Web of Science, Google Scholar
J. Q. Fang, Prog. Phys. 50, 2108 (2001). Google Scholar
X. P. Guan et al. , Chaos Control and Its Applications in Secure Communication ( National Defence Press , Beijing , 2002 ) . Google Scholar
X. X. Liao , Absolute Stability of Nonlinear Control Systems ( Kluwer Academic China Science Press , Beijing , 1993 ) . Crossref, Google Scholar
X. X. Liao , Stability Theory and Application of Dynamical Systems ( National Defence Press , Beijing , 2002 ) . Google Scholar
X. X. Liao, G. R. Chen and H. O. Wang, On global synchronization of chaotic systems, Proc. Amer. Contr. Conf. (2002) pp. 2255–2259. Google Scholar
X. X. Liao and G. R. Chen, Int. J. Syst. Sci. 43, 453 (2003), DOI: 10.1080/00207720310001614079. Google Scholar
X. X. Liao and G. R. Chen, Int. J. Bifurcation and Chaos 13, 207 (2003), DOI: 10.1142/S0218127403006455. Link, Web of Science, Google Scholar
X. X. Liao and P. Yu, Int. J. Bifurcation and Chaos 15, 3687 (2005), DOI: 10.1142/S0218127405013198. Google Scholar
X. X. Liaoet al., Int. J. Bifurcation and Chaos 15, 2227 (2005), DOI: 10.1142/S0218127405013198. Link, Web of Science, Google Scholar
X. X. Liaoet al., J. Auto. Contr. 3, 320 (2005). Google Scholar
J. H. Lü, T. Zhou and S. Zhang, Chin. Phys. 11, 12 (2002). Web of Science, Google Scholar
E. Ott, G. Grebogi and J. A. Yorke, Phys. Rev. Lett. 64, 1196 (1990), DOI: 10.1103/PhysRevLett.64.1196. Crossref, Web of Science, Google Scholar
L. M. Pecora and T. L. Carroll, Phys. Rev. Lett. 64, 821 (1990), DOI: 10.1103/PhysRevLett.64.821. Crossref, Web of Science, Google Scholar
O. E. Rössler, Phys. Lett. A 57, 397 (1976), DOI: 10.1016/0375-9601(76)90101-8. Crossref, Web of Science, Google Scholar
O. E. Rössler, Ann. NY, Acad. Sci. 316, 376 (1979), DOI: 10.1111/j.1749-6632.1979.tb29482.x. Crossref, Google Scholar
C. D. Tao, J. A. Lu and J. H. Lü, Physics 51, 1496 (2002). Google Scholar
T. Zhouet al., Phys. Lett. A 301, 231 (2002), DOI: 10.1016/S0375-9601(02)00973-8. Crossref, Web of Science, Google Scholar