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Q–S synchronization between chaotic systems with double scaling functions

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Abstract

A double function Q–S synchronization (DFQSS) scheme of non-identical chaotic systems is proposed and analyzed with the assumption that all of the parameters are unknown. The sufficient conditions for achieving the double function Q–S synchronization with the desired scaling functions of two different chaotic systems (including the systems of non-identical dimension) are derived based on Lyapunov stability theory. By the adaptive control technique, the control laws and the corresponding parameter update laws are presented such that the DFQSS of non-identical chaotic systems is to be achieved. Numerical simulations and a brief discussion conclude the paper.

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References

  1. Perora, L.M., Carroll, T.L.: Synchronization in chaotic system. Phys. Rev. Lett. 64, 821–824 (1990)

    Article  MathSciNet  Google Scholar 

  2. Mainieri, R., Rehacek, J.: Projective synchronization in three-dimensional chaotic systems. Phys. Rev. Lett. 82, 3042 (1999)

    Article  Google Scholar 

  3. Yan, Z.Y.: Chaos Q–S synchronization between Rösler system and a new unified chaotic system. Phys. Lett. A 334, 406–446 (2005)

    Article  MATH  Google Scholar 

  4. Yan, Z.Y.: Q–S (lag or anticipated) synchronization backstepping scheme in a class of continuous-time hyperchaotic systems—a symbolic numeric computation approach. Chaos 15, 023902 (2005)

    Article  MathSciNet  Google Scholar 

  5. Wang, Q., Chen, Y.: Generalized Q–S (lag, anticipated and complete) synchronization in modified Chua’s circuit and Hindmarsh–Rose systems. Appl. Math. Comput. 181, 8–56 (2006)

    Google Scholar 

  6. Yan, Z.Y.: Q–S (complete or anticipated) synchronization backstepping scheme in a class of discrete-time chaotic (hyperchaotic) systems: asymbolic–numeric computation approach. Chaos 16, 013119 (2006)

    Article  MathSciNet  Google Scholar 

  7. Yang, X.S.: Concepts of synchronization in dynamical systems. Phys. Lett. A 260, 340–344 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  8. Wang, C., Ge, S.S.: Adaptive synchronization of uncertain chaotic systems via backstepping design. Chaos Solitons Fractals 6, 1199–1206 (2001)

    Article  Google Scholar 

  9. Rössler, O.E.: An equation for continuous chaos. Phys. Lett. A 57, 397–398 (1976)

    Article  Google Scholar 

  10. Lü, J., Chen, G., Cheng, D., Celikovsky, S.: Bridge the gap between the Lorenz system and Chen system. Int. J. Bifurc. Chaos 6, 2917–2926 (2002)

    Google Scholar 

  11. Hu, M.F., Xu, Z.: A general scheme for Q–S synchronization of chaotic systems. Nonlinear Anal. 69, 1091–1099 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  12. Ho, M.C., Hung, Y.C., et al.: Reduced-order synchronization of chaotic systems with parameters unknown. Phys. Lett. A 348, 251–259 (2006)

    Article  Google Scholar 

  13. Zhao, J.K., Zhang, K.C.: Adaptive function Q–S synchronization of chaotic systems with unknown parameters. Int. J. Adapt. Control Signal Process. (2009). doi:10.1002/acs.1159

    Google Scholar 

  14. Fang, B.R., Zhou, J.D., Li, Y.M.: Matrix Theory, pp. 256–262. Tsinghua Univ. Press, Beijing (2004)

    Google Scholar 

  15. Li, Y.X., Tang, W.K.S., Chen, G.: Generating hyperchaos via state feedback control. Int. J. Bifurc. Chaos 10, 3367–3375 (2005)

    Google Scholar 

  16. Chen, A., Lu, J., Lü, J., Yu, S.: Generating hyperchaotic Lü attractor via state feedback control. Physica A 364, 103–110 (2006)

    Article  Google Scholar 

  17. Lorenz, E.N.: Deterministic non-periodic flows. J. Atmos. Sci. 20, 130–141 (1963)

    Article  Google Scholar 

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Authors and Affiliations

  1. School of Science, Xi’an Jiaotong University, Xi’an, 710049, China

    Jiakun Zhao

  2. Beijing Education Examination Authority, Beijing, 100083, China

    Tao Ren

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  1. Jiakun Zhao
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  2. Tao Ren
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Correspondence to Jiakun Zhao.

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Zhao, J., Ren, T. Q–S synchronization between chaotic systems with double scaling functions. Nonlinear Dyn 62, 665–672 (2010). https://doi.org/10.1007/s11071-010-9752-0

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  • DOI: https://doi.org/10.1007/s11071-010-9752-0

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