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Lag synchronization of chaotic systems with time-delayed linear terms via impulsive control

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Abstract

In this paper, the lag synchronization of chaotic systems with time-delayed linear terms via impulsive control is investigated. Based on the stability theory of impulsive delayed differential equations, some sufficient conditions are obtained guaranteeing the synchronized behaviours between two delayed chaotic systems. Numerical simulations on time-delayed Lorenz and hyperchaotic Chen systems are also carried out to show the effectiveness of the proposed scheme. Note that under the scheme the chaotic system is controlled only at discrete time instants, and so it reduces the control cost in real applications.

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References

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

    MathSciNet  Google Scholar 

  2. L M Pecora and T Carroll, Phys. Rev. A 2374, 44 (1991)

    Google Scholar 

  3. L M Pecora and T Carroll, IEEE Trans. CAS 453, 38 (1991)

    Google Scholar 

  4. G Grassi and S Mascolo, IEEE Trans. CAS 1143, 44 (1997)

    Google Scholar 

  5. C Li, X Liao and R Zhang, Phys. Rev. Lett. 47, 328 (2004)

    Google Scholar 

  6. C C Wang and J P Su, Chaos, Solitons and Fractals 967, 20 (2004)

    MathSciNet  Google Scholar 

  7. M Hu and Z Xu, Nonlinear Anal.: Real World Applications 1253, 9 (2008)

    MathSciNet  Google Scholar 

  8. C K Duan and S S Yang, Phys. Lett. A 151, 229 (1997)

    MathSciNet  Google Scholar 

  9. J Chen, H Liu, J Lu and Q J Zhang, Comm. Nonlinear Sci. Numer. Simul. 2033, 16 (2011)

    MathSciNet  Google Scholar 

  10. M F Hu, Y Q Yang and Z Y Xu, Phys. Lett. A 3228, 372 (2008)

    MathSciNet  Google Scholar 

  11. X J Wan and J T Sun, Math. Comput. Simul. 81, 1609 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  12. T Yang, Impulsive control theory (Springer-Verlag, Berlin, 2001)

    MATH  Google Scholar 

  13. T Yang and O C Leon, IEEE Trans. CAS-1 44, 976 (1997)

    Article  Google Scholar 

  14. J Sun, Y Zhang, F Qiao and Q Wu, Chaos, Solitons and Fractals 1049, 19 (2004)

    MathSciNet  Google Scholar 

  15. C Li and X Liao, Chaos, Solitons and Fractals 857, 22 (2004)

    Google Scholar 

  16. E M Shahverdiev, S Sivaprakasam and K A Shore, Phys. Lett. A 2033, 292 (2002)

    Google Scholar 

  17. J Yan and J Shen, Nonlinear Anal.: Theory, Methods and Applications 245, 37 (1999)

    Google Scholar 

Download references

Acknowledgements

This work is supported by the Specialized Research Fund for the Doctoral Programme of Higher Education of China (No. 20093401120001), the Natural Science Foundation of Anhui Province (No. 11040606M12), the Natural Science Foundation of Anhui Education Bureau (No. KJ2010A035) and the 211 project of Anhui University(No. KJJQ1102, KJTD002B).

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Authors and Affiliations

  1. School of Mathematics, Anhui University, Hefei-230039, Anhui Province, China

    RANCHAO WU & DONGXU CAO

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  1. RANCHAO WU
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  2. DONGXU CAO
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Correspondence to RANCHAO WU.

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WU, R., CAO, D. Lag synchronization of chaotic systems with time-delayed linear terms via impulsive control. Pramana - J Phys 81, 727–735 (2013). https://doi.org/10.1007/s12043-013-0606-4

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  • DOI: https://doi.org/10.1007/s12043-013-0606-4

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