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The European Physical Journal Special Topics

, Volume 225, Issue 1, pp 51–64 | Cite as

Robust projective lag synchronization in drive-response dynamical networks via adaptive control

Regular Article Synchronization and Control in Time Delayed and other Networks
Part of the following topical collections:
  1. Synchronization and Control in Time-Delayed Complex Networks and Spatio-Temporal Patterns

Abstract

This paper investigates the problem of projective lag synchronization behavior in drive-response dynamical networks (DRDNs) with identical and non-identical nodes. An adaptive control method is designed to achieve projective lag synchronization with fully unknown parameters and unknown bounded disturbances. These parameters were estimated by adaptive laws obtained by Lyapunov stability theory. Furthermore, sufficient conditions for synchronization are derived analytically using the Lyapunov stability theory and adaptive control. In addition, the unknown bounded disturbances are also overcome by the proposed control. Finally, analytical results show that the states of the dynamical network with non-delayed coupling can be asymptotically synchronized onto a desired scaling factor under the designed controller. Simulation results show the effectiveness of the proposed method.

Keywords

Chaotic System European Physical Journal Special Topic Synchronization Error Identical Node Reference Node 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    S.A. Pandit, R.E. Amritkar, Phys. Rev. E 60(2), 1119 (1999)ADSCrossRefGoogle Scholar
  2. 2.
    S.H. Strogatz, Nature 410(6825), 268 (2001)ADSCrossRefGoogle Scholar
  3. 3.
    X. Liu, T. Chen, Physica A 387(16), 4429 (2008)ADSCrossRefGoogle Scholar
  4. 4.
    Y. Xiao, W. Xu, X. Li, S. Tang, Chaos 17(3), 033118 (2007)ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    S. Acharyy, R.E. Amritkar, Eur. Phys. J. Special Topics 222(3–4), 939 (2013)ADSCrossRefGoogle Scholar
  6. 6.
    E.M. Shahverdiev, S. Sivaprakasam, K.A. Shore, Physics Letters A 292(6), 320 (2002)ADSCrossRefGoogle Scholar
  7. 7.
    R. Suresh, K. Srinivasan, D.V. Senthilkumar, I.R. Mohamed, K. Murali, M. Lakshmanan, J. Kurths, Eur. Phys. J. Special Topics 222(3-4), 729 (2013)ADSCrossRefGoogle Scholar
  8. 8.
    Y. Wu, C. Li, Y. Wu, J. Kurths, Comm. Nonlinear Sci. Numer. Simul. 17(1), 349 (2012)ADSMathSciNetCrossRefGoogle Scholar
  9. 9.
    F. Length, Scientific Res. Essays 6(3), 552 (2011)Google Scholar
  10. 10.
    G. Liu-Xiao, X. Zhen-Yuan, H. Man-Ferg, Chinese Physics B 17(11), 4067 (2008)ADSCrossRefGoogle Scholar
  11. 11.
    S. Zhang, Y. Yu, G. Wen, A. Rahmani, Int. J. Modern Phys. C 25(8), 1450029 (2014)ADSMathSciNetCrossRefGoogle Scholar
  12. 12.
    V.H.P. Louzada, N.A.M. Arajo, J.S. Andrade, H.J. Herrmann, Scientific Reports 3 (2013)Google Scholar
  13. 13.
    W. Guo, Nonlinear Analysis: Real World Applications 12(5), 2579 (2011)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Q. Zhang, J. Zhao, Nonlinear Dynamics 67(4), 2519 (2011)CrossRefGoogle Scholar
  15. 15.
    S. Banerjee, S.J.S. Theesar, J. Kurths, Chaos: An Interdisciplinary J. Nonlinear Sci. 23(1), 013118 (2013)MathSciNetCrossRefGoogle Scholar
  16. 16.
    D. Ghosh, S. Banerjee, A.R. Chowdhury, Physics. Letters A 374(21), 2143 (2010)ADSCrossRefGoogle Scholar
  17. 17.
    J.T. Bosworth, P.S. Williams-Hayes, American Institute of Aeronautics and Astronautics (2007)Google Scholar
  18. 18.
    Q. Zhang, Chaos, Solitons Fractals 58, 22 (2014)ADSCrossRefGoogle Scholar
  19. 19.
    Y. Chen, L. Cao, M. Sun, Int. J. Nonlinear Sci. 10(1), 17 (2010)MathSciNetGoogle Scholar
  20. 20.
    D.H. Ji, S.C. Jeong, J.H. Park, S.M. Lee, S.C. Won, Appl. Math. Comput. 218(9), 4872 (2012)MathSciNetCrossRefGoogle Scholar
  21. 21.
    L. Wang, Z. Yuan, X. Chen, Z. Zhou, Comm. Nonlinear Sci. Numer. Simul. 16(2), 987 (2011)ADSMathSciNetCrossRefGoogle Scholar
  22. 22.
    J. Zhou, T. Chen, L. Xiang, Circ. Syst. Signal Proc. 24(5), 599(2005)MathSciNetCrossRefGoogle Scholar
  23. 23.
    G. Al-mahbashi, M.S. Noorani, S. Abu Bakar, Int. J. Modern Phys. C 25(11), (2014)Google Scholar
  24. 24.
    G. Al-mahbashi, M.S. Noorani, S. Abu Bakar, Nonlinear Dyn. 82(3), (2015)Google Scholar
  25. 25.
    C. Feng, X. Xu, S. Wang, Y. Wang, Chaos 18(2), 1(2008)Google Scholar

Copyright information

© EDP Sciences and Springer 2016

Authors and Affiliations

  1. 1.School of mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan MalaysiaSelangor Darul EhsanMalaysia
  2. 2.Faculty of Science, Mathematics Department, University of HailHailSaudi Arabia

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