Advertisement

The European Physical Journal Special Topics

, Volume 228, Issue 6, pp 1493–1514 | Cite as

The coexistence of chaotic synchronization with three different nonautonomous systems under constraint conditions

  • Fuhong MinEmail author
  • Hanyuan Ma
  • Yanmin Lv
  • Lei Zhang
Regular Article Topical issue
  • 10 Downloads
Part of the following topical collections:
  1. Discontinuous Dynamical Systems and Synchronization

Abstract

Because of the inherent randomness and extreme sensitivity to initial values of chaotic systems, chaos synchronization has become the key technology for chaotic applications. With the further research, scholars have found that using continuous systems to simplify discontinuous systems cannot get accurate results, and it needs to use discontinuous models to provide a precise description. Therefore, the synchronization with three different chaotic systems will be studied by using discontinuous dynamical system theory in this paper. Taking Holmes–Duffing system as master system, Pendulum and the Stiffening Spring as slave systems, the motion laws of the three systems in different motion spaces will be discussed systematically with controllers, and the analysis conditions for synchronization to start and disappear will be given. Through numerical simulations, partial synchronization and full synchronization among three systems will be realized, which proves the validity of this method and is conducive to the further study of the synchronization of complex periodic and chaotic motions.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    L.M. Pecora, T.L. Carroll, Phys. Rev. Lett. 64, 1196 (1990)MathSciNetCrossRefGoogle Scholar
  2. 2.
    G. Grassi, D.A. Miller, Int. J. Bifurc. Chaos 17, 1337 (2007)CrossRefGoogle Scholar
  3. 3.
    A. Ouannas, M.M. Al-sawalha, Eur. Phys. J. Special Topics 225, 187 (2016)ADSCrossRefGoogle Scholar
  4. 4.
    L. Zhang, T. Liu, J. Nonlinear Sci. Appl. 9, 1064 (2016)MathSciNetCrossRefGoogle Scholar
  5. 5.
    K. Pyragas, Phys. Lett. A. 170, 421 (1992)ADSCrossRefGoogle Scholar
  6. 6.
    A. Alfi, Int. J. Dyn. Control 2, 1 (2017)Google Scholar
  7. 7.
    A. Elsonbaty, A.M.A. El-Sayed, Nonlinear Dyn. 9, 2637 (2017)CrossRefGoogle Scholar
  8. 8.
    N. Cai, Y. Jing, S. Zhang, Commun. Nonlinear Sci. Numer. Simul. 15, 1613 (2010)ADSMathSciNetCrossRefGoogle Scholar
  9. 9.
    Z.M. Ge, Y.S. Chen, Chaos, Solitons Fractals 26, 881 (2005)ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    M. Siddique, M. Rehan, Nonlinear Dyn. 84, 1 (2016)CrossRefGoogle Scholar
  11. 11.
    A.M.A. El-Sayed, H.M. Nour, A. Elsaid, A.E. Matouk, A. Elsonbaty, Appl. Math. Model. 40, 3516 (2016)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Y. Feng, J. Pu, Z. Wei, Eur. Phys. J. Special Topics 224, 1593 (2015)ADSCrossRefGoogle Scholar
  13. 13.
    A.C.J. Luo, Nonlinear Anal. Hybrid Syst. 2, 1030 (2008)MathSciNetCrossRefGoogle Scholar
  14. 14.
    A.C.J. Luo, Commun. Nonlinear Sci. Numer. Simul. 14, 1901 (2009)ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    A.C.J. Luo, F.H. Min, Nonlinear Anal. Real. World Appl. 12, 1810 (2011)MathSciNetCrossRefGoogle Scholar
  16. 16.
    A.C.J. Luo, F.H. Min, Chaos, Solitons, Fractals 44, 362 (2011)ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    F.H. Min, A.C.J. Luo, Phys. Lett. A 375, 3080 (2011)ADSMathSciNetCrossRefGoogle Scholar
  18. 18.
    F.H. Min, A.C.J. Luo, Int. J. Bifurc. Chaos 25, 1530016 (2015)CrossRefGoogle Scholar
  19. 19.
    A.C.J. Luo, Discontinuous Dynamical Systems on Time-varying Domains, (Higher Education Press, 2009)Google Scholar

Copyright information

© EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Electrical and Automation Engineering, Nanjing Normal UniversityNanjingP.R. China

Personalised recommendations