The European Physical Journal Special Topics

, Volume 223, Issue 8, pp 1509–1518 | Cite as

Outer synchronization of networks with different node dynamics

Regular Article Synchronization of Systems and Networks for Communication
Part of the following topical collections:
  1. Chaos, Cryptography and Communications

Abstract

A new type of outer synchronization between two distinct networks, composed of different classes of oscillators is investigated with the help of open plus closed loop approach, proposed earlier by Jackson and Grosu. It is further assumed that all the members of the network differ in their parameter values. Asymptotic stability of the zero solution of the error equation is proved analytically. Numerical simulation reveals that the same type of members of the two networks gets synchronized.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    D.J. Watts, S.H. Strogatz, Nature 393, 440 (1998)CrossRefADSGoogle Scholar
  2. 2.
    A.-L. Barabási, R. Albert, Science 286, 509 (1999)CrossRefMathSciNetADSGoogle Scholar
  3. 3.
    R. Albert, A.-L. Barabasi, Rev. Mod. Phys. 74, 47 (2002)CrossRefMATHMathSciNetADSGoogle Scholar
  4. 4.
    M.E.J. Newman, SIAM Rev. 45, 167 (2003)CrossRefMATHMathSciNetADSGoogle Scholar
  5. 5.
    S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, D.-U. Hwang, Phys. Reports 424, 175 (2006)CrossRefMathSciNetADSGoogle Scholar
  6. 6.
    M. Barahona, L.M. Pecora, Phys. Rev. Lett. 89, 054101 (2002)CrossRefADSGoogle Scholar
  7. 7.
    S. Jalan, R.E. Amritkar, Phys. Rev. Lett. 90, 014101 (2003)CrossRefADSGoogle Scholar
  8. 8.
    T. Nishikawa, A.E. Motter, Y.-C. Lai, F.C. Hoppensteadt, Phys. Rev. Lett. 91, 014101 (2003)CrossRefADSGoogle Scholar
  9. 9.
    C. Zhou, A.E. Motter, J. Kurths, Phys. Rev. Lett. 96, 034101 (2006)CrossRefADSGoogle Scholar
  10. 10.
    X.F. Wang, Int. J. Bif. Chaos 12, 885 (2002)CrossRefMATHGoogle Scholar
  11. 11.
    P. Erdös, A. Renyi, Publ. Math. Inst. Hung. Acad. Sci 5 (1960)Google Scholar
  12. 12.
    C. Zhou, J. Kurths, Phys. Rev. Lett. 96, 164102 (2006)CrossRefADSGoogle Scholar
  13. 13.
    J. Lü, X. Yu, G. Chen, Phys. A: Stat. Mech. Appl. 334, 281 (2004)CrossRefGoogle Scholar
  14. 14.
    C. Li, W. Sun, D. Xu, Prog. Theor. Phys. 114, 749 (2005)CrossRefMATHADSGoogle Scholar
  15. 15.
    C.P. Li, W.G. Sun, J. Kurths, Phys. A: Stat. Mech. Appl. 361, 24 (2006)CrossRefGoogle Scholar
  16. 16.
    C. Li, G. Chen, Phys. A: Stat. Mech. Appl. 343, 263 (2004)CrossRefGoogle Scholar
  17. 17.
    C. Masoller, A.C. Martíand, D.H. Zanette, Phys. A: Stat. Mech. Appl. 325, 186 (2003)CrossRefMATHGoogle Scholar
  18. 18.
    A.C. Martíand, C. Masoller, Phys. Rev. E 67, 056219 (2003)CrossRefADSGoogle Scholar
  19. 19.
    A.C. Martíand, C. Masoller, Phys. A: Stat. Mech. Appl. 342, 344 (2004)CrossRefGoogle Scholar
  20. 20.
    S. Wei-Gang, X. Cong-Xiang, L. Chang-Pin, F. Jin-Qing, Comm. Theor. Phys. 47, 1073 (2007)CrossRefADSGoogle Scholar
  21. 21.
    C. Li, W. Sun, J. Kurths, Phys. Rev. E 76, 046204 (2007)CrossRefADSGoogle Scholar
  22. 22.
    X. Wu, W. Xing Zheng, J. Zhou, Chaos: An Interdiscipl. J. Nonlinear Sci. 19 (2009)Google Scholar
  23. 23.
    P. He, S.-H. Ma, T. Fan, Chaos: An Interdiscipl. J. Nonlinear Sci. 22 (2012)Google Scholar
  24. 24.
    J.-W. Wang, Q. Ma, L. Zeng, M.S. Abd-Elouahab, Chaos: An Interdiscipl. J. Nonlinear Sci. 21 (2011)Google Scholar
  25. 25.
    E.A. Jackson, Chaos: An Interdiscipl. J. Nonlinear Sci. 7, 550 (1997)CrossRefMATHGoogle Scholar
  26. 26.
    E.A. Jackson, I. Grosu, Phys. D: Nonlinear Phenom. 85, 1 (1995)CrossRefMATHADSGoogle Scholar
  27. 27.
    I. Grosu, Phys. Rev. E 56, 3709 (1997)CrossRefADSGoogle Scholar
  28. 28.
    H.K. Khalil, Nonlinear Systems (Maxwell Macmillan, Singapore, 1992)Google Scholar

Copyright information

© EDP Sciences and Springer 2014

Authors and Affiliations

  1. 1.High Energy Physics Division, Department of Physics, Jadavpur UniversityCalcuttaIndia

Personalised recommendations