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The European Physical Journal D

, Volume 62, Issue 1, pp 51–56 | Cite as

Synchronization regions of two pulse-coupled electronic piecewise linear oscillators

  • N. Rubido
  • C. Cabeza
  • S. Kahan
  • G.M. Ramírez Ávila
  • Arturo C. MartiEmail author
Article

Abstract.

Stable synchronous states of different order were analytically, numerically and experimentally characterized in pulse-coupled light-controlled oscillators (LCOs). The Master-Slave (MS) configuration was studied in conditions where different time-scale parameters were tuned under varying coupling strength. Arnold tongues calculated analytically – based on the piecewise two-time-scale model for LCOs – and obtained numerically were consistent with experimental results. The analysis of the stability pattern and tongue shape for (1 : n) synchronization was based on the construction of return maps representing the Slave LCO evolution induced by the action of the Master LCO. The analysis of these maps showed that both tongue shape and stability pattern remained invariant. Considering the wide variation range of LCO parameters, the obtained results could have further applications on ethological models.

Keywords

Coupling Strength Wide Variation Range Synchronization Region Arnold Tongue Point Sink 
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.
    C. Schäfer, M.G. Rosenblum, H.H. Abel, J. Kurths, Phys. Rev. E 60, 857 (1999)CrossRefADSGoogle Scholar
  2. 2.
    A. Pikovsky, M. Rosenblum, J. Kurths, Synchronization: A Universal Concept in Nonlinear Sciences (Cambridge University Press, Cambridge, UK, 2001)Google Scholar
  3. 3.
    Edited by A. Pikovsky, Y. Maistrenko, Synchronization: Theory and Application (Kluwer Academic Publishers, Dordrecht, 2003)Google Scholar
  4. 4.
    S.C. Manrubia, A.S. Mikhailov, D.H. Zanette, Emergence of Dynamical Order (World Scientific Publishing, Singapore, 2004)Google Scholar
  5. 5.
    S.H. Strogatz, Sync: The Emerging Science of Spontaneous Order (Hyperion Press, NY, 2003)Google Scholar
  6. 6.
    V.Y. Argonov, S.V. Prants, Phys. Rev. A 71, 053408 (2005)CrossRefADSGoogle Scholar
  7. 7.
    W. Lauterborn, T. Kurz, U. Parlitz, Int. J. Bif. Chaos 7, 2003 (1997)CrossRefzbMATHGoogle Scholar
  8. 8.
    J.C. Neu, SIAM J. Appl. Math. 38, 305 (1980)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    V. Astakhov, A. Shabunin, V. Demidov, A. Provata, F. Baras, G. Nicolis, V. Anishchenko, Chaos Solit. Fract. 15, 395 (2003)CrossRefzbMATHADSGoogle Scholar
  10. 10.
    H. Fukuda, H. Morimura, S. Kai, Physica D 205, 80 (2005)CrossRefADSGoogle Scholar
  11. 11.
    B. Blasius, A. Huppert, L. Stone, Nature 399, 354 (1999)CrossRefADSGoogle Scholar
  12. 12.
    L. Glass, Nature 410, 277 (2001)CrossRefADSGoogle Scholar
  13. 13.
    D. Gonze, S. Bernard, C. Waltermann, A. Kramer, H. Herzel, Biophys. J. 89, 120 (2005)CrossRefGoogle Scholar
  14. 14.
    E. Despland, S.J. Simpson, Proc. R. Soc. B 273, 1517 (2006)CrossRefGoogle Scholar
  15. 15.
    L.O. Chua, J. Circ. Syst. Comp. 3, 93 (1993)CrossRefMathSciNetGoogle Scholar
  16. 16.
    K. Murali, M. Lakshmanan, L.O. Chua, Int. J. Bif. Chaos 5, 563 (1995)CrossRefzbMATHGoogle Scholar
  17. 17.
    A. Kittel, J. Parisi, K. Pyragas, Physica D 112, 459 (1998)CrossRefzbMATHADSGoogle Scholar
  18. 18.
    J. Cosp, J. Madrenas, E. Alarcón, E. Vidal, G. Villar, IEEE Trans. Neural Netw. 15, 1315 (2004)CrossRefGoogle Scholar
  19. 19.
    P.A. Pisarchik, R. Jaimes-Reátegui, J.H. García-López, Int. J. Bif. Chaos 18, 1801 (2008)CrossRefGoogle Scholar
  20. 20.
    N.F. Rulkov, Phys. Rev. Lett. 86, 183 (2001)CrossRefADSGoogle Scholar
  21. 21.
    N.F. Rulkov, Phys. Rev. E 65, 041922 (2002)CrossRefADSMathSciNetGoogle Scholar
  22. 22.
    R.E. Mirollo, S.H. Strogatz, SIAM J. App. Math. 50, 1645 (1990)CrossRefzbMATHMathSciNetGoogle Scholar
  23. 23.
    G.M. Ramírez Ávila, J.L. Guisset, J.L. Deneubourg, Physica D 182, 254 (2003)CrossRefzbMATHADSMathSciNetGoogle Scholar
  24. 24.
    N. Rubido, C. Cabeza, A.C. Martí, G.M. Ramírez Ávila, Phil. Trans. Royal Soc. A 367, 3267 (2009)CrossRefzbMATHADSGoogle Scholar
  25. 25.
    J.L. Guisset, J.L. Deneubourg, G.M. Ramírez Ávila (2002), eprint arXiv:nlin/0206036v1Google Scholar
  26. 26.
    D. Somers, N. Kopell, Biol. Cybern. 68, 393 (1993)CrossRefGoogle Scholar
  27. 27.
    S.R. Campbell, D. Wang, C. Jayaprakash, IEEE Trans. Neural Netw. 15, 1027 (2004)CrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • N. Rubido
    • 1
  • C. Cabeza
    • 1
  • S. Kahan
    • 1
  • G.M. Ramírez Ávila
    • 2
    • 3
  • Arturo C. Marti
    • 1
    Email author
  1. 1.Instituto de Física, Universidad de la RepúblicaMontevideoUruguay
  2. 2.Institut für Physik, Humboldt Universität zu BerlinBerlinGermany
  3. 3.Instituto de Investigaciones Físicas, Universidad de San AndrésLa PazBolivia

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