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JETP Letters

, Volume 108, Issue 8, pp 543–547 | Cite as

Cloning of Chimera States in a Multiplex Network of Two-Frequency Oscillators with Linear Local Couplings

  • A. S. Dmitrichev
  • D. S. ShchapinEmail author
  • V. I. Nekorkin
Nonlinear Phenomena
  • 14 Downloads

Abstract

Cloning of chimera states, which is a new effect caused by the short-term interaction in a multiplex network, has been described. This effect is observed when two ring networks of linearly coupled two-frequency (bistable) oscillators are combined into the multiplex network. At certain values of the strength and duration of the inter-ring (multiplex) interaction, a copy of a chimera state with accuracy to phases in the incoherent part is formed in the ring with an initially random phase distribution. It has been shown that the effect is structurally stable and is due to the competition of self-sustained oscillations in individual rings.

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References

  1. 1.
    Y. Kuramoto and D. Battogtokh, Nonlinear Phenom. Complex Syst. 5, 380 (2002).Google Scholar
  2. 2.
    D. M. Abrams and S. H. Strogatz, Phys. Rev. Lett. 93, 174102 (2004).ADSCrossRefGoogle Scholar
  3. 3.
    E. Schöll, Eur. Phys. J. Spec. Top. 225, 891 (2016).CrossRefGoogle Scholar
  4. 4.
    L. M. Mukhametov, A. Y. Supin, and I. G. Polyakova, Brain Res. 134, 581 (1977).CrossRefGoogle Scholar
  5. 5.
    O. I. Lyamin, P. R. Manger, S. A. Ridgway, L. M. Mukhametov, and J. M. Siegel, Neurosci. Biobehav. Rev. 32, 1451 (2008).CrossRefGoogle Scholar
  6. 6.
    E. A. Martens, S. Thutupallic, A. Fourrierec, and O. Hallatschek, Proc. Natl. Acad. Sci. 110, 10563 (2013).ADSCrossRefGoogle Scholar
  7. 7.
    T. Kapitaniak, P. Kuzma, J. Wojewoda, K. Czolczynski, and Y. Maistrenko, Sci. Rep. 4, 6379 (2014).ADSCrossRefGoogle Scholar
  8. 8.
    J. Wojewoda, K. Czolczynski, Y. Maistrenko, and T. Kapitaniak, Sci. Rep. 6, 34329 (2016).ADSCrossRefGoogle Scholar
  9. 9.
    D. Dudkowski, J. Grabski, J. Wojewoda, P. Perlikowski, Y. Maistrenko, and T. Kapitaniak, Sci. Rep. 6, 29833 (2016).ADSCrossRefGoogle Scholar
  10. 10.
    A. M. Hagerstrom, T. E. Murphy, R. Roy, P. Hovel, I. Omelchenko, and E. Schöll, Nat. Phys. 8, 658 (2012).CrossRefGoogle Scholar
  11. 11.
    L. Larger, B. Penkovsky, and Y. Maistrenko, Nat. Commun. 6, 7752 (2015).ADSCrossRefGoogle Scholar
  12. 12.
    M. R. Tinsley, S. Nkomo, and K. Showalter, Nat. Phys. 8, 662 (2012).CrossRefGoogle Scholar
  13. 13.
    L. Schmidt, K. Schönleber, K. Krischer, and V. Garcia-Morales, Chaos 24, 013102 (2014).ADSMathSciNetCrossRefGoogle Scholar
  14. 14.
    M. Wickramasinghe and I. Z. Kiss, PLOS One 8, e80586 (2013).ADSCrossRefGoogle Scholar
  15. 15.
    M. Wickramasinghe and I. Z. Kiss, Phys. Chem. Chem. Phys. 16, 18360 (2014).CrossRefGoogle Scholar
  16. 16.
    A. G. Smart, Phys. Today 65, 17 (2012).CrossRefGoogle Scholar
  17. 17.
    L. Larger, B. Penkovsky, and Y. Maistrenko, Phys. Rev. Lett. 111, 054103 (2013).ADSCrossRefGoogle Scholar
  18. 18.
    L. V. Gambuzza, A. Buscarino, S. Chessari, L. Fortuna, R. Meucci, and M. Frasca, Phys. Rev. E 90, 032905 (2014).ADSCrossRefGoogle Scholar
  19. 19.
    D. S. Shchapin, A. S. Dmitrichev, and V. I. Nekorkin, JETP Lett. 106, 617 (2017).ADSCrossRefGoogle Scholar
  20. 20.
    R. G. Andrzejak, G. Ruzzene, and I. Malvestio, Chaos 27, 053114 (2017).ADSMathSciNetCrossRefGoogle Scholar
  21. 21.
    C. Tian, H. Bi, X. Zhang, S. Guan, and Z. Liu, Phys. Rev. E 96, 052209 (2017).CrossRefGoogle Scholar
  22. 22.
    S. Majhi, M. Perc, and D. Ghosh, Chaos 27, 073109 (2017).ADSMathSciNetCrossRefGoogle Scholar
  23. 23.
    S. R. Ujjwal, N. Punetha, and R. Ramaswamy, Phys. Rev. E 93, 012207 (2016).ADSCrossRefGoogle Scholar
  24. 24.
    V. A. Maksimenko, V. V. Makarov, B. K. Bera, D. Ghosh, S. K. Dana, M. V. Goremyko, N. S. Frolov, A. A. Koronovskii, and A. E. Hramov, Phys. Rev. E 94, 052205 (2016).ADSCrossRefGoogle Scholar
  25. 25.
    M. T. Heath, Scientific Computing: An Introductory Survey (McGraw-Hill, New York, 2002).zbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Inc. 2018

Authors and Affiliations

  • A. S. Dmitrichev
    • 1
  • D. S. Shchapin
    • 1
    Email author
  • V. I. Nekorkin
    • 1
    • 2
  1. 1.Institute of Applied PhysicsRussian Academy of SciencesNizhny NovgorodRussia
  2. 2.Lobachevsky State University of Nizhny NovgorodNizhny NovgorodRussia

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