Skip to main content
SpringerLink
Log in

Chimera Structures in the Ensembles of Nonlocally Coupled Chaotic Oscillators

  • Published:
Radiophysics and Quantum Electronics Aims and scope

We study the structure and properties of the chimera states in the ensembles of chaotic oscillators with nonlocal coupling. It is shown that the phase and amplitude chimera states in the ensembles of chaotic oscillators with nonhyperbolic and hyperbolic attractors can be obtained using the models in the forms of two-dimensional Hénon and Lozi maps. The mechanisms of birth, the structure, and the lifetime of the phase and amplitude chimeras and the regime of solitary states are studied. The chimera states in two coupled ensembles of chaotic maps are considered. The possibility of realizing a new type of the chimera structure, namely, the chimera consisting of the solitary states is demonstrated. The effects of the external and mutual synchronizations of the chimera states are described by an example of two coupled ensembles of logistic maps with nonlocal coupling. A qualitative analogy of the obtained results with the classical effect of synchronization of periodic self-sustained oscillations is discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. V. S. Afraimovich, V. I. Nekorkin, G. V. Osipov, and V. D. Shalfeev, Stability, Structures and Chaos in Nonlinear Synchronization Networks, World Scientific, Singapore (1995).

    Book  MATH  Google Scholar 

  2. G. V. Osipov, J. Kurths, and Ch. Zhou, Synchronization in Oscillatory Networks, Springer, Berlin (2007).

    Book  MATH  Google Scholar 

  3. Y. Kuramoto and D. Battogtokh, Nonlinear Phenom. Complex Syst., 5, No. 4, 380 (2002).

    Google Scholar 

  4. D. M. Abrams and S. H. Strogatz, Phys. Rev. Lett., 93, No. 17, 174102 (2004).

    Article  ADS  Google Scholar 

  5. M. J. Panaggio and D. M. Abrams, Nonlinearity, 28, R67 (2015).

    Article  ADS  Google Scholar 

  6. D. M. Abrams, R. E. Mirollo, S. H. Strogatz, and D. A. Wiley, Phys. Rev. Lett., 101, 084103 (2008).

    Article  ADS  Google Scholar 

  7. C.R. Laing, Phys. Rev. E, 81, 066221 (2010).

    Article  ADS  MathSciNet  Google Scholar 

  8. E. A. Martens, C. R. Laing, and S. H. Strogatz, Phys. Rev. Lett., 104, 044101 (2010).

    Article  ADS  Google Scholar 

  9. A. E. Motter, Nat. Phys., 6, 164 (2010).

    Article  Google Scholar 

  10. M. Wolfrum and O. E. Omel’chenko, Phys. Rev. E, 84, 015201 (2011).

    Article  ADS  Google Scholar 

  11. I. Omelchenko, Y. Maistrenko, P. Hövel, and E. Schöll, Phys. Rev. Lett., 106, 234102 (2011).

    Article  ADS  Google Scholar 

  12. I. Omelchenko, B. Riemenschneider, P. Hövel, Y. Maistrenko, and E. Schöll, Phys. Rev. E, 85, 026212 (2012).

    Article  ADS  Google Scholar 

  13. Y. Maistrenko, A. Vasylenko, O. Sudakov, et al., Int. J. Bifurc. Chaos, 24, 1440014 (2014).

    Article  Google Scholar 

  14. A. Zakharova, M. Kapeller, and E. Schöll, Phys. Rev. Lett., 112, 154101 (2014).

    Article  ADS  Google Scholar 

  15. A. Yeldesbay, A. Pikovsky, and M. Rosenblum, Phys. Rev. Lett., 112, 144103 (2014).

    Article  ADS  Google Scholar 

  16. D. Dudkowski, Y. Maistrenko, and T. Kapitaniak, Phys. Rev. E, 90, 032920 (2014).

    Article  ADS  Google Scholar 

  17. N. Semenova, A. Zakharova, E. Schöll, and V. Anishchenko, Europhys. Lett., 112, 40002 (2015).

    Article  ADS  Google Scholar 

  18. S. Olmi, E. A. Martens, S. Thutupalli, and A. Torcini, Phys. Rev. E, 92, 030901(R) (2015).

    Article  ADS  Google Scholar 

  19. J. Hizanidis, E. Panagakou, I. Omelchenko, et. al., Phys. Rev. E, 92, 012915 (2015).

    Article  ADS  MathSciNet  Google Scholar 

  20. T. E. Vadivasova, G. I. Strelkova, S. A. Bogomolov, and V. S. Anishchenko, Chaos, 26, 093108 (2016).

    Article  ADS  MathSciNet  Google Scholar 

  21. F. P. Kemeth, S. W. Haugland, L. Schmidt, et al., Chaos, 26, 094815 (2016).

    Article  ADS  Google Scholar 

  22. S. Ulonska, I. Omelchenko, A. Zakharova, and E. Schöll, Chaos, 26, 094825 (2016).

    Article  ADS  MathSciNet  Google Scholar 

  23. N. I. Semenova, A. Zakharova, V. Anishchenko, and E. Schöll, Phys. Rev. Lett., 117, 01410 (2016).

    Article  Google Scholar 

  24. E. Schöll, Eur. Phys. J. Spec. Top., 225, 891 (2016).

    Article  Google Scholar 

  25. V. Semenov, A. Zakharova, Y. Maistrenko, and E. Schöll, Europhys. Lett., 115, 10005 (2016).

    Article  ADS  Google Scholar 

  26. J. Sawicki, I. Omelchenko, A. Zakharova, and E. Schöll, Eur. Phys. J. Spec. Top., 226, 1883 (2017).

    Article  Google Scholar 

  27. E. Rybalova, N. Semenova, G. Strelkova, and V. Anishchenko, Eur. Phys. J. Spec. Top., 226, 1857 (2017).

    Article  Google Scholar 

  28. N. I. Semenova, G. I. Strelkova, V. S. Anishchenko, and A. Zakharova, Chaos, 27, 061102 (2017).

    Article  ADS  MathSciNet  Google Scholar 

  29. S. A. Bogomolov, A.V. Slepnev, G. I. Strelkova, et al., Commun. Nonlinear Sci. Numer. Simul., 43, 25 (2017).

    Article  ADS  MathSciNet  Google Scholar 

  30. M. S. Santos, J. D. Szezezh Jr., A. M. Batista, et al., Phys. Lett. A, 379, 2188 (2015).

    Article  ADS  Google Scholar 

  31. A. Zakharova, N. Semenova, V. Anishchenko, and E. Schöll, Chaos, 27, 114320 (2017).

    Article  ADS  MathSciNet  Google Scholar 

  32. I. A. Shepelev, A. V. Bukh, T. E. Vadivasova, et al., Commun. Nonlinear Sci. Numer. Simul., 54, 50 (2018).

    Article  ADS  MathSciNet  Google Scholar 

  33. A. M. Hagerstrom, T. E. Murphy, R. Roy, et al., Nat. Phys., 8, 658 (2012).

    Article  Google Scholar 

  34. M. R. Tinsley, S. Nkomo, and K. Showalter, Nat. Phys., 8, 662 (2012).

    Article  Google Scholar 

  35. L. Larger, B. Penkovsky, and Y. L. Maistrenko, Phys. Rev. Lett., 111, 054103 (2013).

    Article  ADS  Google Scholar 

  36. E. A. Martens, S. Thutupalli, A. Fourriere, and O. Hallatschek, Proc. Natl. Acad. Sci. USA, 110, 10563 (2013).

    Article  ADS  Google Scholar 

  37. T. Kapitaniak, P. Kuzma, J. Wojewoda, et al., Sci. Rep., 4, 6379 (2014).

    Article  Google Scholar 

  38. L. Larger, B. Penkovsky, and Y. Maistrenko, Nat. Commun., 6, 7752 (2015).

    Article  ADS  Google Scholar 

  39. S. A. Bogomolov, G. I. Strelkovva, E. Schöll, and V. S. Anishchenko, Tech. Phys. Lett., 42, No. 7, 765 (2016).

    Article  ADS  Google Scholar 

  40. S. Watanabe, S. H. Strogatz, H. S. J. van der Zant, and T. P. Orlando, Phys. Rev. Lett., 74, 379 (1995).

    Article  ADS  Google Scholar 

  41. R. D. Li and T. Erneux, Phys. Rev. A, 49, 1301 (1993).

    Article  ADS  Google Scholar 

  42. J. Hizanidis, N. E. Kouvaris, G. Zamora-López, et al., Sci. Rep., 6, 19845 (2016).

    Article  ADS  Google Scholar 

  43. N. C. Rattenborg, C. J. Amlaner, and S. L. Lima, Neurosci. Biobehav. Rev., 24, 817 (2000).

    Article  Google Scholar 

  44. A. E. Motter, S. A. Myers, M. Anghel, and T. Nishikawa, Nat. Phys., 9, 191 (2013).

    Article  Google Scholar 

  45. T. Nishikawa and A. E. Motter, New J. Phys., 17, 015012 (2015).

    Article  ADS  Google Scholar 

  46. N. I. Semenova, E. V. Rybalova, G. I. Strelkova, and V. S. Anishchenko, Reg. Chaot. Dyn., 22, 148 (2017).

    Article  Google Scholar 

  47. V. S. Anishchenko, Complex Oscillations in Simple Systems [in Russian], Nauka, Moscow (1990).

    Google Scholar 

  48. T. E. Vadivasova, G. I. Strelkova, S. A. Bogomolov, and V. S. Anishchenko, Tekh. Phys. Lett., 43, No. 1, 118 (2017).

    Article  Google Scholar 

  49. V. Dziubak, Y. Maistrenko, and E. Schöll, Phys. Rev. E, 87, 032907 (2013).

    Article  ADS  Google Scholar 

  50. A. Bukh, N. Semenova, E. Rybalova, et al., Chaos, 27, 111102 (2017).

    Article  ADS  MathSciNet  Google Scholar 

  51. A. V. Bukh, G. I. Strelkova, and V. S. Anishchenko, arXiv, 1802.02771v1 (2018).

Download references

Author information

Authors and Affiliations

  1. N. G. Chernyshevsky Saratov National Research State University, Saratov, Russia

    V. S. Anishchenko & G. I. Strelkova

Authors
  1. V. S. Anishchenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. I. Strelkova
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. S. Anishchenko.

Additional information

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 61, No. 8–9, pp. 739–753, August 2018.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Anishchenko, V.S., Strelkova, G.I. Chimera Structures in the Ensembles of Nonlocally Coupled Chaotic Oscillators. Radiophys Quantum El 61, 659–671 (2019). https://doi.org/10.1007/s11141-019-09926-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11141-019-09926-5

Search

Navigation