Chimera Structures in the Ensembles of Nonlocally Coupled Chaotic Oscillators

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.

References

  1. 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).

    Google Scholar 

  2. 2.

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

    Google Scholar 

  3. 3.

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

    Google Scholar 

  4. 4.

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

    ADS  Article  Google Scholar 

  5. 5.

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

    ADS  Article  Google Scholar 

  6. 6.

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

    ADS  Article  Google Scholar 

  7. 7.

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

    ADS  MathSciNet  Article  Google Scholar 

  8. 8.

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

    ADS  Article  Google Scholar 

  9. 9.

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

    Article  Google Scholar 

  10. 10.

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

    ADS  Article  Google Scholar 

  11. 11.

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

    ADS  Article  Google Scholar 

  12. 12.

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

    ADS  Article  Google Scholar 

  13. 13.

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

    Article  Google Scholar 

  14. 14.

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

    ADS  Article  Google Scholar 

  15. 15.

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

    ADS  Article  Google Scholar 

  16. 16.

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

    ADS  Article  Google Scholar 

  17. 17.

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

    ADS  Article  Google Scholar 

  18. 18.

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

    ADS  Article  Google Scholar 

  19. 19.

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

    ADS  MathSciNet  Article  Google Scholar 

  20. 20.

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

    ADS  MathSciNet  Article  Google Scholar 

  21. 21.

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

    ADS  Article  Google Scholar 

  22. 22.

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

    ADS  MathSciNet  Article  Google Scholar 

  23. 23.

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

    Article  Google Scholar 

  24. 24.

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

    Article  Google Scholar 

  25. 25.

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

    ADS  Article  Google Scholar 

  26. 26.

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

    Article  Google Scholar 

  27. 27.

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

    Article  Google Scholar 

  28. 28.

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

    ADS  MathSciNet  Article  Google Scholar 

  29. 29.

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

    ADS  MathSciNet  Article  Google Scholar 

  30. 30.

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

    ADS  Article  Google Scholar 

  31. 31.

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

    ADS  MathSciNet  Article  Google Scholar 

  32. 32.

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

    ADS  MathSciNet  Article  Google Scholar 

  33. 33.

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

    Article  Google Scholar 

  34. 34.

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

    Article  Google Scholar 

  35. 35.

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

    ADS  Article  Google Scholar 

  36. 36.

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

    ADS  Article  Google Scholar 

  37. 37.

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

    Article  Google Scholar 

  38. 38.

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

    ADS  Article  Google Scholar 

  39. 39.

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

    ADS  Article  Google Scholar 

  40. 40.

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

    ADS  Article  Google Scholar 

  41. 41.

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

    ADS  Article  Google Scholar 

  42. 42.

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

    ADS  Article  Google Scholar 

  43. 43.

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

    Article  Google Scholar 

  44. 44.

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

    Article  Google Scholar 

  45. 45.

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

    ADS  Article  Google Scholar 

  46. 46.

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

    Article  Google Scholar 

  47. 47.

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

    Google Scholar 

  48. 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. 49.

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

    ADS  Article  Google Scholar 

  50. 50.

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

    ADS  MathSciNet  Article  Google Scholar 

  51. 51.

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

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Correspondence to V. S. Anishchenko.

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

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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

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