Advertisement

The European Physical Journal Special Topics

, Volume 227, Issue 10–11, pp 1221–1230 | Cite as

Effects of structure-dynamics correlation on hierarchical transitions in heterogeneous oscillatory networks

  • Oleg V. MaslennikovEmail author
  • Vladimir I. NekorkinEmail author
Regular Article
Part of the following topical collections:
  1. Advances in Nonlinear Dynamics of Complex Networks: Adaptivity, Stochasticity, Delays

Abstract

The impact of frequency-degree and amplitude-degree correlation is studied for heterogeneous networks of coupled Stuart–Landau oscillators. It is shown that increasing coupling strength gives rise to hierarchical processes of oscillation quenching. In case of frequency-degree correlated networks, higher-frequency oscillators gradually become almost quenched while low-frequency ones still remain oscillating. In case of amplitude-degree correlated networks, there appear three distinct domains, two contain low-amplitude oscillations with positive and negative means, and the third includes high-amplitude oscillations around the origin.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, D.-U. Hwang, Phys. Rep. 424, 175 (2006) ADSMathSciNetCrossRefGoogle Scholar
  2. 2.
    M. Newman, A.-L. Barabasi, D.J. Watts, The structure and dynamics of networks (Princeton University Press, Princeton, New Jersey, USA, 2011) Google Scholar
  3. 3.
    O.V. Maslennikov, V.I. Nekorkin, Phys. Usp. 60, 694 (2017) ADSCrossRefGoogle Scholar
  4. 4.
    A.-L. Barabási, R. Albert, Science 286, 509 (1999) ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    G. Bianconi, A.-L. Barabási, Europhys. Lett. 54, 436 (2001) ADSCrossRefGoogle Scholar
  6. 6.
    G. Caldarelli, A. Capocci, P. De Los Rios, M.A. Munoz, Phys. Rev. Lett. 89, 258702 (2002) ADSCrossRefGoogle Scholar
  7. 7.
    M. Boguñá, R. Pastor-Satorras, Phys. Rev. E 68, 036112 (2003) ADSCrossRefGoogle Scholar
  8. 8.
    K.-I. Goh, B. Kahng, D. Kim, Phys. Rev. Lett. 87, 278701 (2001) CrossRefGoogle Scholar
  9. 9.
    B. Söderberg, Phys. Rev. E 66, 066121 (2002) ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    D. Garlaschelli, M.I. Loffredo, Phys. Rev. Lett. 93, 188701 (2004) ADSCrossRefGoogle Scholar
  11. 11.
    V.D.P. Servedio, G. Caldarelli, P. Buttà, Phys. Rev. E 70, 056126 (2004) ADSCrossRefGoogle Scholar
  12. 12.
    S. Fortunato, A. Flammini, F. Menczer, Phys. Rev. Lett. 96, 218701 (2006) ADSCrossRefGoogle Scholar
  13. 13.
    D. Garlaschelli, A. Capocci, G. Caldarelli, Nat. Phys. 3, 813 (2007) CrossRefGoogle Scholar
  14. 14.
    J. Gómez-Gardenes, S. Gómez, A. Arenas, Y. Moreno, Phys. Rev. Lett. 106, 128701 (2011) ADSCrossRefGoogle Scholar
  15. 15.
    B. Coutinho, A. Goltsev, S. Dorogovtsev, J. Mendes, Phys. Rev. E 87, 032106 (2013) ADSCrossRefGoogle Scholar
  16. 16.
    I. Leyva, R. Sevilla-Escoboza, J. Buldú, I. Sendina-Nadal, J. Gómez-Gardeñes, A. Arenas, Y. Moreno, S. Gómez, R. Jaimes-Reátegui, S. Boccaletti, Phys. Rev. Lett. 108, 168702 (2012) ADSCrossRefGoogle Scholar
  17. 17.
    P.S. Skardal, J. Sun, D. Taylor, J.G. Restrepo, Europhys. Lett. 101, 20001 (2013) ADSCrossRefGoogle Scholar
  18. 18.
    I. Leyva, A. Navas, I. Sendina-Nadal, J. Almendral, J. Buldú, M. Zanin, D. Papo, S. Boccaletti, Sci. Rep. 3, 1281 (2013) ADSCrossRefGoogle Scholar
  19. 19.
    R.S. Pinto, A. Saa, Phys. Rev. E 91, 022818 (2015) ADSCrossRefGoogle Scholar
  20. 20.
    S. Jiang, W. Fang, S. Tang, S. Pei, S. Yan, Z. Zheng, J. Korean. Phys. Soc. 67, 389 (2015) ADSCrossRefGoogle Scholar
  21. 21.
    P. Kundu, P. Khanra, C. Hens, P. Pal, Phys. Rev. E 96, 052216 (2017) ADSMathSciNetCrossRefGoogle Scholar
  22. 22.
    W. Liu, X. Wang, S. Guan, C.-H. Lai, New J. Phys. 11, 093016 (2009) ADSCrossRefGoogle Scholar
  23. 23.
    G. Bordyugov, A. Pikovsky, M. Rosenblum, Phys. Rev. E 82, 035205 (2010) ADSMathSciNetCrossRefGoogle Scholar
  24. 24.
    A.A. Selivanov, J. Lehnert, T. Dahms, P. Hövel, A.L. Fradkov, E. Schöll, Phys. Rev. E 85, 016201 (2012) ADSCrossRefGoogle Scholar
  25. 25.
    A. Koseska, E. Volkov, J. Kurths, Phys. Rep. 531, 173 (2013) ADSMathSciNetCrossRefGoogle Scholar
  26. 26.
    L. Schmidt, K. Schönleber, K. Krischer, V. García-Morales, Chaos 24, 013102 (2014) ADSMathSciNetCrossRefGoogle Scholar
  27. 27.
    H. Bi, X. Hu, X. Zhang, Y. Zou, Z. Liu, S. Guan, Europhys. Lett. 108, 50003 (2014) ADSCrossRefGoogle Scholar
  28. 28.
    A. Zakharova, M. Kapeller, E. Schöll, Phys. Rev. Lett. 112, 154101 (2014) ADSCrossRefGoogle Scholar
  29. 29.
    L.V. Gambuzza, J. Gómez-Gardeñes, M. Frasca, Sci. Rep. 6, 24915 (2016) ADSCrossRefGoogle Scholar
  30. 30.
    A. Bergner, M. Frasca, G. Sciuto, A. Buscarino, E.J. Ngamga, L. Fortuna, J. Kurths, Phys. Rev. E 85, 026208 (2012) ADSCrossRefGoogle Scholar
  31. 31.
    L.V. Gambuzza, A. Cardillo, A. Fiasconaro, L. Fortuna, J. Gómez-Gardenes, M. Frasca, Chaos 23, 043103 (2013) ADSCrossRefGoogle Scholar
  32. 32.
    J. Gómez-Gardeñes, Y. Moreno, Phys. Rev. E 73, 056124 (2006) ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Applied Physics of the Russian Academy of SciencesNizhny NovgorodRussia

Personalised recommendations