Clustering and phase synchronization in populations of coupled phase oscillators

Regular Article


In many species daily rhythms are endogenously generated by groups of coupled neurons that play the role of a circadian pacemaker. The adaptation of the circadian clock to environmental and seasonal changes has been proposed to be regulated by a dual oscillator system. In order to gain insight into this model, we analyzed the synchronization properties of two fully coupled groups of Kuramoto oscillators. Each group has an internal coupling parameter and the interaction between the two groups can be controlled by two parameters allowing for symmetric or non-symmetric coupling. We show that even for such a simple model counterintuitive behaviours take place, such as a global decrease in synchrony when the coupling between the groups is increased. Through a detailed analysis of the local synchronization processes we explain this behaviour.


Statistical and Nonlinear Physics 


  1. 1.
    Clocks and Rhythms, in Cold Spring Harbor Symposia on Quantitative Biology (Cold Spring Harbor Laboratory Press, 2008), Vol. 72 Google Scholar
  2. 2.
    S. Daan, C.S. Pittendrigh, J. Comp. Physiol. 106, 253 (1976) CrossRefGoogle Scholar
  3. 3.
    C. Helfrich-Förster, J. Biol. Rhythms 24, 259 (2009)CrossRefGoogle Scholar
  4. 4.
    V. Sheeba, M. Kaneko, V. Sharma, T. Holmes, Crit. Rev. Biochem. Mol. Biol. 43, 37 (2008)CrossRefGoogle Scholar
  5. 5.
    D. Stoleru, Y. Peng, J. Agosto, M. Rosbash, Nature 431, 862 (2004) CrossRefADSGoogle Scholar
  6. 6.
    Z. Yao, O.T. Shafer, Science 343, 1516 (2014) CrossRefADSGoogle Scholar
  7. 7.
    S. Risau Gusman, P. Gleiser, J. Biol. Rhythms 29, 401 (2014)CrossRefGoogle Scholar
  8. 8.
    M. Hafner, H. Koeppl, D. Gonze, PLoS Comput. Biol. 8, e1002419 (2012) CrossRefADSGoogle Scholar
  9. 9.
    Y. Kuramoto, Chemical Oscillations, Waves and Turbulence (Springer, 1984)Google Scholar
  10. 10.
    T. Winfree, The Geometry of Biological Time, Interdisciplinary Applied Mathematics (Springer, 2001)Google Scholar
  11. 11.
    A. Pikovsky, M. Rosenblum, J. Kurths, Synchronization. A Universal Concept in Nonlinear Sciences (Cambridge University Press, 2001)Google Scholar
  12. 12.
    S. Strogatz, Sync. The Emerging Science of Spontaneous Order (Hyperion, 2003)Google Scholar
  13. 13.
    S. Manrubia, A. Mikhailov, D. Zanette, Emergence of Dynamical Order. Synchronization Phenomena in Complex Systems (World Scientific, 2004)Google Scholar
  14. 14.
    J. Acebrón, L. Bonilla, C.P. Vicente, F. Ritort, R. Spigler, Rev. Mod. Phys. 77, 137 (2005)CrossRefADSGoogle Scholar
  15. 15.
    K. Okuda, Y. Kuramoto, Prog. Theor. Phys. 86, 1159 (1991) MathSciNetCrossRefADSGoogle Scholar
  16. 16.
    E. Montbrió, J. Kurths, B. Blasius, Phys. Rev. E 70, 056125 (2004) CrossRefADSGoogle Scholar
  17. 17.
    J. Sheeba, V. Chandrasekar, A. Stefanovska, P. McClintock, Phys. Rev. E 78, 025201 (2008) CrossRefADSGoogle Scholar
  18. 18.
    E. Barreto, B. Hunt, E. Ott, P. So, Phys. Rev. E 77, 036107 (2008) MathSciNetCrossRefADSGoogle Scholar
  19. 19.
    D. Abrams, R. Mirollo, S. Strogatz, D. Wiley, Phys. Rev. Lett. 101, 084103 (2008) CrossRefADSGoogle Scholar
  20. 20.
    I. Kiss, M. Quigg, S.H. Chun, H. Kori, J. Hudson, Biophys. J. 94, 1121 (2008) CrossRefGoogle Scholar
  21. 21.
    E.A. Martens, E. Barreto, S.H. Strogatz, E. Ott, P. So, T. Antonsen, Phys. Rev. E 79, 026204 (2009) MathSciNetCrossRefADSGoogle Scholar
  22. 22.
    E. Ott, T. Antonsen, Chaos 18, 037113 (2008) MathSciNetCrossRefADSGoogle Scholar
  23. 23.
    I. Kiss, Y. Zhai, J. Hudson, Science 296, 1676 (2002) CrossRefADSGoogle Scholar
  24. 24.
    H. Sakaguchi, Prog. Theor. Phys. 79, 39 (1988)MathSciNetCrossRefADSGoogle Scholar
  25. 25.
    J.R. Engelbrecht, R. Mirollo, Phys. Rev. Lett. 109, 034103 (2012) CrossRefADSGoogle Scholar
  26. 26.
    D. Pazo, E. Montbrio, Phys. Rev. X 4, 011009 (2014) Google Scholar
  27. 27.
    A. Mikhailov, D. Zanette, Y. Zhai, I. Kiss, J. Hudson, Proc. Natl. Acad. Sci. 101, 10890 (2004) CrossRefADSGoogle Scholar
  28. 28.
    U. Abraham, A. Granada, P. Westermark, M. Heine, A. Kramer, H. Herzel, Mol. Syst. Biol. 6, 438 (2010)CrossRefGoogle Scholar
  29. 29.
    L. Buzna, S. Lozano, A. Díaz-Guilera, Phys. Rev. E 80, 066120 (2009) CrossRefADSGoogle Scholar
  30. 30.
    J. Schaap, H. Albus, H.T. vanderLeest, P. Eilers, L. Détári, J. Meijer, Proc. Natl. Acad. Sci. 100, 15994 (2003) CrossRefADSGoogle Scholar
  31. 31.
    H. de la Iglesia, J. Meyer, A. Carpino Jr, W. Schwartz, Science 290, 799 (2000) CrossRefADSGoogle Scholar
  32. 32.
    D. Li, C. Zhou, Frontiers Syst. Neurosc. 5, 100 (2011)CrossRefGoogle Scholar
  33. 33.
    T. Yoshii, C. Wülbeck, H. Sehadova, S. Veleri, D. Bichler, R. Stanewsky, C. Helfrich-Förster, J. Neurosci. 29, 2597 (2009) CrossRefGoogle Scholar
  34. 34.
    C. Wülbeck, E. Grieshaber, C. Helfrich-Förster, J. Biol. Rhythms 23, 409 (2008)CrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Centro Atómico Bariloche, BarilocheRío NegroArgentina
  2. 2.Consejo Nacional de Investigaciones Científicas y TécnicasBuenos AiresArgentina

Personalised recommendations