Synchronization and structure in an adaptive oscillator network

  • P. M. Gleiser
  • D. H. Zanette
Statistical and Nonlinear Physics


We analyze the interplay of synchronization and structure evolution in an evolving network of phase oscillators. An initially random network is adaptively rewired according to the dynamical coherence of the oscillators, in order to enhance their mutual synchronization. We show that the evolving network reaches a small-world structure. Its clustering coefficient attains a maximum for an intermediate intensity of the coupling between oscillators, where a rich diversity of synchronized oscillator groups is observed. In the stationary state, these synchronized groups are directly associated with network clusters.


05.45.Xt Synchronization; coupled oscillators 05.65.+b Self-organized systems 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. N. Wiener, Cybernetics, or Control and Communication in the Animal and the Machine (MIT Press, Cambridge, 1948) Google Scholar
  2. A.T. Winfree, J. Theor. Biol. 16, 15 (1967) CrossRefGoogle Scholar
  3. C.M. Gray, P. König, A. Engel, W. Singer, Nature 338, 334 (1989) CrossRefADSGoogle Scholar
  4. S.H. Strogatz, Sync. The Emerging Science of Spontaneous Order (Hyperion, New York, 2003) Google Scholar
  5. J. Buck, E. Buck, Science 159, 1319 (1968) CrossRefADSGoogle Scholar
  6. J. Buck, E. Buck, Sci. Am. 234, 74 (1976) CrossRefGoogle Scholar
  7. S.H. Strogatz, D.M. Abrams, A. McRobie, B. Eckhardt, E. Ott, Nature 438, 43 (2005) CrossRefADSGoogle Scholar
  8. L.G. Moyano, G. Abramson, D.H. Zanette, Eur. Phys. J. B 22, 223 (2001) CrossRefADSGoogle Scholar
  9. M. Ipsen, A.S. Mikhailov, Phys. Rev. E 66, 046109 (2002) CrossRefADSGoogle Scholar
  10. P. Gong, C. Van Leeuwen, Europhys. Lett. 67, 328 (2004) CrossRefADSGoogle Scholar
  11. Y. Kuramoto, Chemical Oscillations, Waves and Turbulence (Springer, Berlin, 1984) Google Scholar
  12. J.A. Acebrón, L.L. Bonilla, C.J. Pérez Vicente, F. Ritort, R. Spigler, Rev. Mod. Phys. 77, 137 (2005) CrossRefADSGoogle Scholar
  13. S.C. Manrubia, A.S. Mikhailov, D.H. Zanette, Emergence of Dynamical Order. Synchronization Phenomena in Complex Systems (World Scientific, Singapore, 2004) Google Scholar
  14. D. Van Den Berg, C. Van Leeuwen, Europhys. Lett. 65, 459 (2004) CrossRefADSGoogle Scholar
  15. H. Hong, M.Y. Choi, B.J. Kim Phys, Rev. E 65, 026139 (2002) Google Scholar
  16. T. Ichinomiya, Phys. Rev. E 70, 026116 (2004) CrossRefADSGoogle Scholar
  17. D.-S. Lee, Phys. Rev. E 72, 026208 (2005) CrossRefADSGoogle Scholar
  18. D.J. Watts, S.H. Strogatz, Nature 393, 440 (1998) CrossRefADSGoogle Scholar
  19. P.N. McGraw, M. Menzinger, Phys. Rev. E 72, 015101 (2005) MathSciNetCrossRefADSGoogle Scholar
  20. Google Scholar

Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006

Authors and Affiliations

  1. 1.Consejo Nacional de Investigaciones Científicas y Técnicas Centro Atómico Bariloche and Instituto BalseiroBarilocheArgentina

Personalised recommendations