Advertisement

Pramana

, Volume 83, Issue 6, pp 945–953 | Cite as

Dependence of synchronization frequency of Kuramoto oscillators on symmetry of intrinsic frequency in ring network

  • ARINDAM SAHAEmail author
  • R E AMRITKAR
Article

Abstract

Kuramoto oscillators have been proposed earlier as a model for interacting systems that exhibit synchronization. In this article, we study the difference between networks with symmetric and asymmetric distribution of natural frequencies. We first indicate that synchronization frequency of oscillators in a completely connected network is always equal to the mean of the natural frequency distribution. In particular, shape of the natural frequency distribution does not affect the synchronization frequency in this case. Then, we analyse the case of oscillators in a directed ring network, where asymmetry in the natural frequency distribution is seen to shift the synchronization frequency of the network. We also present an estimate of the shift in the frequencies for slightly asymmetric distributions.

Keywords

Kuramoto synchronization asymmetry frequency distribution 

PACS No

05.45.Xt 

References

  1. [1]
    J Buck, Quart. Rev. Biol. 63(3), 265 (1988)Google Scholar
  2. [2]
    Z Néda, E Ravasz, T Vicsek, Y Brechet and A L Barabási, Phys. Rev. E 61(6), 6987 (2000)Google Scholar
  3. [3]
    W Gerstner, Phys. Rev. E 51(1), 738 (1995)Google Scholar
  4. [4]
    Kurt Wiesenfeld, Pere Colet and Steven H Strogatz, Phys. Rev. E 57, 1563 (1998)Google Scholar
  5. [5]
    Kurt Wiesenfeld, Pere Colet and Steven H Strogatz, Phys. Rev. Lett. 76(3), 404 (1996)Google Scholar
  6. [6]
    Y Kuramoto, Chemical oscillations, waves, and turbulence (Dover Publications, 2003)Google Scholar
  7. [7]
    N Wiener, Nonlinear problem in random theory edited by Norbert Wiener, ISBN 0-262-73012-X (The MIT Press, Cambridge, Massachusetts, USA, 1966) p. 142Google Scholar
  8. [8]
    N Wiener, Scient. Amer. 179(5), 14 (1948)Google Scholar
  9. [9]
    S H Strogatz, Phys. D: Nonlinear Phenom. 143(1), 1 (2000)Google Scholar
  10. [10]
    Radford M Neal, Ann. Stat. 31(3), 705 (2003)Google Scholar
  11. [11]
    Christian P Robert and George Casella, Monte Carlo statistical methods (Citeseer, 2004) Vol. 319Google Scholar
  12. [12]
    S M Ross, Simulation (Elsevier Academic Press, Amsterdam, 2006)Google Scholar
  13. [13]
    J Aitchison and J A C Brown, The lognormal distribution (University of Cambridge, Department of Applied Economics, Monograph No. 5, 1957)Google Scholar

Copyright information

© Indian Academy of Sciences 2014

Authors and Affiliations

  1. 1.Department of Physical SciencesIndian Institute of Science Education and ResearchKolkataIndia
  2. 2.Department of Theoretical PhysicsPhysical Research LaboratoryAhmedabadIndia

Personalised recommendations