Skip to main content

Modeling collective motion: variations on the Vicsek model


We argue that the model introduced by Vicsek et al. in which self-propelled particles align locally with neighbors is, because of its simplicity, central to most studies of collective motion or “active” matter. After reviewing briefly its main properties, we show how it can be expanded into three main directions: changing the symmetry of the particles and/or of their interactions, adding local cohesion, and taking into account the fluid in which the particles move.

This is a preview of subscription content, access via your institution.


  1. V. Narayan et al. Science 317, 105 (2007)

    Article  ADS  Google Scholar 

  2. T. Vicsek et al. Phys. Rev. Lett. 75, 1226 (1995); A. Czirók, H.E. Stanley, T. Vicsek, J. Phys. A 30, 1375 (1997)

    Article  ADS  Google Scholar 

  3. H. Chaté, F. Ginelli, G. Grégoire, F. Raynaud, Phys. Rev. E 77, 046113 (2008); G. Grégoire, H. Chaté, Phys. Rev. Lett. 92, 025702 (2004)

    Article  ADS  Google Scholar 

  4. J. Toner, Y. Tu, Phys. Rev. Lett. 75, 4326 (1995); Phys. Rev. E 58, 4828 (1998); J. Toner, Y. Tu, M. Ulm, Phys. Rev. Lett. 80, 4819 (1998)

    Article  ADS  Google Scholar 

  5. H. Chaté, F. Ginelli, R. Montagne, Phys. Rev. Lett. 96, 180602 (2006)

    Article  ADS  Google Scholar 

  6. H. Chaté et al. unpublished

  7. R.A. Simha, S. Ramaswamy, Physica A 306, 262 (2002); Phys. Rev. Lett. 89, 058101 (2002); S. Ramaswamy, R.A. Simha, J. Toner, Europhys. Lett. 62, 196 (2003)

    MATH  Article  ADS  Google Scholar 

  8. F. Peruani, A. Deutsch, M. Bär, Phys. Rev. E 74, 0309904(R) (2006)

    Article  Google Scholar 

  9. A. Kudrolli, G. Lumay, D. Volfson, L.S. Tsimring, Phys. Rev. Lett. 100, 058001 (2008)

    Article  ADS  Google Scholar 

  10. P. Kraikivski, R. Lipowsky, J. Kierfeld, Biophysical J. 483 (2007); D. Karpeev et al. Phys. Rev. E 76, 051905 (2007)

  11. A. Huth, C. Wissel, J. Theor. Biol. 156, 365 (1992)

    Article  Google Scholar 

  12. G. Grégoire, H. Chaté, Y. Tu, Physica D 181, 157 (2003); see also Phys. Rev. Lett. 86, 556 (2001); Phys. Rev. E 64, 011902 (2001)

    MATH  Article  ADS  MathSciNet  Google Scholar 

  13. M. Ballerini et al. Proc. Natl. Acad. Sci. USA 105, 1232 (2008)

    Article  ADS  Google Scholar 

  14. See for instance B.L. Partridge, T.J. Pitcher, Nature (London) 279, 418 (1979); P.B.S. Lissaman, C.A. Shollenberger, Science 168, 1003 (1970); D. Weihs, Nature 241, 290 (1973); J.P. Badgerow, F.R. Hainsworth, J. Theor. Biol. 93, 41 (1981)

    Article  ADS  Google Scholar 

  15. A. Sokolov, I.S. Aranson, J.O. Kassler, R.E. Goldstein, Phys. Rev. Lett. 98, 158102 (2007)

    Article  ADS  Google Scholar 

  16. H. Diamant, B. Cui, B. Lin, S.A. Rice, J. Phys.: Condens. Matter 17, S2787 (2005)

    Article  ADS  Google Scholar 

  17. J.P. Hernández-Ortiz, J.J. de Pablo, M.D. Graham, Phys. Rev. Lett. 98, 140602 (2007); D. Saintillan, M.J. Shelley Phys. Rev. Lett. 99, 058102 (2007)

    Article  ADS  Google Scholar 

  18. E. Bertin, M. Droz, G. Grégoire, Phys. Rev. E 74, 022101 (2006); I.S. Aranson, A. Sokolov, J.O. Kessler, R.E. Goldstein, Phys. Rev. E 75, 040901(R) (2007)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to H. Chaté.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Chaté, H., Ginelli, F., Grégoire, G. et al. Modeling collective motion: variations on the Vicsek model. Eur. Phys. J. B 64, 451–456 (2008).

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI:


  • 64.70.qj Dynamics and criticality
  • 87.18.Nq Large-scale biological processes and integrative biophysics