Advertisement

The European Physical Journal B

, Volume 71, Issue 4, pp 557–564 | Cite as

Consensus and ordering in language dynamics

Topical issue on The Physics Approach to Risk: Agent-Based Models and Networks

Abstract

We consider two social consensus models, the AB-model and the Naming Game restricted to two conventions, which describe a population of interacting agents that can be in either of two equivalent states (A or B) or in a third mixed (AB) state. Proposed in the context of language competition and emergence, the AB state was associated with bilingualism and synonymy respectively. We show that the two models are equivalent in the mean field approximation, though the differences at the microscopic level have non-trivial consequences. To point them out, we investigate an extension of these dynamics in which confidence/trust is considered, focusing on the case of an underlying fully connected graph, and we show that the consensus-polarization phase transition taking place in the Naming Game is not observed in the AB model. We then consider the interface motion in regular lattices. Qualitatively, both models show the same behavior: a diffusive interface motion in a one-dimensional lattice, and a curvature driven dynamics with diffusing stripe-like metastable states in a two-dimensional one. However, in comparison to the Naming Game, the AB-model dynamics is shown to slow down the diffusion of such configurations.

PACS

64.60.Cn Order-disorder transformations 87.23.Ge Dynamics of social systems 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    C. Castellano, S. Fortunato, V. Loreto, Rev. Modern Phys. 81, 591 (2009)CrossRefADSGoogle Scholar
  2. 2.
    D.M. Abrams, S.H. Strogatz, Nature 424, 900 (2003)CrossRefADSGoogle Scholar
  3. 3.
    M.A. Nowak, D.C. Krakauer, Proc. Natl. Acad. Sci. USA 96, 8028 (1999)CrossRefADSGoogle Scholar
  4. 4.
    M.A. Nowak, N.L. Komarova, P. Niyogi, Science 291, 114 (2001)CrossRefMathSciNetADSGoogle Scholar
  5. 5.
    L. Steels, Artificial Life 2, 319 (1995)ADSCrossRefGoogle Scholar
  6. 6.
    A. Baronchelli, M. Felici, V. Loreto, E. Caglioti, L. Steels, J. Statis. Mech. P06014 (2006)Google Scholar
  7. 7.
    D. Stauffer, C. Schulze, Phys. Life Rev. 2, 89 (2005)CrossRefADSGoogle Scholar
  8. 8.
    T. Tesileanu, H. Meyer-Ortmanns, Intern. J. Modern Phys. C 17, 259 (2006)MATHCrossRefADSGoogle Scholar
  9. 9.
    K. Kosmidis, J.M. Halley, P. Argyrakis, Physica A 353, 595 (2005)CrossRefADSGoogle Scholar
  10. 10.
    D. Stauffer, X. Castelló, V.M. Eguíluz, M. San Miguel, Physica A 374, 835 (2007)CrossRefADSGoogle Scholar
  11. 11.
    C. Schulze, D. Stauffer, Comput. Sci. Engineering 8, 60 (2006)CrossRefGoogle Scholar
  12. 12.
    W.S.-Y. Wang, J.W. Minett, Trends in Ecology and Evolution 20, 263 (2005)CrossRefGoogle Scholar
  13. 13.
    J.W. Minett, W.S.-Y. Wang, Lingua 118, 19 (2008)CrossRefGoogle Scholar
  14. 14.
    X. Castelló, V.M. Eguíluz, M. San Miguel, New J. Phys. 8, 308 (2006)CrossRefADSGoogle Scholar
  15. 15.
    X. Castelló, R. Toivonen, V.M. Eguíluz, J. Saramäki, K. Kaski, M. San Miguel, Europhys. Lett. 79, 66006 (2007)CrossRefADSGoogle Scholar
  16. 16.
    R. Toivonen, X. Castelló, V.M. Eguíluz, J. Saramäki, K. Kaski, M. San Miguel, Phys. Rev. E 79, 016109 (2008)CrossRefADSGoogle Scholar
  17. 17.
    A. Baronchelli, V. Loreto, L. Steels, Intern. J. Modern Phys. C 19, 785 (2008)MATHCrossRefADSGoogle Scholar
  18. 18.
    A. Baronchelli, L. Dall’Asta, A. Barrat, V. Loreto, Phys. Rev. E 73, 015102 (2005)CrossRefADSGoogle Scholar
  19. 19.
    L. Dall’Asta, A. Baronchelli, A. Barrat, V. Loreto, Europhys. Lett. 73, 969 (2006)CrossRefMathSciNetADSGoogle Scholar
  20. 20.
    L. Dall’Asta, A. Baronchelli, A. Barrat, V. Loreto, Phys. Rev. E 74, 036105 (2006)CrossRefADSGoogle Scholar
  21. 21.
    L. Dall’Asta, A. Baronchelli, J. Phys. A: Mathematical and General 39, 14851 (2006)MATHCrossRefMathSciNetADSGoogle Scholar
  22. 22.
    A. Puglisi, A. Baronchelli, V. Loreto, Proc. Natl. Acad. Sci. USA 105, 7936 (2008)CrossRefADSGoogle Scholar
  23. 23.
    A. Baronchelli, L. Dall’Asta, A. Barrat, V. Loreto, Phys. Rev. E 76, 051102 (2007)CrossRefADSGoogle Scholar
  24. 24.
    R. Holley, T. Liggett, Ann. Probab. 4, 195 (1975)CrossRefMathSciNetGoogle Scholar
  25. 25.
    H.U. Stark, C.J. Tessone, F. Schweitzer, Adv. Complex Syst. 11, 551 (2008)MATHCrossRefMathSciNetGoogle Scholar
  26. 26.
    L. Dall’Asta, C. Castellano, Europhys. Lett. 77, 60005 (2007)CrossRefMathSciNetADSGoogle Scholar
  27. 27.
    C. Castellano, M. Marsili, A. Vespignani, Phys. Rev. Lett. 85, 3536 (2000)CrossRefADSGoogle Scholar
  28. 28.
    F. Vazquez, S. Redner, Europhys. Lett. 78, 18002 (2007)CrossRefADSGoogle Scholar
  29. 29.
    J.D. Gunton, M. San Miguel, P. Sahni, Phase Transitions and Critical Phenomena, Vol. 8, Chapter. The dynamics of first order phase transitions, Academic Press, London, (1983), pp. 269–446Google Scholar
  30. 30.
    R.A. Blythe, J. Statis. Mech. P02059 (2009)Google Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.IFISC, Institut de Física Interdisciplinària i Sistemes Complexos (CSIC-UIB), Campus Universitat Illes BalearsPalma de MallorcaSpain
  2. 2.Departament de Física i Enginyeria NuclearUniversitat Politècnica de CatalunyaBarcelonaSpain
  3. 3.Dipartimento di Fisica“Sapienza” Università di RomaRomaItaly
  4. 4.Fondazione ISITorinoItaly

Personalised recommendations