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Dynamical model for competing opinions

S. R. Souza1,2,* and S. Gonçalves2,†

  • 1Instituto de Física, Universidade Federal do Rio de Janeiro, Cidade Universitária, Caixa Postale 68528, Rio de Janeiro 21941-972, Brazil
  • 2Instituto de Física, Universidade Federal do Rio Grande do Sul, Avenida Bento Gonçalves 9500, Caixa Postale 15051, Porto Alegre 91501-970, Brazil

  • *srsouza@if.ufrj.br
  • †sgonc@if.ufrgs.br
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Phys. Rev. E 85, 056103 – Published 3 May, 2012

DOI: https://doi.org/10.1103/PhysRevE.85.056103

Abstract

We propose an opinion model based on agents located at the vertices of a regular lattice. Each agent has an independent opinion (among an arbitrary, but fixed, number of choices) and its own degree of conviction. The latter changes every time two agents which have different opinions interact with each other. The dynamics leads to size distributions of clusters (made up of agents which have the same opinion and are located at contiguous spatial positions) which follow a power law, as long as the range of the interaction between the agents is not too short; i.e., the system self-organizes into a critical state. Short range interactions lead to an exponential cutoff in the size distribution and to spatial correlations which cause agents which have the same opinion to be closely grouped. When the diversity of opinions is restricted to two, a nonconsensus dynamic is observed, with unequal population fractions, whereas consensus is reached if the agents are also allowed to interact with those located far from them. The individual agents' convictions, the preestablished interaction range, and the locality of the interaction between a pair of agents (their neighborhood has no effect on the interaction) are the main characteristics which distinguish our model from previous ones.

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References (33)

  1. C. Castellano, S. Fortunato, and V. Loreto, Rev. Mod. Phys. 81, 591 (2009).
  2. H. Ohtsuki, C. Hauert, E. Lieberman, and M. A. Nowak, Nature (London) 441, 502 (2006).
  3. S. Moss de Oliveira, P. M. C. de Oliveira, and D. Stauffer, Evolution, Money War and Computers (Teubner, Sttutgart, 1999).
  4. S. Bornholdt, M. H. Jensen, and K. Sneppen, Phys. Rev. Lett. 106, 058701 (2011).
  5. R. Axelrod, J. Conflict Res. 41, 203 (1997).
  6. K. Klemm, V. M. Eguíluz, R. Toral, and M. San Miguel, Phys. Rev. E 67, 026120 (2003).
  7. J. C. González-Avella, V. M. Eguíluz, M. G. Cosenza, K. Klemm, J. L. Herrera, and M. San Miguel, Phys. Rev. E 73, 046119 (2006).
  8. L. Laloux, P. Cizeau, J.-P. Bouchaud, and M. Potters, Phys. Rev. Lett. 83, 1467 (1999).
  9. A. Charkraborti, I. M. Toke, M. Patriarca, and F. Abergel, Quant. Finance 11, 911 (2011).
  10. L. Kador, Phys. Rev. E 60, 1441 (1999).
  11. R. Donangelo, A. Hansen, K. Sneppen, and S. R. Souza, Phys. A 348, 496 (2005).
  12. D. Stauffer, S. Moss de Oliveira, P. M. C. de Oliveira, and J. S. Sá Martins, Biology, Sociology, Geology by Computational Physicists (Elsevier, Amsterdam, 2006).
  13. D. Stauffer and A. Aharony, Introduction to Percolation Theory, 2nd ed. (Taylor & Francis, Philadelphia, 2003).
  14. M. F. Laguna, S. R. Gusman, G. Abramson, S. G. Calves, and J. R. Iglesias, Phys. A 351, 580 (2005).
  15. M. S. de la Lama, I. G. Szendro, J. R. Iglesias, and H. S. Wio, Eur. Phys. J. B 51, 435 (2006).
  16. P. L. Krapivsky and S. Redner, Phys. Rev. Lett. 90, 238701 (2003).
  17. J. Shao, S. Havlin, and H. E. Stanley, Phys. Rev. Lett. 103, 018701 (2009).
  18. D. ben-Avraham, Phys. Rev. E 83, 050101 (2011).
  19. S. Galam, Europhys. Lett. 70, 705 (2005).
  20. R. Lambiotte and S. Redner, Europhys. Lett. 82, 18007 (2008).
  21. The upper bound for Ci used in the initialization does not play a relevant role in the evolution since it is adjusted by the system during the dynamics.
  22. P. Bak, C. Tang, and K. Wiesenfeld, Phys. Rev. Lett. 59, 381 (1987).
  23. M. Paczuski, S. Maslov, and P. Bak, Phys. Rev. E 53, 414 (1996).
  24. P. Bak, C. Tang, and K. Wiesenfeld, Phys. Rev. A 38, 364 (1988).
  25. K. Sneppen, Phys. Rev. Lett. 69, 3539 (1992).
  26. P. Bak, How Nature Works: The Science of Self-Organized Criticality (Copernicus, New York, 1996).
  27. P. Bak and K. Sneppen, Phys. Rev. Lett. 71, 4083 (1993).
  28. R. Korsnes, S. R. Souza, R. Donangelo, A. Hansen, M. Paczuski, and K. Sneppen, Phys. A 331, 291 (2004).
  29. A. Chmel, V. N. Smirnov, and L. V. Panov, Ocean Sci. 3, 291 (2007).
  30. J. Sá-Martins and P. M. C. de Oliveira, Braz. J. Phys. 34, 1077 (2004).
  31. N. Jan and D. Stauffer, Int. Mod. Phys. C 9, 341 (1998).
  32. D. Wilkinson and J. F. Willemsen, J. Phys. A 16, 3365 (1983).
  33. S. Schwarzer, S. Havlin, and A. Bunde, Phys. Rev. E 59, 3262 (1999).

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Phys. Rev. E 85, 056103– Published 3 May, 2012
  • Received 7 January 2012

©2012 American Physical Society

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