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The European Physical Journal B

, Volume 57, Issue 2, pp 147–152 | Cite as

Can a few fanatics influence the opinion of a large segment of a society?

  • D. StaufferEmail author
  • M. Sahimi
Topical Issue on Physics in Society

Abstract.

Models that provide insight into how extreme positions regarding any social phenomenon may spread in a society or at the global scale are of great current interest. A realistic model must account for the fact that globalization, internet, and other means of mass communications have given rise to scale-free networks of interactions between people. We propose a novel model which takes into account the nature of the interactions network, and provides some key insights into this phenomenon. These include, (1) the existence of a fundamental difference between a hierarchical network whereby people are influenced by those that are higher in the hierarchy but not by those below them, and a symmetrical network where person-on-person influence works mutually, and (2) that a few “fanatics” can influence a large fraction of the population either temporarily (in the hierarchical networks) or permanently (in symmetrical networks). Even if the “fanatics” disappear, the population may still remain susceptible to the positions originally advocated by them. The model is, however, general and applicable to any phenomenon for which there is a degree of enthusiasm or susceptibility to in the population.

PACS.

02.50.Ey Stochastic processes 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion 89.65.-s Social and economic systems 89.75.-k Complex systems 

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References

  1. R. Albert, A.L. Barabási, Rev. Mod. Phys. 74, 47 (2002); J.F.F. Mendes, S.N. Dorogovtsev, Evolution of Networks: From Biological Nets to the Internet and the WWW (Oxford University Press, London, 2003) CrossRefADSMathSciNetGoogle Scholar
  2. C. Castillo-Chavez, B. Song, in Bioterrorism - Mathematical Modeling Applications in Homeland Security, edited by H.T. Banks, C. Castillo-Chavez (SIAM, Philadelphia, 2003), p. 155 Google Scholar
  3. N.T.J. Bailey, The Mathematical Theory of Infectious Disease, 2nd edn. (Griffin, London, 1975) Google Scholar
  4. R.M. Anderson, R.M. May, Infectious Diseases of Humans (Oxford University Oxford, Oxford, 1991); J.D. Murray, Mathematical Biology (Springer, Berlin, 1993); V. Capasso, Mathematical Structures of Epidemic Systems (Springer, Berlin, 1993); Epidemic Models, edited by D. Mollison (Cambridge University Press, Cambridge, 1995) Google Scholar
  5. See, for example, I.B. Schwartz, H.L. Smith, J. Math. Biol. 18, 233 (1983); A.L. Lloyd, R.M. May, J. Theor. Biol. 179, 1 (1996); M.J. Keeling, P. Rohani, B.T. Grenfell, Physica D 148, 317 (2001); M. Kamo, A. Sasaki, Physica D 165, 228 (2002); H.W. Hethcote, SIAM Rev. 42, 4999 (2000) CrossRefMathSciNetGoogle Scholar
  6. H.C. Tuckwell, L. Toubiana, J.-F. Vibert, Phys. Rev. E 57, 2163 (1998); H.C. Tuckwell, L. Toubiana, J.-F. Vibert, Phys. Rev. E 61, 5611 (2000); H.C. Tuckwell, L. Toubiana, J.-F. Vibert, Phys. Rev. E 64, 041918 (2001) CrossRefADSGoogle Scholar
  7. D.H. Zanette, Phys. Rev. E 64, 050901 (2001); D.H. Zanette, Phys. Rev. E 65, 041908 (2002) CrossRefADSGoogle Scholar
  8. D.J. Watts, S.H. Strogatz, Nature (London) 393, 440 (1998); D.J. Watts, Small Worlds (Princeton University Press, Princeton, 1999) CrossRefADSGoogle Scholar
  9. Z.-G. Shao, J.-P. Sang, X.-W. Zou, Z.-J. Tan, Z.-Z. Jin, Physica A 351, 662 (2005) CrossRefADSGoogle Scholar
  10. R. Pastor-Satorras, A. Vespignani, Phys. Rev. Lett. 86, 3200 (2001); Phys. Rev. E 63, 066117 (2001); see also, R. Cohen, K. Erez, D. ben-Avraham, S. Havlin, Phys. Rev. Lett. 85, 4626 (2000) CrossRefADSGoogle Scholar
  11. S. Galam, Eur. Phys. J. B 26, 269 (2002); S. Galam, Physica A 330, 139 (2003); S. Galam, Phys. Rev. E 71, 046123 (2005); S. Galam, A. Mauger, Phys. Rev. E 323, 695 (2003) CrossRefADSGoogle Scholar
  12. G. Weisbuch, G. Deffuant, F. Amblard, Physica A 353, 55 (2005) CrossRefGoogle Scholar
  13. A. Claudet, M. Young, K.S. Gedlitz, J. Conflict Resol. 51, 58 (2007) CrossRefGoogle Scholar
  14. M.E.J. Newman, S.H. Strogatz, D.J. Watts, Phys Rev. E 64, 026118 (2001); S.N. Dorogovtsev, J.F.F. Mendes, A.N. Sanukhin, Phys Rev. E 64, 025101 (2001); A.D. Sánchez, J.M. López, M.A. Rodríguez, Phys. Rev. Lett. 88, 048701 (2002) CrossRefADSGoogle Scholar
  15. D. Stauffer, H. Meyer-Ortmanns, Int. J. Mod. Phys. C 15, 241 (2004) CrossRefADSGoogle Scholar
  16. B. Chopard, M. Droz, S. Galam, Eur. Phys. J. B 16, 575 (2000); S. Galam, J.P. Radomski, Phys. Rev. E 63, 51907 (2001) CrossRefADSGoogle Scholar
  17. M.A. Sumour, M.M. Shabat, Int. J. Mod. Phys. C 16, 584 (2005); F.W.S Lima, D. Stauffer, Physica A 359, 423 (2006); M.A. Sumour, A.H. El-Astal, F.W.S. Lima, M.M. Shabat, H.M. Khalil, Int. J. Mod. Phys. C 18 (2007), in press CrossRefADSGoogle Scholar
  18. D. Stauffer, M. Sahimi, Physica A 364, 537 (2006) CrossRefADSGoogle Scholar

Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Authors and Affiliations

  1. 1.Mork Family Department of Chemical Engineering and Materials ScienceUniversity of Southern CaliforniaLos AngelesUSA

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