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Critical behavior of the contact process on small-world networks

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Abstract

We investigate the role of clustering on the critical behavior of the contact process (CP) on small-world networks using the Watts-Strogatz (WS) network model with an edge rewiring probability p. The critical point is well predicted by a homogeneous cluster-approximation for the limit of vanishing clustering (p → 1). The critical exponents and dimensionless moment ratios of the CP are in agreement with those predicted by the mean-field theory for any p > 0. This independence on the network clustering shows that the small-world property is a sufficient condition for the mean-field theory to correctly predict the universality of the model. Moreover, we compare the CP dynamics on WS networks with rewiring probability p = 1 and random regular networks and show that the weak heterogeneity of the WS network slightly changes the critical point but does not alter other critical quantities of the model.

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References

  1. D. Watts, S. Strogatz, Nature 393, 440 (1998)

    Article  ADS  Google Scholar 

  2. M. Newman, Networks: an introduction (Oxford University Press, Oxford, 2010)

  3. R. Albert, A.L. Barabási, Rev. Mod. Phys. 74, 47 (2002)

    Article  MATH  ADS  Google Scholar 

  4. R. Pastor-Satorras, A. Vespignani, Phys. Rev. E 63, 066117 (2001)

    Article  ADS  Google Scholar 

  5. R. Pastor-Satorras, A. Vespignani, Phys. Rev. E 63, 66117 (2001)

    Article  ADS  Google Scholar 

  6. A. Barrat, M. Barthlemy, A. Vespignani, Dynamical Processes on Complex Networks (Cambridge University Press, Cambridge, 2008)

  7. M. Catanzaro, M. Boguñá, R. Pastor-Satorras, Phys. Rev. E 71, 27103 (2005)

    Article  ADS  Google Scholar 

  8. P. Colomer-de Simon, M. Boguná, Phys. Rev. E 86, 026120 (2012)

    Article  ADS  Google Scholar 

  9. A. Barrat, M. Weigt, Eur. Phys. J. B 13, 547 (2000)

    Article  ADS  Google Scholar 

  10. C. Moore, M.E.J. Newman, Phys. Rev. E 61, 5678 (2000)

    Article  ADS  Google Scholar 

  11. D.H. Zanette, Phys. Rev. E 64, 050901 (2001)

    Article  ADS  Google Scholar 

  12. C. Castellano, R. Pastor-Satorras, Phys. Rev. Lett. 96, 038701 (2006)

    Article  ADS  Google Scholar 

  13. H. Hong, M. Ha, H. Park, Phys. Rev. Lett. 98, 258701 (2007)

    Article  ADS  Google Scholar 

  14. S.C. Ferreira, R.S. Ferreira, C. Castellano, R. Pastor-Satorras, Phys. Rev. E 84, 066102 (2011)

    Article  ADS  Google Scholar 

  15. S.C. Ferreira, C. Castellano, R. Pastor-Satorras, Phys. Rev. E 86, 041125 (2012)

    Article  ADS  Google Scholar 

  16. T.E. Harris, Ann. Prob. 2, 969 (1974)

    Article  MATH  Google Scholar 

  17. J. Marro, R. Dickman, Nonequilibrium phase transitions in lattice models (Cambridge University Press, Cambridge, 2005)

  18. C. Castellano, R. Pastor-Satorras, Phys. Rev. Lett. 100, 148701 (2008)

    Article  ADS  Google Scholar 

  19. M. Boguñá, C. Castellano, R. Pastor-Satorras, Phys. Rev. E 79, 036110 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  20. S.C. Ferreira, R.S. Ferreira, R. Pastor-Satorras, Phys. Rev. E 83, 066113 (2011)

    Article  ADS  Google Scholar 

  21. S.N. Dorogovtsev, A.V. Goltsev, J.F.F. Mendes, Rev. Mod. Phys. 80, 1275 (2008)

    Article  ADS  Google Scholar 

  22. M. Barthélémy, L.A.N. Amaral, Phys. Rev. Lett. 82, 3180 (1999)

    Article  ADS  Google Scholar 

  23. M.M. de Oliveira, R. Dickman, Phys. Rev. E 71, 16129 (2005)

    Article  Google Scholar 

  24. R.S. Sander, S.C. Ferreira, R. Pastor-Satorras, Phys. Rev. E 87, 022820 (2013)

    Article  ADS  Google Scholar 

  25. M. Muñoz, R. Juhász, C. Castellano, G. Ódor, Phys. Rev. Lett. 105, 128701 (2010)

    Article  ADS  Google Scholar 

  26. R. Dickman, J.K.L. da Silva, Phys. Rev. E 58, 4266 (1998)

    Article  ADS  Google Scholar 

  27. M. Henkel, H. Hinrichsen, S. Lübeck, Non-Equilibrium Phase Transitions: Absorbing Phase Transitions (Springer, Berlin, 2008), Vol. 1

  28. C.P. Herrero, Phys. Rev. E 65, 066110 (2002)

    Article  ADS  Google Scholar 

  29. J. Joo, J.L. Lebowitz, Phys. Rev. E 70, 036114 (2004)

    Article  MathSciNet  ADS  Google Scholar 

  30. D. ben Avraham, J. Köhler, Phys. Rev. A 45, 8358 (1992)

    Article  ADS  Google Scholar 

Download references

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Authors and Affiliations

  1. Departamento de Física, Universidade Federal de Viçosa, 36570-000, Viçosa, Minas Gerais, Brazil

    Ronan S. Ferreira & Silvio C. Ferreira

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  1. Ronan S. Ferreira
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  2. Silvio C. Ferreira
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Correspondence to Ronan S. Ferreira.

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Ferreira, R.S., Ferreira, S.C. Critical behavior of the contact process on small-world networks. Eur. Phys. J. B 86, 462 (2013). https://doi.org/10.1140/epjb/e2013-40534-0

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