Advertisement

The European Physical Journal Special Topics

, Volume 212, Issue 1, pp 99–113 | Cite as

Detecting and describing dynamic equilibria in adaptive networks

  • S. WielandEmail author
  • A. Parisi
  • A. Nunes
Review

Abstract

We review modeling attempts for the paradigmatic contact process (or SIS model) on adaptive networks. Elaborating on one particular proposed mechanism of topology change (rewiring) and its mean field analysis, we obtain a coarse-grained view of coevolving network topology in the stationary active phase of the system. Introducing an alternative framework applicable to a wide class of adaptive networks, active stationary states are detected, and an extended description of the resulting steady-state statistics is given for three different rewiring schemes. We find that slight modifications of the standard rewiring rule can result in either minuscule or drastic change of steady-state network topologies.

Keywords

European Physical Journal Special Topic Degree Distribution Adaptive Network Moment Closure Motif Density 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    R. Albert, A.-L. Barabási, Rev. Mod. Phys. 74, 47 (2002)ADSzbMATHCrossRefGoogle Scholar
  2. 2.
    S.N. Dorogovtsev, J.F.F. Mendes, Evolution of Networks: From Biological Nets to the Internet and WWW (Oxford University Press, New York, NY, USA, 2003)Google Scholar
  3. 3.
    M.E.J. Newman, SIAM Review 45, 167 (2003)MathSciNetADSzbMATHCrossRefGoogle Scholar
  4. 4.
    S. Boccaletti, V. Latora Y. Moreno, M. Chavez, D. Hwang, Phys. Rep. 424, 175 (2006)MathSciNetADSCrossRefGoogle Scholar
  5. 5.
    T. Gross, B. Blasius, J. R. Soc. Interface 5, 259 (2008)CrossRefGoogle Scholar
  6. 6.
    T. Gross, H. Sayama (eds.), Adaptive networks: Theory, Models and Applications (Springer, New York, 2009)Google Scholar
  7. 7.
    H. Ebel, S. Bornholdt, Phys. Rev. E 66, 056118 (2002)ADSCrossRefGoogle Scholar
  8. 8.
    M.G. Zimmermann, V.M. Eguíluz, M. San Miguel, Phys. Rev. E 69, 065102 (2004)ADSCrossRefGoogle Scholar
  9. 9.
    M.G. Zimmermann, V.M. Eguíluz, Phys. Rev. E 72, 056118 (2005)MathSciNetADSCrossRefGoogle Scholar
  10. 10.
    A. Szolnoki, M. Perc, EPL 86, 30007 (2009)ADSCrossRefGoogle Scholar
  11. 11.
    F. Fu, T. Wu, L. Wang, Phys. Rev. E 79, 036101 (2009)MathSciNetADSCrossRefGoogle Scholar
  12. 12.
    M. Perc, A. Szolnoki, Biosystems 99, 109 (2010)CrossRefGoogle Scholar
  13. 13.
    P. Holme, M.E.J. Newman, Phys. Rev. E 74, 056108 (2006)ADSCrossRefGoogle Scholar
  14. 14.
    B. Kozma, A. Barrat, Phys. Rev. E 77, 016102 (2008)ADSCrossRefGoogle Scholar
  15. 15.
    F. Vazquez, V.M. Eguíluz, M.S. Miguel, Phys. Rev. Lett. 100, 108702 (2008)ADSCrossRefGoogle Scholar
  16. 16.
    I.J. Benczik, S.Z. Benczik, B. Schmittmann, R.K.P. Zia, Phys. Rev. E 79, 046104 (2009)ADSCrossRefGoogle Scholar
  17. 17.
    S. Funk, M. Salathé, V.A.A. Jansen, J. R. Soc. Interface 7, 1247 (2010)CrossRefGoogle Scholar
  18. 18.
    D.H. Zanette, S. Gil, Phys. D. 224, 156 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    T. Gross, C. Dommar D’Lima, B. Blasius, Phys. Rev. Lett. 96, 208701 (2006)ADSCrossRefGoogle Scholar
  20. 20.
    S. Risau-Gusman, D.H. Zanette, J. Theor. Biol. 257, 52 (2009)CrossRefGoogle Scholar
  21. 21.
    I.Z. Kiss, L. Berthouze, T.J. Taylor, P.L. Simon, Proc. R. Soc. A 468, 1332 (2012)ADSCrossRefGoogle Scholar
  22. 22.
    B. Drossel, P.G. Higgs, A.J. Mckane, J. Theor. Biol. 208, 91 (2001)CrossRefGoogle Scholar
  23. 23.
    U. Dieckmann, M. Doebeli, J.A.J Metz, D. Tautz (eds.),Adaptive Speciation (Cambridge University Press, Cambridge, 2004)Google Scholar
  24. 24.
    W.X. Wang, B.H. Wang, B. Hu, G. Yan, Q. Ou, Phys. Rev. Lett. 94, 188702 (2005)ADSCrossRefGoogle Scholar
  25. 25.
    M. Lim, D. Braha, S. Wijesinghe, S. Tucker, Y. Bar-Yam, EPL 79, 58005 (2007)MathSciNetADSCrossRefGoogle Scholar
  26. 26.
    Y.B. Xie, W.X. Wang, B.H. Wang, Phys. Rev. E 75, 026111 (2007)ADSCrossRefGoogle Scholar
  27. 27.
    J.L. Herrera, M.G. Cosenza, K. Tucci, J.C. González-Avella, EPL 95, 58006 (2011)ADSCrossRefGoogle Scholar
  28. 28.
    C. Zhang, J. Zhang, G. Xie, L. Wang, M. Perc, PLoS ONE 6, e26724 (2011)CrossRefGoogle Scholar
  29. 29.
    C. Lagorio, M. Dickison, F. Vazquez, L.A. Braunstein, P.A. Macri, M.V. Migueles, S. Havlin, H.E. Stanley, Phys. Rev. E 83, 026102 (2011)ADSCrossRefGoogle Scholar
  30. 30.
    O. Gräser, C. Xu, P.M. Hui, EPL 87, 38003 (2009)ADSCrossRefGoogle Scholar
  31. 31.
    G. Demirel, R. Prizak, P. Reddy, T. Gross, Eur. Phy. J. B 84, 541 (2011)ADSCrossRefGoogle Scholar
  32. 32.
    G.A. Böhme, T. Gross, Phys. Rev. E 83, 035101 (2011)ADSCrossRefGoogle Scholar
  33. 33.
    G. Zschaler, G.A. Böhme, M. Seißinger, C. Huepe, T. Gross, Phys. Rev. E 85, 046107 (2012)ADSCrossRefGoogle Scholar
  34. 34.
    S. Bornholdt K. Sneppen, Phys. Rev. Lett. 81, 236 (1998)ADSCrossRefGoogle Scholar
  35. 35.
    P. Holme, G. Ghoshal, Phys. Rev. Lett. 96, 098701 (2006)ADSCrossRefGoogle Scholar
  36. 36.
    J.M. Pacheco, A. Traulsen, M.A. Nowak, Phys. Rev. Lett. 97, 258103 (2006)ADSCrossRefGoogle Scholar
  37. 37.
    S. Van Segbroeck, F.C. Santos, T. Lenaerts, J.M. Pacheco, Phys. Rev. Lett. 102, 058105 (2009)ADSCrossRefGoogle Scholar
  38. 38.
    S. Van Segbroeck, F.C. Santos, J.M. Pacheco. PLoS Comput Biol. 6, e1000895 (2010)CrossRefGoogle Scholar
  39. 39.
    D.H. Zanette S. Risau-Gusman, J. Biol. Phys. 34, 135 (2008)CrossRefGoogle Scholar
  40. 40.
    L.B. Shaw, I.B. Schwartz, Phys. Rev. E 77, 066101 (2008)MathSciNetADSCrossRefGoogle Scholar
  41. 41.
    R. Pastor-Satorras, A. Vespignani, Phys. Rev. Lett. 86, 3200 (2001)ADSCrossRefGoogle Scholar
  42. 42.
    Y. Moreno, M. Nekovee, F. Pacheco, Phys. Rev. E 69, 066130 (2004)ADSCrossRefGoogle Scholar
  43. 43.
    V. Marceau, P.A. Noël, L.H. Dufresne, A. Allard, L.J. Dubé, Phys. Rev. E 82, 036116 (2010)MathSciNetADSCrossRefGoogle Scholar
  44. 44.
    T. Gross, I.G. Kevrekidis, EPL 82, 38004 (2008)MathSciNetCrossRefGoogle Scholar
  45. 45.
    S. Wieland, T. Aquino, A. Nunes, EPL 97, 18003 (2012)ADSCrossRefGoogle Scholar
  46. 46.
    B. Guerra, J. Gómez-Gardeñes, Phys. Rev. E 82, 035101 (2010)ADSCrossRefGoogle Scholar
  47. 47.
    J. Bryden, S. Funk, N. Geard, S. Bullock, V.A.A. Jansen, J. R. Soc. Interface 8, 1031 (2011)CrossRefGoogle Scholar
  48. 48.
    D.T. Gillespie, J. Comput. Phys. 22, 403 (1976)MathSciNetADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences and Springer 2012

Authors and Affiliations

  1. 1.Centro de Física da Matéria Condensada and Departamento de FísicaFaculdade de Ciências da Universidade de LisboaLisboaPortugal

Personalised recommendations