Skip to main content
SpringerLink
Log in

Continuous transition from the extensive to the non-extensive statistics in an agent-based herding model

  • Regular Article
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

Systems with long-range interactions often exhibit power-law distributions and can by described by the non-extensive statistical mechanics framework proposed by Tsallis. In this contribution we consider a simple model reproducing continuous transition from the extensive to the non-extensive statistics. The considered model is composed of agents interacting among themselves on a certain network topology. To generate the underlying network we propose a new network formation algorithm, in which the mean degree scales sub-linearly with a number of nodes in the network (the scaling depends on a single parameter). By changing this parameter we are able to continuously transition from short-range to long-range interactions in the agent-based model.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Dynamics and Thermodynamics of Systems with Long-Range Interactions, edited by T. Dauxois, S. Ruffo, E. Arimondo, M. Wilkens (Springer, New York, 2002), Vol. 602

  2. T. Padmanabhan, Phys. Rep. 188, 285 (1990)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  3. D.R. Nicholson, Introduction to Plasma Theory (John Wiley, New York, 1983)

  4. P.H. Chavanis, C. Sire, Phys. Fluids 13, 71804 (2001)

    Article  MathSciNet  Google Scholar 

  5. J. Barré, T. Dauxois, G. De Ninno, D. Fanelli, S. Ruffo, Phys. Rev. E 69, 045501(R) (2004)

    Article  ADS  Google Scholar 

  6. Y. Elskens, D.F. Escande, Microscopic Dynamics of Plasmas and Chaos (IOP, Bristol, 2002)

  7. A. Campa, T. Dauxois, S. Ruffo, Phys. Rep. 480, 57 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  8. F. Bouchet, S. Gupta, D. Mukamel, Physica A 389, 4389 (2010)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  9. D. Mukamel, S. Ruffo, N. Schreiber, Phys. Rev. Lett. 95, 240604 (2005)

    Article  ADS  Google Scholar 

  10. W. Thirring, Z. Phys. 235, 339 (1970)

    Article  ADS  Google Scholar 

  11. F. Bouchet, T. Dauxois, D. Mukamel, S. Ruffo, Phys. Rev. E 77, 011125 (2008)

    Article  ADS  Google Scholar 

  12. D. Lynden-Bell, Mon. Not. R. Astron. Soc. 136, 101 (1967)

    Article  ADS  Google Scholar 

  13. V. Latora, A. Rapisarda, C. Tsallis, Phys. Rev. E 64, 056134 (2001)

    Article  ADS  Google Scholar 

  14. Y.Y. Yamaguchi, Phys. Rev. E 68, 066210 (2003)

    Article  ADS  Google Scholar 

  15. C. Tsallis, Introduction to Nonextensive Statistical Mechanics – Approaching a Complex World (Springer, New York, 2009)

  16. C. Tsallis, Braz. J. Phys. 39, 337 (2009)

    Article  ADS  Google Scholar 

  17. L. Telesca, Tectonophysics 494, 155 (2010)

    Article  ADS  Google Scholar 

  18. B. Liu, J. Goree, Phys. Rev. Lett. 100, 055003 (2008)

    Article  ADS  Google Scholar 

  19. R.M. Pickup, R. Cywinski, C. Pappas, B. Farago, P. Fouquet, Phys. Rev. Lett. 102, 097202 (2009)

    Article  ADS  Google Scholar 

  20. C. Beck, S. Miah, Phys. Rev. E 87, 031002 (2013)

    Article  ADS  Google Scholar 

  21. C.M. Gell-Mann, C. Tsallis, Nonextensive Entropy – Interdisciplinary Applications (Oxford University Press, NY, 2004)

  22. S. Abe, Astrophys. Space Sci. 305, 241 (2006)

    Article  ADS  MATH  Google Scholar 

  23. S. Picoli, R.S. Mendes, L.C. Malacarne, R.P.B. Santos, Braz. J. Phys. 39, 468 (2009)

    Article  ADS  Google Scholar 

  24. C. Borghesi, J.C. Raynal, J.P. Bouchaud, PLoS ONE 7, e36289 (2012)

    Article  ADS  Google Scholar 

  25. N.K. Vitanov, M. Ausloos, in Models of Science Dynamics, edited by A. Scharnhorst, K. Börner, P. van den Besselaar (Springer, Berlin, 2012), pp. 69–127

  26. V.M. Yakovenko, J.B. Rosser, Rev. Mod. Phys. 81, 1703 (2009)

    Article  ADS  Google Scholar 

  27. F. Tramontana, Int. Rev. Econ. 57, 347 (2010)

    Article  Google Scholar 

  28. F. Westerhoff, New J. Phys. 12, 075035 (2010)

    Article  ADS  Google Scholar 

  29. M. Cristelli, L. Pietronero, A. Zaccaria, Critical Overview of Agent-Based Models for Economics, in Proceedings of the School of Physics “E. Fermi”, Course CLXXVI, edited by F. Mallnace, H.E. Stanley (SIF-IOS, Bologna-Amsterdam, 2012), pp. 235–282

  30. A. Chakraborti, I.M. Toke, M. Patriarca, F. Abergel, Quant. Finance 7, 1013 (2011)

    Article  Google Scholar 

  31. R. Frederick, Proc. Natl. Acad. Sci. USA 110, 3703 (2013)

    Article  ADS  Google Scholar 

  32. S. Alfarano, T. Lux, F. Wagner, J. Econ. Dyn. Control 32, 101 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  33. A. Kononovicius, V. Gontis, Physica A 391, 1309 (2012)

    Article  ADS  Google Scholar 

  34. L. Feng, B. Li, B. Podobnik, T. Preis, H.E. Stanley, Proc. Natl. Acad. Sci. 22, 8388 (2012)

    Article  ADS  Google Scholar 

  35. J.N. Tenenbaum, S. Havlin, H.E. Stanley, Phys. Rev. E 86, 046107 (2012)

    Article  ADS  Google Scholar 

  36. A. Bashan, R.P. Bartsch, J.W. Kantelhardt, S. Havlin, P.C. Ivanov, Nat. Commun. 3, 702 (2012)

    Article  ADS  Google Scholar 

  37. S. Alfarano, M. Milakovic, J. Econ. Dyn. Control 33, 78 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  38. A.E. Biondo, A. Pluchino, A. Rapisarda, D. Helbing, Phys. Rev. E 88, 062814 (2013)

    Article  ADS  Google Scholar 

  39. B. Barzel, A.L. Barabasi, Nat. Phys. 9, 673 (2013)

    Article  Google Scholar 

  40. M.E.J. Newman, Networks: An Introduction (Oxford University Press, Oxford, 2010)

  41. A. Kirman, in Money and Financial Markets, edited by M.P. Taylor (Blackwell, Cambridge, 1991), p. 354

  42. A. Kirman, Q. J. Econ. 108, 137 (1993)

    Article  Google Scholar 

  43. A. Kirman, G. Teyssière, Stud. Nonlinear Dyn. Econ. 5, 137 (2002)

    Google Scholar 

  44. A. Kononovicius, V. Daniunas, Soc. Tech. 3, 85 (2013)

    Google Scholar 

  45. N.G. van Kampen, Stochastic process in Physics and Chemistry (North Holland, Amsterdam, 2007)

  46. A. Traulsen, J.C. Claussen, C. Hauert, Phys. Rev. Lett. 95, 238701 (2005)

    Article  ADS  Google Scholar 

  47. A. Traulsen, J.C. Claussen, C. Hauert, Phys. Rev. E 74, 011901 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  48. A. Traulsen, J.C. Claussen, C. Hauert, Phys. Rev. E 85, 041901 (2012)

    Article  ADS  Google Scholar 

  49. R. Albert, A.L. Barabasi, Rev. Mod. Phys. 74, 47 (2002)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  50. P. Holme, B.J. Kim, Phys. Rev. E 65, 026107 (2002)

    Article  ADS  Google Scholar 

  51. P. Moriano, J. Finke, J. Stat. Mech. 2013, P06010 (2013)

    Article  MathSciNet  Google Scholar 

  52. M.O. Jackson, B.W. Rogers, Am. Econ. Rev. 97, 890 (2007)

    Article  Google Scholar 

  53. J. Leskovec, J. Kleinberg, C. Faloutsos, TKDD 1, 1217301 (2007)

    Article  Google Scholar 

  54. L. Akoglu, C. Faloutsos, Data Mining Knowledge Discovery 19, 194 (2009)

    Article  MathSciNet  Google Scholar 

  55. A. Bonato, J. Janssen, P. Pralat, A geometric model for on-line social networks, in Proc. Int. Workshop on Modeling Social Media (ACM, New York, 2010), p. 1835984

  56. E.R. Colman, G.J. Rodgers, Physica A 392, 5501 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  57. J. Ruseckas, B. Kaulakys, V. Gontis, Europhys. Lett. 96, 60007 (2011)

    Article  ADS  Google Scholar 

  58. L. Borland, Phys. Lett. A 245, 67 (1998)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  59. A.R. Plastino, A. Plastino, Phys. Lett. A 193, 140 (1994)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  60. F.Q. Potiguar, U.M.S. Costa, Physica A 321, 482 (2003)

    Article  ADS  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Theoretical Physics and Astronomy, Vilnius University, A. Goštauto 12, 01108, Vilnius, Lithuania

    Aleksejus Kononovicius & Julius Ruseckas

Authors
  1. Aleksejus Kononovicius
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Julius Ruseckas
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Aleksejus Kononovicius.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kononovicius, A., Ruseckas, J. Continuous transition from the extensive to the non-extensive statistics in an agent-based herding model. Eur. Phys. J. B 87, 169 (2014). https://doi.org/10.1140/epjb/e2014-50349-0

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/e2014-50349-0

Keywords

Search

Navigation