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Phase diagram of a model of self-organizing hierarchies

Author

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  • Bonabeau, Eric
  • Theraulaz, Guy
  • Deneubourg, Jean-Louis

Abstract

We introduce a simple model of self-organizing hierarchies in animal societies which relies on a basic positive feedback mechanism reinforcing the ability of a given individual to win or lose in a hierarchical interaction, depending on how many times it won or lost in previous interactions. If a forgetting strength is included, which determines the rate at which events in the past are forgotten and no longer influence the force of an individual, subcritical or supercritical bifurcations in the formation of the hierarchical structure are observed as the density ϱ of individuals is varied. The nature of the transition is shown to depend on a parameter η, analogous to the inverse of a temperature, defining the amount of determinism in the outcomes of the fights. We therefore observe a dynamical tricritical point in the ϱ-η plane.

Suggested Citation

  • Bonabeau, Eric & Theraulaz, Guy & Deneubourg, Jean-Louis, 1995. "Phase diagram of a model of self-organizing hierarchies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 217(3), pages 373-392.
    • Handle: RePEc:eee:phsmap:v:217:y:1995:i:3:p:373-392
    DOI: 10.1016/0378-4371(95)00064-E
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    Citations

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    Cited by:

    1. Kułakowski, Krzysztof, 2009. "Opinion polarization in the Receipt–Accept–Sample model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(4), pages 469-476.
    2. E. Samanidou & E. Zschischang & D. Stauffer & T. Lux, 2007. "Agent-based Models of Financial Markets," Papers physics/0701140, arXiv.org.
    3. Karataieva, Tatiana & Koshmanenko, Volodymyr & Krawczyk, Małgorzata J. & Kułakowski, Krzysztof, 2019. "Mean field model of a game for power," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 535-547.
    4. E. Samanidou & E. Zschischang & D. Stauffer & T. Lux, 2001. "Microscopic Models of Financial Markets," Papers cond-mat/0110354, arXiv.org.
    5. Deffuant, Guillaume & Roubin, Thibaut, 2022. "Do interactions among unequal agents undermine those of low status?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 592(C).
    6. Ohnishi, Teruaki, 2012. "Evolution of groups with a hierarchical structure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(23), pages 5978-5986.
    7. Jędrzejewski, Arkadiusz & Sznajd-Weron, Katarzyna, 2018. "Impact of memory on opinion dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 306-315.
    8. Krawczyk, Małgorzata J. & Kułakowski, Krzysztof, 2017. "Paradox of integration—A computational model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 409-414.

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