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Bonabeau hierarchy models revisited

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  • Lacasa, Lucas
  • Luque, Bartolo

Abstract

What basic processes generate hierarchy in a collective? The Bonabeau model provides us a simple mechanism based on randomness which develops self-organization through both winner/looser effects and relaxation process. A phase transition between egalitarian and hierarchic states has been found both analytically and numerically in previous works. In this paper we present a different approach: by means of a discrete scheme we develop a mean field approximation that not only reproduces the phase transition but also allows us to characterize the complexity of hierarchic phase. In the same philosophy, we study a new version of the Bonabeau model, developed by Stauffer et al. Several previous works described numerically the presence of a similar phase transition in this later version. We find surprising results in this model that can be interpreted properly as the non-existence of phase transition in this version of Bonabeau model, but a changing in fixed point structure.

Suggested Citation

  • Lacasa, Lucas & Luque, Bartolo, 2006. "Bonabeau hierarchy models revisited," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 366(C), pages 472-484.
    • Handle: RePEc:eee:phsmap:v:366:y:2006:i:c:p:472-484
    DOI: 10.1016/j.physa.2005.10.046
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    Cited by:

    1. 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.

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