Bonabeau hierarchy models revisited

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.