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Mean-field analysis of phase transitions in the emergence of hierarchical society
Phys. Rev. E 76, 036105 – Published 10 September, 2007
DOI: https://doi.org/10.1103/PhysRevE.76.036105
Abstract
Emergence of hierarchical society is analyzed by use of a simple agent-based model. We extend the mean-field model of Bonabeau et al. [Physica A 217, 373 (1995)] to societies obeying complex diffusion rules where each individual selects a moving direction following their power rankings. We apply this mean-field analysis to the pacifist society model recently investigated by use of Monte Carlo simulation [Physica A 367, 435 (2006)]. We show analytically that the self-organization of hierarchies occurs in two steps as the individual density is increased and there are three phases: one egalitarian and two hierarchical states. We also highlight that the transition from the egalitarian phase to the first hierarchical phase is a continuous change in the order parameter and the second transition causes a discontinuous jump in the order parameter.
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References (16)
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Bonabeau et al. derived these solutions from a steady state condition (16) in their paper [1]. However, Eq. (16) is inconsistent with Eqs. (2) and (15) of the paper. It seems to state , but this equation is incorrect except for . Unfortunately a detailed derivation of Eq. (16) was not described. Therefore we can only consider that it would be a miscalculation or misprint.