Mean-field analysis of phase transitions in the emergence of hierarchical society

Authored by Tsuyoshi Okubo

Date Published: 2007-09

DOI: 10.1103/physreve.76.036105

Sponsors: Japanese Society for the Promotion of Science (JSPS)

Platforms: No platforms listed

Model Documentation: Other Narrative Mathematical description

Model Code URLs: Model code not found

Abstract

Emergence of hierarchical society is analyzed by use of a simple agent-based model. We extend the mean-field model of Bonabeau [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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