Physics – Condensed Matter – Statistical Mechanics
Scientific paper
1999-11-25
European Physical Journal B, vol. 15, no. 4 (2000) 723-732
Physics
Condensed Matter
Statistical Mechanics
Revised text version. Accepted for publication in European Physics Journal B. For related work see http://summa.physik.hu-be
Scientific paper
10.1007/s100510051177
The concept of active Brownian particles is used to model a collective opinion formation process. It is assumed that individuals in community create a two-component communication field that influences the change of opinions of other persons and/or can induce their migration. The communication field is described by a reaction-diffusion equation, the opinion change of the individuals is given by a master equation, while the migration is described by a set of Langevin equations, coupled by the communication field. In the mean-field limit holding for fast communication we derive a critical population size, above which the community separates into a majority and a minority with opposite opinions. The existence of external support (e.g. from mass media) changes the ratio between minority and majority, until above a critical external support the supported subpopulation exists always as a majority. Spatial effects lead to two critical ``social'' temperatures, between which the community exists in a metastable state, thus fluctuations below a certain critical wave number may result in a spatial opinion separation. The range of metastability is particularly determined by a parameter characterizing the individual response to the communication field. In our discussion, we draw analogies to phase transitions in physical systems.
Holyst Janusz
Schweitzer Frank
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