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The concept of active Brownian particles is used to model a collectiveopinion formation process. It is assumed that individuals in community create atwo-component communication field that influences the change of opinions ofother persons and/or can induce their migration. The communication field isdescribed by a reaction-diffusion equation, the opinion change of theindividuals is given by a master equation, while the migration is described bya set of Langevin equations, coupled by the communication field. In themean-field limit holding for fast communication we derive a critical populationsize, above which the community separates into a majority and a minority withopposite opinions. The existence of external support (e.g. from mass media)changes the ratio between minority and majority, until above a criticalexternal support the supported subpopulation exists always as a majority.Spatial effects lead to two critical ``social'' temperatures, between which thecommunity exists in a metastable state, thus fluctuations below a certaincritical wave number may result in a spatial opinion separation. The range ofmetastability is particularly determined by a parameter characterizing theindividual response to the communication field. In our discussion, we drawanalogies to phase transitions in physical systems.

Modelling collective opinion formation by means of active Brownian particles