Eur. Phys. J. B 51, 435-442 (2006)
https://doi.org/10.1140/epjb/e2006-00232-8

Van Kampen's expansion approach in an opinion formation model

¹ Instituto de Física de Cantabria, Universidad de Cantabria and CSIC, 390005-, Santander, Spain
² Instituto de Física, Universidade Federal de Rio Grande do Sul, 91501-970 Porto Alegre, Brazil
³ Programa de Pós Graduação em Economia, Universidade Federal de Rio Grande do Sul, Av. João Pessoa 52, 90040-000 Porto Alegre, Brazil

Corresponding authors: ^a msanchez@ifca.unican.es - ^b szendro@ifca.unican.es - ^c iglesias@if.ufrgs.br - ^d wio@ifca.unican.es

Received: 8 March 2006
Revised: 1 May 2006
Published online: 13 June 2006

Abstract

We analyze a simple opinion formation model consisting of two parties, A and B, and a group I, of undecided agents. We assume that the supporters of parties A and B do not interact among them, but only interact through the group I, and that there is a nonzero probability of a spontaneous change of opinion (, ). From the master equation, and via van Kampen's Ω-expansion approach, we have obtained the “macroscopic” evolution equation, as well as the Fokker-Planck equation governing the fluctuations around the deterministic behavior. Within the same approach, we have also obtained information about the typical relaxation behavior of small perturbations.