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
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.
PACS: 05.45.-a – Nonlinear dynamics and chaos / 05.40.Ca – Noise / 82.40.Ck – Pattern formation in reactions with diffusion, flow and heat transfer
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2006