Van Kampen's expansion approach in an opinion formation model

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 (<InlineEquation ID="Equ1"> <EquationSource Format="TEX">$A \leftrightarrows I$</EquationSource> </InlineEquation>, <InlineEquation ID="Equ2"> <EquationSource Format="TEX">$B \leftrightarrows I$</EquationSource> </InlineEquation>). 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. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006