Van Kampen's expansion approach in an opinion formation model

Details Van Kampen's expansion approach in an opinion formation model Van Kampen's expansion approach in an opinion formation model

2006-03-07

arxiv.org/abs/physics/0603047v1

Physics

Physics and Society

17 pages, 6 figures, submited to Europ.Phys.J.B

Scientific paper

10.1140/epjb/e2006-00232-8

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 (A->I, B->I). From the master equation, and via van Kampen's Omega-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.

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