Continuum dynamics of the intention field under weakly cohesive social interaction
File(s)
Published version
Accepted version
Author(s)
Degond, P
Liu, J-G
Merino-Aceituno, S
Tardiveau, T
Type
Journal Article
Abstract
We investigate the long-time dynamics of an opinion formation model inspired by a work by Borghesi, Bouchaud and Jensen. First, we derive a Fokker–Planck-type equation under the assumption that interactions between individuals produce little consensus of opinion (grazing collision approximation). Second, we study conditions under which the Fokker–Planck equation has non-trivial equilibria and derive the macroscopic limit (corresponding to the long-time dynamics and spatially localized interactions) for the evolution of the mean opinion. Finally, we compare two different types of interaction rates: the original one given in the work of Borghesi, Bouchaud and Jensen (symmetric binary interactions) and one inspired from works by Motsch and Tadmor (non-symmetric binary interactions). We show that the first case leads to a conservative model for the density of the mean opinion whereas the second case leads to a non-conservative equation. We also show that the speed at which consensus is reached asymptotically for these two rates has fairly different density dependence.
Date Issued
2017-01-09
Date Acceptance
2016-08-06
Citation
Mathematical Models and Methods in Applied Sciences, 2017, 27 (1)
ISSN
1793-6314
Publisher
World Scientific Publishing
Journal / Book Title
Mathematical Models and Methods in Applied Sciences
Volume
27
Issue
1
Copyright Statement
© The Author(s)
This is an open access article published by World Scientific Publishing and distributed under the terms of the Creative Commons Attribution (CC BY) 4.0 License, which permits use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
This is an open access article published by World Scientific Publishing and distributed under the terms of the Creative Commons Attribution (CC BY) 4.0 License, which permits use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
License URL
Sponsor
The Royal Society
Engineering & Physical Science Research Council (EPSRC)
Grant Number
WM130048
EP/M006883/1
Subjects
Science & Technology
Physical Sciences
Mathematics, Applied
Mathematics
Opinion formation
grazing limit
non-symmetric rate
continuum limit
Deffuant-Weisbuch model
OPINION FORMATION
SZNAJD MODEL
DRIVEN
POLARIZATION
DIFFUSION
FISH
Publication Status
Published
Article Number
159