Continuum dynamics of the intention field under weakly cohesive social interaction

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Title: Continuum dynamics of the intention field under weakly cohesive social interaction
Authors: Degond, P
Liu, J-G
Merino-Aceituno, S
Tardiveau, T
Item 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.
Issue Date: 9-Jan-2017
Date of Acceptance: 6-Aug-2016
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.
Sponsor/Funder: The Royal Society
Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: WM130048
Keywords: Science & Technology
Physical Sciences
Mathematics, Applied
Opinion formation
grazing limit
non-symmetric rate
continuum limit
Deffuant-Weisbuch model
82C21, 82C22, 82C26, 82C31, 82C40, 82C70, 91B12, 91B14, 91B70, 91B72
0102 Applied Mathematics
Applied Mathematics
Publication Status: Published
Article Number: 159
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences

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