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Noisy bounded confidence models for opinion dynamics: the effect of boundary conditions on phase transitions
File(s)
hxab044.pdf (2.51 MB)
Published version
Author(s)
Goddard, BD
Gooding, B
Short, H
Pavliotis, GA
Type
Journal Article
Abstract
We study SDE and PDE models for opinion dynamics under bounded confidence, for a range of different boundary conditions, with and without the inclusion of a radical population. We perform exhaustive numerical studies with pseudo-spectral methods to determine the effects of the boundary conditions, suggesting that the no-flux case most faithfully reproduces the underlying mechanisms in the associated deterministic models of Hegselmann and Krause. We also compare the SDE and PDE models, and use tools from analysis to study phase transitions, including a systematic description of an appropriate order parameter.
Date Issued
2021-11-13
Date Acceptance
2021-10-04
Citation
IMA Journal of Applied Mathematics, 2021, 87 (1), pp.80-110
URI
URL
DOI
ISSN
0272-4960
Publisher
Oxford University Press (OUP)
Start Page
80
End Page
110
Journal / Book Title
IMA Journal of Applied Mathematics
Volume
87
Issue
1
Copyright Statement
© The Author(s) 2021. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.
License URL
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Identifier
https://academic.oup.com/imamat/advance-article/doi/10.1093/imamat/hxab044/6427747
Grant Number
EP/P031587/1
Subjects
0102 Applied Mathematics
0103 Numerical and Computational Mathematics
0199 Other Mathematical Sciences
Applied Mathematics
Publication Status
Published
Date Publish Online
2021-11-13