Noisy bounded confidence models for opinion dynamics: the effect of boundary conditions on phase transitions

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 cond...

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Bibliographic Details
Published inIMA journal of applied mathematics Vol. 87; no. 1; pp. 80 - 110
Main Authors Goddard, B D, Gooding, B, Short, H, Pavliotis, G A
Format Journal Article
LanguageEnglish
Published Oxford University Press 22.01.2022
Subjects
82C26
bounded confidence
65M70
opinion dynamics
phase transitions
no-flux boundary conditions
2000 Math Subject Classification: 82C22
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Summary: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.
ISSN:0272-4960
1464-3634
DOI:10.1093/imamat/hxab044