Düring, Bertram, Torregrossa, Marco and Wolfram, Marie-Therese (2018) Boltzmann and Fokker-Planck equations modelling the Elo rating system with learning effects. Journal of Nonlinear Science . doi:10.1007/s00332-018-9512-8 (In Press)

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Abstract

We propose a mathematical model for opinion formation in a society which is built of two groups, one group of 'ordinary' people and one group of 'strong opinion leaders'. Our approach is based on an opinion formation model introduced in Toscani (2006) and borrows ideas from the kinetic theory of mixtures of rarefied gases. Starting from microscopic interactions among individuals, we arrive at a macroscopic description of the opinion formation process which is characterized by a system of Fokker-Planck type equations. We discuss the steady states of this system, extend it to incorporate emergence and decline of opinion leaders, and present numerical results.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH):	Soccer players -- Rating of -- Mathematical models, Fédération internationale de football association, Fokker-Planck equation
Journal or Publication Title:	Journal of Nonlinear Science
Publisher:	Springer
ISSN:	0938-8974
Official Date:	22 November 2018
Dates:	Date Event 22 November 2018 Available 2 November 2018 Accepted
Date of first compliant deposit:	5 November 2018
DOI:	10.1007/s00332-018-9512-8
Status:	Peer Reviewed
Publication Status:	In Press
Publisher Statement:	This is a post-peer-review, pre-copyedit version of an article published in Journal of Nonlinear Science. The final authenticated version is available online at: https://doi.org/10.1007/s00332-018-9512-8
Access rights to Published version:	Open Access
RIOXX Funder/Project Grant:	Project/Grant ID RIOXX Funder Name Funder ID RPG-2015-69 Leverhulme Trust http://dx.doi.org/10.13039/501100000275 NST 0001 Österreichischen Akademie der Wissenschaften UNSPECIFIED EP/P01240X/1 [EPSRC] Engineering and Physical Sciences Research Council http://dx.doi.org/10.13039/501100000266

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