Boltzmann and Fokker–Planck equations modelling opinion formation in the presence of strong leaders
By Bertram Düring, Peter A. Markowich, Jan‐Frederik Pietschmann, Marie-Therese Wolfram. Proceedings of the Royal Society A, 2009
235 citations recorded by the source corpus.
We propose a mathematical model for opinion formation in a society that 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 (Toscani 2006 Commun. Math. Sci.4, 481–496) 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 that 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.
Subfields: Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/61d7b9ee0bb82f48a8a1e5bbc74bb5e97a0eade7
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In Statistical and Nonlinear Physics
- A. Pulvirenti
- G. Furioli
- E. Terraneo
- Eitan Tadmor
- Sébastien Motsch
- Giuseppe Toscani
- José Antonio Carrillo
- Roman Shvydkoy
Citations in the corpus
- Fokker–Planck equations in the modeling of socio-economic phenomena (2017, background): “[30, 36, 42, 56, 89] Likewise, the dynamics of opinion formation in a multi-agent society has received growing attention.[12, 13, 14, 15, 19, 20, 21, 34, 41, 46, 52, 53, 54, 55, 91, 96] In view of the relation between parameters in the microscopic interaction rules, the society develops a certain 1”
- On the control through leadership of the Hegselmann–Krause opinion formation model (2015, background): “[3, 6, 14, 17, 30, 33] for results on multi-agent systems with leadership.”
- Heterophilious Dynamics Enhances Consensus (2013, background): “Self-organized dynamics is found in many other areas, from pedestrian and traffic dynamics [64, 92], social networks and economics [48, 66, 69, 77, 83], complex networks [5, 44, 91], and opinion dynamics [7, 23, 42, 49, 50, 63, 75, 105, 110, 109], all the way to applications in marketing [2, 3], pro”