Boltzmann and Fokker–Planck equations modelling opinion formation in the presence of strong leaders | Zendy

Bertram Düring | Zendy; Peter A. Markowich | Zendy; JanFrederik Pietschmann | Zendy; Marie-Thérèse Wolfram | Zendy

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Boltzmann and Fokker–Planck equations modelling opinion formation in the presence of strong leaders

Author(s) -

Bertram Düring,

Peter A. Markowich,

JanFrederik Pietschmann,

Marie-Thérèse Wolfram

Publication year - 2009

Publication title -

proceedings of the royal society a mathematical physical and engineering sciences

Language(s) - English

Resource type - Journals

eISSN - 1471-2946

pISSN - 1364-5021

DOI - 10.1098/rspa.2009.0239

Subject(s) - opinion leadership , statistical physics , kinetic energy , boltzmann constant , fokker–planck equation , group (periodic table) , mathematics , physics , sociology , thermodynamics , classical mechanics , mathematical analysis , social science , partial differential equation , quantum mechanics

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.

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