Boltzmann and Fokker-Planck equations modelling opinion formation in the presence of strong leaders
Boltzmann and Fokker-Planck equations modelling opinion formation in the presence of strong leaders
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DOI：
10.1098/rspa.2009.0239
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发表时间：
2009-12-08
影响因子：
3.5
通讯作者：
Wolfram, Marie-Therese
中科院分区：
文献类型：
--
作者：
Duering, Bertram;Markowich, Peter;Wolfram, Marie-Therese
我们提出了一个在一个由两个群体组成的社会中意见形成的数学模型，一个群体是“普通人”，另一个群体是“强有力的意见领袖”。我们的方法是基于Toscani(Toscani，2006)中介绍的意见形成模型。数学课。SCI。4,481-496)，并借用稀薄气体混合物的动力学理论。从个体之间的微观相互作用出发，我们得出了意见形成过程的宏观描述，其特征是一组福克-普朗克型方程。我们讨论了该系统的稳态，将其扩展到考虑意见领袖的出现和衰落，并给出了数值结果。
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.