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Diffusive and Anti-Diffusive Behavior for Kinetic Models of Opinion Dynamics

1
Institute of Applied Mathematics and Mechanics, Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, ul. Banacha 2, 02-097 Warsaw, Poland
2
Institute of Mathematics, University of Gdańsk, ul. Wita Stwosza 57, 80–308 Gdańsk, Poland
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Symmetry 2019, 11(8), 1024; https://doi.org/10.3390/sym11081024
Received: 12 July 2019 / Revised: 30 July 2019 / Accepted: 31 July 2019 / Published: 8 August 2019
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Abstract

In the present paper, we study a class of nonlinear integro-differential equations of a kinetic type describing the dynamics of opinion for two types of societies: conformist ( σ = 1 ) and anti-conformist ( σ = 1 ). The essential role is played by the symmetric nature of interactions. The class may be related to the mesoscopic scale of description. This means that we are going to statistically describe an individual state of an agent of the system. We show that the corresponding equations result at the macroscopic scale in two different pictures: anti-diffusive ( σ = 1 ) and diffusive ( σ = 1 ). We provide a rigorous result on the convergence. The result captures the macroscopic behavior resulting from the mesoscopic one. In numerical examples, we observe both unipolar and bipolar behavior known in political sciences. View Full-Text
Keywords: opinion dynamics; symmetric interactions; kinetic equations; integro-differential equations; conformist society; individualistic society opinion dynamics; symmetric interactions; kinetic equations; integro-differential equations; conformist society; individualistic society
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Lachowicz, M.; Leszczyński, H.; Puźniakowska–Gałuch, E. Diffusive and Anti-Diffusive Behavior for Kinetic Models of Opinion Dynamics. Symmetry 2019, 11, 1024.

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