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

Autor: Mirosław Lachowicz, Henryk Leszczyński, Elżbieta Puźniakowska–Gałuch
Jazyk: angličtina
Rok vydání: 2019
Předmět:
Zdroj: Symmetry, Vol 11, Iss 8, p 1024 (2019)
Druh dokumentu: article
ISSN: 2073-8994
65645162
DOI: 10.3390/sym11081024
Popis: 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.
Databáze: Directory of Open Access Journals
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