Diffusive and anti-diffusive behavior for kinetic models of opinion dynamics

Mirosław Lachowicz , Henryk Leszczyński , Elżbieta Puźniakowska-Gałuch


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.
Author Mirosław Lachowicz
Mirosław Lachowicz,,
, Henryk Leszczyński (FMPI / IM)
Henryk Leszczyński,,
- Institute of Mathematics
, Elżbieta Puźniakowska-Gałuch (FMPI / IM)
Elżbieta Puźniakowska-Gałuch,,
- Institute of Mathematics
Journal seriesSymmetry-Basel, ISSN 2073-8994, (A 30 pkt)
Issue year2019
Publication size in sheets0.7
Article number1024
Keywords in Englishopinion dynamics, symmetric interactions, kinetic equations, integro-differential equations, conformist society, individualistic society
ASJC Classification3101 Physics and Astronomy (miscellaneous); 2600 General Mathematics; 1601 Chemistry (miscellaneous); 1701 Computer Science (miscellaneous)
URL https://doi.org/10.3390/sym11081024
Languageen angielski
LicenseJournal (articles only); published final; Uznanie Autorstwa (CC-BY); with publication
Score (nominal)30
ScoreMinisterial score = 30.0, 12-08-2019, ArticleFromJournal
Publication indicators Scopus SNIP (Source Normalised Impact per Paper): 2016 = 0.64; WoS Impact Factor: 2017 = 1.256 (2) - 2017=1.213 (5)
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