Diffusive and Anti-Diffusive Behavior for Kinetic Models of Opinion Dynamics
Institute of Applied Mathematics and Mechanics, Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, ul. Banacha 2, 02-097 Warsaw, Poland
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.
Received: 12 July 2019 / Revised: 30 July 2019 / Accepted: 31 July 2019 / Published: 8 August 2019
PDF [396 KB, uploaded 13 August 2019]
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 (
) and anti-conformist (
). 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 (
) and diffusive (
). 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.
This is an open access article distributed under the Creative Commons Attribution License
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
Share & Cite This Article
MDPI and ACS Style
Lachowicz, M.; Leszczyński, H.; Puźniakowska–Gałuch, E. Diffusive and Anti-Diffusive Behavior for Kinetic Models of Opinion Dynamics. Symmetry 2019, 11, 1024.
Lachowicz M, Leszczyński H, Puźniakowska–Gałuch E. Diffusive and Anti-Diffusive Behavior for Kinetic Models of Opinion Dynamics. Symmetry. 2019; 11(8):1024.
Lachowicz, Mirosław; Leszczyński, Henryk; Puźniakowska–Gałuch, Elżbieta. 2019. "Diffusive and Anti-Diffusive Behavior for Kinetic Models of Opinion Dynamics." Symmetry 11, no. 8: 1024.
Show more citation formats
Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.
[Return to top]
For more information on the journal statistics, click here
Multiple requests from the same IP address are counted as one view.