Journal Article

PUBDB-2026-01174

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Asymptotic and Stability Analysis of Kinetic Models for Opinion Formation on Networks: An Allen–Cahn Approach

Burger, M. (Corresponding author)DESY* ; Loy, N. (Corresponding author) ; Rossi, A. (Corresponding author)Extern*

2025
SIAM Philadelphia, Pa.

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Please use a persistent id in citations: doi:10.1137/24M1671128

Report No.: arXiv:2407.03375

Abstract: We present the analysis of stationary equilibria and their stability in the case of an opinion formation process in the presence of binary opposite opinions evolving according to majority-like rules on social networks. The starting point is a kinetic Boltzmann-type model implementing microscopic interaction rules that can be either binary or ternary for the opinion exchange among individuals holding a certain degree of connectivity. The key idea is to derive from the kinetic model an Allen–Cahn type equation for the fraction of individuals holding one of the two opinions. The latter can be studied by means of a linear stability analysis and by exploiting integral operator analysis. While this is true for ternary interactions, for binary interactions the derived equation of interest is a linear scattering equation that can be studied by means of general relative entropy tools and integral operators. We extend the analysis to a continuous opinion model and coevolving networks.

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Contributing Institute(s):

1. Computational Imaging (FS-CI)

Research Program(s):

1. 623 - Data Management and Analysis (POF4-623) (POF4-623)

Experiment(s):

1. No specific instrument

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Database coverage:
; Clarivate Analytics Master Journal List ; Current Contents - Physical, Chemical and Earth Sciences ; Ebsco Academic Search ; Essential Science Indicators ; IF < 5 ; JCR ; SCOPUS ; Science Citation Index Expanded ; Web of Science Core Collection

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Linked articles:

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Preprint Burger, M. (Corresponding author)DESY* ; Loy, N. ; Rossi, A.
Asymptotic and stability analysis of kinetic models for opinion formation on networks: an Allen-Cahn approach
[10.3204/PUBDB-2026-01195]     Files  Fulltext by arXiv.org BibTeX | EndNote: XML, Text | RIS

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