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PUBDB-2026-01195

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. ; Rossi, A.

2024

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Please use a persistent id in citations: doi:10.3204/PUBDB-2026-01195

Report No.: arXiv:2407.03375

Abstract: We present the analysis of the stationary equilibria and their stability in case of an opinion formation process in presence of binary opposite opinions evolving according to majority-like rules on social networks. The starting point is a kinetic Boltzmann-type model derived from microscopic interactions rules 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.

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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:
; ; Published

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Linked articles:

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Journal Article Burger, M. (Corresponding author)DESY* ; Loy, N. (Corresponding author) ; Rossi, A. (Corresponding author)Extern*
Asymptotic and Stability Analysis of Kinetic Models for Opinion Formation on Networks: An Allen–Cahn Approach
SIAM journal on applied dynamical systems 24(2), 1042 - 1069 (2025) [10.1137/24M1671128]2025     Files  Fulltext by arXiv.org BibTeX | EndNote: XML, Text | RIS

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