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Asymptotic and Stability Analysis of Kinetic Models for Opinion Formation on Networks: An Allen--Cahn Approach.

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Title: Asymptotic and Stability Analysis of Kinetic Models for Opinion Formation on Networks: An Allen--Cahn Approach.
Authors: Burger, Martin1 martin.burger@desy.de, Loy, Nadia2 nadia.loy@polito.it, Rossi, Alex3 alex.rossi@fau.de
Source: SIAM Journal on Applied Dynamical Systems. 2025, Vol. 24 Issue 2, p1042-1069. 28p.
Subjects: Boltzmann's equation, Integral operators, Social norms, Linear statistical models, Linear equations
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. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
Description
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. [ABSTRACT FROM AUTHOR]
ISSN:15360040
DOI:10.1137/24M1671128