Asymptotic and stability analysis of kinetic models for opinion formation on networks: an Allen-Cahn approach

M. Burger; N. Loy; A. Rossi

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arXiv · 2407.03375

Asymptotic and stability analysis of kinetic models for opinion formation on networks: an Allen-Cahn approach

M. Burger·N. Loy·A. Rossi

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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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M. Burger, N. Loy, A. Rossi. 2024-07-01. Asymptotic and stability analysis of kinetic models for opinion formation on networks: an Allen-Cahn approach. https://arxiv.org/abs/2407.03375

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