Modeling change in public sentiment with nonlocal reaction-diffusion equations

Joseph L. Shomberg

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arXiv · 2105.03920

Modeling change in public sentiment with nonlocal reaction-diffusion equations

Joseph L. Shomberg

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Abstract

This is a brief "proof of concept" article that shows nonlocal diffusion is well suited to the study of pattern formation and the particular application of public sentiment. We use a nonlocal reaction-diffusion equation to model the evolution of public sentiment in a population that interacts with other individuals. We employ a pseudo-random convolution kernel as a symmetric matrix of lognormally distributed values. This kernel models the influence of individuals when interacting with others. Change in sentiment emerges and may converge to a polarized state. Other more complicated states occur whereby a mixed polarization emerges.

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Joseph L. Shomberg. 2021-05-09. Modeling change in public sentiment with nonlocal reaction-diffusion equations. https://arxiv.org/abs/2105.03920

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