Modeling change in public sentiment with nonlocal reaction-diffusion equations

TL;DR

This paper demonstrates that nonlocal reaction-diffusion equations effectively model the evolution and pattern formation of public sentiment, capturing phenomena like polarization and mixed states through a pseudo-random convolution kernel.

Contribution

It introduces a novel application of nonlocal reaction-diffusion equations with a lognormal convolution kernel to model public sentiment dynamics.

Findings

Sentiment can converge to polarized states.

Mixed polarization states can emerge.

Nonlocal diffusion captures complex sentiment patterns.

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.