Noisy bounded confidence models for opinion dynamics: the effect of boundary conditions on phase transitions

TL;DR

This paper investigates how different boundary conditions affect phase transitions in noisy bounded confidence models for opinion dynamics, comparing SDE and PDE approaches and emphasizing the no-flux boundary case.

Contribution

It provides a comprehensive numerical analysis of boundary effects on opinion phase transitions, highlighting the no-flux boundary as most representative of deterministic models.

Findings

No-flux boundary conditions best replicate deterministic model mechanisms

Boundary conditions significantly influence phase transition behavior

Comparison of SDE and PDE models reveals consistent dynamics

Abstract

We study SDE and PDE models for opinion dynamics under bounded confidence, for a range of different boundary conditions, with and without the inclusion of a radical population. We perform exhaustive numerical studies with pseudospectral methods to determine the effects of the boundary conditions, suggesting that the no-flux case most faithfully reproduce the underlying mechanisms in the associated deterministic models of Hegselmann and Krause. We also compare the SDE and PDE models, and use tools from analysis to study phase transitions, including a systematic description of an order parameter.