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

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