Emergence of condensation patterns in kinetic equations for opinion dynamics
Abstract
In this work, we define a class of models to understand the impact of population size on opinion formation dynamics, a phenomenon usually related to group conformity. To this end, we introduce a new kinetic model in which the interaction frequency is weighted by the kinetic density. In the quasi-invariant regime, this model reduces to a Kaniadakis-Quarati-type equation with nonlinear drift, originally introduced for the dynamics of bosons in a spatially homogeneous setting. From the obtained PDE for the evolution of the opinion density, we determine the regime of parameters for which a critical mass exists and triggers blow-up of the solution. Therefore, the model is capable of describing strong conformity phenomena in cases where the total density of individuals holding a given opinion exceeds a fixed critical size. In the final part, several numerical experiments demonstrate the features of the introduced class of models and the related consensus effects.
- Publication:
-
arXiv e-prints
- Pub Date:
- May 2024
- DOI:
- 10.48550/arXiv.2405.03507
- arXiv:
- arXiv:2405.03507
- Bibcode:
- 2024arXiv240503507C
- Keywords:
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- Nonlinear Sciences - Adaptation and Self-Organizing Systems;
- Mathematical Physics;
- Physics - Physics and Society;
- 35Q91;
- 91D30;
- 91B74;
- 35Q84;
- 82B40