تقرير
Emergence of condensation patterns in kinetic equations for opinion dynamics
| العنوان: | Emergence of condensation patterns in kinetic equations for opinion dynamics |
|---|---|
| المؤلفون: | Calzola, Elisa, Dimarco, Giacomo, Toscani, Giuseppe, Zanella, Mattia |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics Mathematical Physics Nonlinear Sciences Physics (Other) |
| مصطلحات موضوعية: | Nonlinear Sciences - Adaptation and Self-Organizing Systems, Mathematical Physics, Physics - Physics and Society, 35Q91, 91D30, 91B74, 35Q84, 82B40 |
| الوصف: | 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. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2405.03507 |
| رقم الأكسشن: | edsarx.2405.03507 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |