Emergence of condensation patterns in kinetic equations for opinion dynamics
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916384159563776 |
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| author | Calzola, Elisa Dimarco, Giacomo Toscani, Giuseppe Zanella, Mattia |
| author_facet | Calzola, Elisa Dimarco, Giacomo Toscani, Giuseppe Zanella, Mattia |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_03507 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Emergence of condensation patterns in kinetic equations for opinion dynamics Calzola, Elisa Dimarco, Giacomo Toscani, Giuseppe Zanella, Mattia Adaptation and Self-Organizing Systems Mathematical Physics Physics and Society 35Q91, 91D30, 91B74, 35Q84, 82B40 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. |
| title | Emergence of condensation patterns in kinetic equations for opinion dynamics |
| topic | Adaptation and Self-Organizing Systems Mathematical Physics Physics and Society 35Q91, 91D30, 91B74, 35Q84, 82B40 |
| url | https://arxiv.org/abs/2405.03507 |