Opinion Dynamics with Continuous Age Structure
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911373084065792 |
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| author | Nugent, Andrew Gomes, Susana N. Wolfram, Marie-Therese |
| author_facet | Nugent, Andrew Gomes, Susana N. Wolfram, Marie-Therese |
| contents | We extend a classical model of continuous opinion formation to explicitly include an age-structured population. We begin by considering a stochastic differential equation model which incorporates ageing dynamics and birth/death processes, in a bounded confidence type opinion formation model. We then derive and analyse the corresponding mean field partial differential equation and compare the complex dynamics on the microscopic and macroscopic levels using numerical simulations. We rigorously prove the existence of stationary states in the mean field model, but also demonstrate that these stationary states are not necessarily unique. Finally we establish connections between this and other existing models in various scenarios. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_04319 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Opinion Dynamics with Continuous Age Structure Nugent, Andrew Gomes, Susana N. Wolfram, Marie-Therese Analysis of PDEs We extend a classical model of continuous opinion formation to explicitly include an age-structured population. We begin by considering a stochastic differential equation model which incorporates ageing dynamics and birth/death processes, in a bounded confidence type opinion formation model. We then derive and analyse the corresponding mean field partial differential equation and compare the complex dynamics on the microscopic and macroscopic levels using numerical simulations. We rigorously prove the existence of stationary states in the mean field model, but also demonstrate that these stationary states are not necessarily unique. Finally we establish connections between this and other existing models in various scenarios. |
| title | Opinion Dynamics with Continuous Age Structure |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2503.04319 |