1. Continuum modeling for opinion formation on a network
- Author
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Favre, Gianluca, Jankowiak, Gaspard, Merino-Aceituno, Sara, and Trussardi, Lara
- Subjects
Mathematics - Analysis of PDEs - Abstract
We consider Abelson's model for opinion dynamics, where individuals interact if they are connected via a fixed network. Our aim is to develop a continuous description for these dynamics that captures well the global dynamics when the number of individuals grows to infinity. We aim at having a simple continuum description on which computations and comparison with the discrete dynamics are feasible. The difficulty lies in the network of connections being described through the labeling of the individuals: this makes the system not amenable to standard mean-field limits. We overcome this difficulty by introducing an evolving label-free network description. We compare the discrete model considered, and the continuum model proposed in the case of consensus dynamics, and carry out simulations for a system with three communities. Moreover, we propose extensions of the model to incorporate phenomena like creation and destruction of connections (dynamical networks), noise, and directional networks.
- Published
- 2024