| Issue |
Math. Model. Nat. Phenom.
Volume 20, 2025
|
|
|---|---|---|
| Article Number | 25 | |
| Number of page(s) | 34 | |
| Section | Fractional Dynamics in Natural Phenomena | |
| DOI | https://doi.org/10.1051/mmnp/2025025 | |
| Published online | 08 October 2025 | |
Emergence of complexity in opinion propagation: A reaction-diffusion model
1
Université Paris Cité et Sorbonne Université, Laboratoire Jacques-Louis Lions (LJLL), Paris, France.
2
Universitée de Bretagne Occidentale, Laboratoire de Mathématiques de Bretagne Atlantique (LMBA), Brest, France
* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
17
December
2024
Accepted:
29
August
2025
Abstract
We analyze a model designed to describe the spread and accumulation of opinions in a population. Inspired by the social contagion paradigm, our model is built on the classical SIR model of Kermack and McKendrick and consists in a system of reaction-diffusion equations. In the scenario we consider, individuals within the population can adopt new opinions via interactions with others, following some simple rules. The individuals can gradually adopt more complex opinions over time. Our main result is the characterization of a maximal complexity of opinions that can persist and propagate. In addition, we show how the parameters of the model influence this maximal complexity. Notably, we show that it grows almost exponentially with the size of the population, suggesting that large communities can foster the emergence of more complex opinions.
Mathematics Subject Classification: 35K40 / 35K57 / 35B40 / 91D25
Key words: Reaction–diffusion systems / SIR models / Fisher-KPP dynamics / spreading speed / propagation properties / social contagion / propagation of opinions / emergence of complexity
© The authors. Published by EDP Sciences, 2025
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.