Opinion Dynamics on a General Compact Riemannian Manifold
| Autor: | Nastassia Pouradier Duteil, Sean T. McQuade, Aylin Aydoğdu |
|---|---|
| Přispěvatelé: | Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL) |
| Rok vydání: | 2017 |
| Předmět: |
Statistics and Probability
0209 industrial biotechnology Closed manifold [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS] 02 engineering and technology Isometry (Riemannian geometry) 01 natural sciences Pseudo-Riemannian manifold Combinatorics symbols.namesake 020901 industrial engineering & automation Hermitian manifold [MATH]Mathematics [math] 0101 mathematics Ricci curvature Mathematics Computer Science::Information Retrieval Applied Mathematics Mathematical analysis General Engineering Riemannian manifold Computer Science Applications 010101 applied mathematics Projection (relational algebra) symbols Energy (signal processing) |
| Zdroj: | Networks and Heterogeneous Media Networks and Heterogeneous Media, AIMS-American Institute of Mathematical Sciences, 2017, 12 (3), pp.489-523. ⟨10.3934/nhm.2017021⟩ |
| ISSN: | 1556-181X 1556-1801 |
| DOI: | 10.3934/nhm.2017021 |
| Popis: | This work formulates the problem of defining a model for opinion dynamics on a general compact Riemannian manifold. Two approaches to modeling opinions on a manifold are explored. The first defines the distance between two points using the projection in the ambient Euclidean space. The second approach defines the distance as the length of the geodesic between two agents. Our analysis focuses on features such as equilibria, the long term behavior, and the energy of the system, as well as the interactions between agents that lead to these features. Simulations for specific manifolds, \begin{document} $\mathbb{S}^1, \mathbb{S}^2,$ \end{document} and \begin{document} $\mathbb{T}^2$ \end{document} , accompany the analysis. Trajectories given by opinion dynamics may resemble \begin{document} $n-$ \end{document} body Choreography and are called "social choreography". Conditions leading to various types of social choreography are investigated in \begin{document} $\mathbb{R}^2$ \end{document} . |
| Databáze: | OpenAIRE |
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