Mean-field and graph limits for collective dynamics models with time-varying weights
| Autor: | Nathalie Ayi, Nastassia Pouradier Duteil |
|---|---|
| Přispěvatelé: | Sorbonne Université (SU), Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Modelling and Analysis for Medical and Biological Applications (MAMBA), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité) |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Subordination (linguistics)
Applied Mathematics 010102 general mathematics Context (language use) 01 natural sciences 010101 applied mathematics Mathematics - Analysis of PDEs Mean field theory FOS: Mathematics Key (cryptography) Applied mathematics Graph (abstract data type) [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] Uniqueness Limit (mathematics) 0101 mathematics Collective dynamics Analysis Analysis of PDEs (math.AP) Mathematics |
| Zdroj: | Journal of Differential Equations Journal of Differential Equations, 2021, ⟨10.1016/j.jde.2021.07.010⟩ |
| ISSN: | 0022-0396 1090-2732 |
| DOI: | 10.1016/j.jde.2021.07.010⟩ |
| Popis: | International audience; In this paper, we study a model for opinion dynamics where the influence weights of agents evolve in time via an equation which is coupled with the opinions' evolution. We explore the natural question of the large population limit with two approaches: the now classical mean-field limit and the more recent graph limit. After establishing the existence and uniqueness of solutions to the models that we will consider, we provide a rigorous mathematical justification for taking the graph limit in a general context. Then, establishing the key notion of indistinguishability, which is a necessary framework to consider the mean-field limit, we prove the subordination of the mean-field limit to the graph one in that context. This actually provides an alternative proof for the mean-field limit. We conclude by showing some numerical simulations to illustrate our results. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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