Mean-field and graph limits for collective dynamics models with time-varying weights - Inria - Institut national de recherche en sciences et technologies du numérique
Journal Articles Journal of Differential Equations Year : 2021

Mean-field and graph limits for collective dynamics models with time-varying weights

Abstract

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.
Fichier principal
Vignette du fichier
MeanField-GraphLimit_official.pdf (942.76 Ko) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-03065067 , version 1 (15-12-2020)

Identifiers

Cite

Nathalie Ayi, Nastassia Pouradier Duteil. Mean-field and graph limits for collective dynamics models with time-varying weights. Journal of Differential Equations, 2021, ⟨10.1016/j.jde.2021.07.010⟩. ⟨hal-03065067⟩
155 View
341 Download

Altmetric

Share

More