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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.
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https://hal.inria.fr/hal-03065067
Contributor : Nathalie Ayi Connect in order to contact the contributor
Submitted on : Tuesday, December 15, 2020 - 2:42:19 PM
Last modification on : Thursday, January 27, 2022 - 2:44:58 PM
Long-term archiving on: : Tuesday, March 16, 2021 - 6:17:46 PM

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

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