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 (but weaker) proof for the mean-field limit. We conclude by showing some numerical simulations to illustrate our results.

References in corpus (2)

• The derivation of Swarming models: Mean-Field Limit and Wasserstein distances
• Generalized Wasserstein distance and its application to transport equations with source

Cited by in corpus (8)

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• Consensus based optimization with memory effects: random selection and applications
• Mean field limit for one dimensional opinion dynamics with Coulomb interaction and time dependent weights
• Large population limits of Markov processes on random networks
• Mean field limits of co-evolutionary signed heterogeneous networks
• Continuum limit for interacting systems on adaptive networks
• Capturing the critical coupling of large random Kuramoto networks with graphons
• Persistence of steady-states for dynamical systems on large networks