论文标题
集体动力学模型的平均场和图形限值
Mean-field and graph limits for collective dynamics models with time-varying weights
论文作者
论文摘要
在本文中，我们研究了一种观点动态的模型，在这种模型中，代理的影响通过方程式与观点的演变相结合的方程式进化。我们使用两种方法探索了大人口限制的自然问题：现在经典的平均场限制和最新的图形限制。在建立了我们将考虑的模型的解决方案的存在和唯一性之后，我们为在一般环境中采取图形限制提供了严格的数学理由。然后，建立不可区分性的关键概念，这是考虑平均场限制的必要框架，我们证明了在该上下文中平均场限制对图的均值的从属。实际上，这为平均场限制提供了替代（但较弱的）证明。最后，我们显示了一些数值模拟来说明我们的结果。
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.
