时变权集体动力学的平均场极限
Mean-field limit of collective dynamics with time-varying weights
摘要：
在本文中，我们推导出平均场极限的集体动力学模型与时变权重，保持系统的总质量，以及不变性的代理商的重量动力学。极限方程是一个带源的输运方程，其中（非局部）输运项对应于位置动力学，（非局部）源项来自智能体之间的权重重新分配。我们证明了微观和宏观模型的解的存在性和唯一性，并引入了一个新的经验措施，考虑到权重。我们得到的收敛的微观模型的宏观表现出连续性的宏观解决方案的初始数据，在Wasserstein和有界Lipschitz拓扑。
英文摘要：
In this paper, we derive the mean-field limit of a collective dynamics model with time-varying weights, for weight dynamics that preserve the total mass of the system as well as indistinguishability of the agents. The limit equation is a transport equation with source, where the (non-local) transport term corresponds to the position dynamics, and the (non-local) source term comes from the weight redistribution among the agents. We show existence and uniqueness of the solution for both microscopic and macroscopic models and introduce a new empirical measure taking into account the weights. We obtain the convergence of the microscopic model to the macroscopic one by showing continuity of the macroscopic solution with respect to the initial data, in the Wasserstein and Bounded Lipschitz topologies.
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