We provide a numerical study of the macroscopic model of Barré et al. (Multiscale Model Simul, 2017, to appear) derived from an agent-based model for a system of particles interacting through a dynamical network of links. Assuming that the network remodeling process is very fast, the macroscopic model takes the form of a single aggregation–diffusion equation for the density of particles. The theoretical study of the macroscopic model gives precise criteria for the phase transitions of the steady states, and in the one-dimensional case, we show numerically that the stationary solutions of the microscopic model undergo the same phase transitions and bifurcation types as the macroscopic model. In the two-dimensional case, we show that the numerical simulations of the macroscopic model are in excellent agreement with the predicted theoretical values. This study provides a partial validation of the formal derivation of the macroscopic model from a microscopic formulation and shows that the former is a consistent approximation of an underlying particle dynamics, making it a powerful tool for the modeling of dynamical networks at a large scale.

中文翻译：

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由动态网络介导的粒子相互作用：宏观描述的评估。

我们提供了Barré等人宏观模型的数值研究。（多尺度模型Simul，2017年出现）源自基于代理的模型，该模型用于通过动态链接网络相互作用的粒子系统。假设网络重塑过程非常快，则宏观模型采用单个聚集-扩散方程式来表示粒子的密度。宏观模型的理论研究为稳态的相变提供了精确的标准，在一维情况下，我们通过数值表明微观模型的静态解经历了与宏观模型相同的相变和分叉类型。在二维情况下，我们表明宏观模型的数值模拟与预测的理论值非常吻合。