群体中集体运动和决策的多尺度分析：带记忆方法的对流扩散方程
Multiscale analysis of collective motion and decision-making in swarms: An advection-diffusion equation with memory approach
摘要：
我们提出了一个（时间）多尺度方法的粗粒度分析的自推进粒子模型的群体，包括一个混合物的“天真”和“知情”的个人，用于解决集体运动和集体决策相关的问题-在动物群体。该方法基于将粒子配置投影到单个“元粒子”上，该元粒子由群伸长以及平均群速度和位置组成。该配置的集体状态可以与元粒子跟随的随机行走的瞬态和渐近输运性质相关联。这些属性可以准确地预测的对流扩散方程与记忆（ADEM），其参数是从一个平均群速度时间序列从一个单一的模拟运行的个人为基础的模型。
英文摘要：
We propose a (time) multiscale method for the coarse-grained analysis of self--propelled particle models of swarms comprising a mixture of `naïve' and `informed' individuals, used to address questions related to collective motion and collective decision--making in animal groups. The method is based on projecting the particle configuration onto a single `meta-particle' that consists of the group elongation and the mean group velocity and position. The collective states of the configuration can be associated with the transient and asymptotic transport properties of the random walk followed by the meta-particle. These properties can be accurately predicted by an advection-diffusion equation with memory (ADEM) whose parameters are obtained from a mean group velocity time series obtained from a single simulation run of the individual-based model.
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