Department of Ecology and Evolutionary Biology, Princeton University, Princeton, NJ 08544, USA.
J Theor Biol. 2010 Jun 7;264(3):893-913. doi: 10.1016/j.jtbi.2010.02.030. Epub 2010 Feb 21.
We propose a (time) multiscale method for the coarse-grained analysis of collective motion and decision-making in self-propelled particle models of swarms comprising a mixture of 'naïve' and 'informed' individuals. The method is based on projecting the particle configuration onto a single 'meta-particle' that consists of the elongation of the flock together with the mean group velocity and position. We find that the collective states can be associated with the transient and asymptotic transport properties of the random walk followed by the meta-particle, which we assume follows a continuous time random walk (CTRW). These properties can be accurately predicted at the macroscopic level 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.
我们提出了一种（时间）多尺度方法，用于对由“天真”和“知情”个体混合组成的群体自推进粒子模型中的集体运动和决策进行粗粒度分析。该方法基于将粒子配置投影到单个“元粒子”上，该元粒子由群体的伸长以及平均群速度和位置组成。我们发现，集体状态可以与元粒子所遵循的随机游走的瞬态和渐近输运性质相关联，我们假设元粒子遵循连续时间随机游走（CTRW）。这些性质可以通过具有记忆的对流-扩散方程（ADEM）在宏观水平上进行准确预测，该方程的参数是从基于个体的模型的单个模拟运行中获得的平均群速度时间序列中得到的。
