Kolpas Allison, Moehlis Jeff, Frewen Thomas A, Kevrekidis Ioannis G
Department of Mathematics, University of California, Santa Barbara, CA 93106, USA.
Math Biosci. 2008 Jul-Aug;214(1-2):49-57. doi: 10.1016/j.mbs.2008.06.003. Epub 2008 Jun 14.
We study the effects of a signalling constraint on an individual-based model of self-organizing group formation using a coarse analysis framework. This involves using an automated data-driven technique which defines a diffusion process on the graph of a sample dataset formed from a representative stationary simulation. The eigenvectors of the graph Laplacian are used to construct 'diffusion-map' coordinates which provide a geometrically meaningful low-dimensional representation of the dataset. We show that, for the parameter regime studied, the second principal eigenvector provides a sufficient representation of the dataset and use it as a coarse observable. This allows the computation of coarse bifurcation diagrams, which are used to compare the effects of the signalling constraint on the population-level behavior of the model.
我们使用一个粗略分析框架来研究信号约束对基于个体的自组织群体形成模型的影响。这涉及使用一种自动化的数据驱动技术，该技术在由代表性的平稳模拟形成的样本数据集的图上定义一个扩散过程。图拉普拉斯算子的特征向量用于构建“扩散映射”坐标，这些坐标提供了数据集在几何上有意义的低维表示。我们表明，对于所研究的参数范围，第二主特征向量提供了数据集的充分表示，并将其用作粗略可观测量。这使得能够计算粗略分岔图，用于比较信号约束对模型群体水平行为的影响。
