Coarse analysis of collective motion with different communication mechanisms

Publication Year
2008

Type

Journal Article
Abstract

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. (C) 2008 Elsevier Inc. All rights reserved.

Journal
Mathematical Biosciences
Volume
214
Issue
1-2
Pages
49-57
Date Published
07/2008
ISBN
0025-5564
Short Title
Math. Biosci.