Coarse analysis of collective motion with different communication mechanisms

Authored by Ioannis G Kevrekidis, Allison Kolpas, Jeff Moehlis, Thomas A Frewen

Date Published: 2008

DOI: 10.1016/j.mbs.2008.06.003

Sponsors: United States Defense Advanced Research Planning Agency (DARPA) United States National Science Foundation (NSF)

Platforms: No platforms listed

Model Documentation: Other Narrative Mathematical description

Model Code URLs: Model code not found

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.

Tags

patterns systems birds Flight Fish schools Diffusion maps