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Zbl 1143.92043
Kolpas, Allison; Moehlis, Jeff; Frewen, Thomas A.; Kevrekidis, Ioannis G.
Coarse analysis of collective motion with different communication mechanisms. (English)
[J] Math. Biosci. 214, No. 1-2, 49-57 (2008). ISSN 0025-5564

Summary: 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.

MSC 2000:: *92D50 Animal behavior
60J70 Appl. of diffusion theory
94A99 Communication and information

Keywords: collective motion; coarse analysis; diffusion maps; schooling model

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