Coarse analysis of collective motion with different communication mechanisms |
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Authors: | Kolpas Allison Moehlis Jeff Frewen Thomas A Kevrekidis Ioannis G |
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Institution: | Department of Mathematics, University of California, Santa Barbara, CA 93106, USA. allie@math.ucsb.edu |
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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. |
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Keywords: | Collective motion Coarse analysis Diffusion maps |
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