@article{39261,
  keywords = {systems, fish schools, diffusion maps, patterns, birds, coarse analysis, collective motion, flight},
  author = {Allison Kolpas and Jeff Moehlis and Thomas Frewen and Ioannis Kevrekidis},
  title = {Coarse analysis of collective motion with different communication mechanisms},
  abstract = { <p>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 {\textquoteright}diffusion-map{\textquoteright} 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.</p> },
  year = {2008},
  journal = {Mathematical Biosciences},
  volume = {214},
  pages = {49-57},
  month = {07/2008},
  isbn = {0025-5564},
  language = {English},
}