Coarse analysis of collective motion with different communication mechanisms

Allison Kolpas, Jeff Moehlis, Thomas A. Frewen, Yannis Kevrekidis

Research output: Contribution to journalArticle

24 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)49-57
Number of pages9
JournalMathematical Biosciences
Volume214
Issue number1-2
DOIs
StatePublished - Jul 1 2008

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modeling and Simulation
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Agricultural and Biological Sciences(all)
  • Applied Mathematics

Keywords

  • Coarse analysis
  • Collective motion
  • Diffusion maps

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