Coarse analysis of collective motion with different communication mechanisms

Allison Kolpas, Jeff Moehlis, Thomas A. Frewen, Ioannis G. Kevrekidis

Research output: Contribution to journalArticlepeer-review

25 Scopus citations


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
Issue number1-2
StatePublished - Jul 2008

All Science Journal Classification (ASJC) codes

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


  • Coarse analysis
  • Collective motion
  • Diffusion maps


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