Heterogeneous animal group models and their group-level alignment dynamics: An equation-free approach

Sung Joon Moon, B. Nabet, Naomi Ehrich Leonard, Simon Asher Levin, Yannis Kevrekidis

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

We study coarse-grained (group-level) alignment dynamics of individual-based animal group models for heterogeneous populations consisting of informed (on preferred directions) and uninformed individuals. The orientation of each individual is characterized by an angle, whose dynamics are nonlinearly coupled with those of all the other individuals, with an explicit dependence on the difference between the individual's orientation and the instantaneous average direction. Choosing convenient coarse-grained variables (suggested by uncertainty quantification methods) that account for rapidly developing correlations during initial transients, we perform efficient computations of coarse-grained steady states and their bifurcation analysis. We circumvent the derivation of coarse-grained governing equations, following an equation-free computational approach.

Original languageEnglish (US)
Pages (from-to)100-112
Number of pages13
JournalJournal of Theoretical Biology
Volume246
Issue number1
DOIs
StatePublished - May 7 2007

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-graining
  • Equation-free multiscale approach
  • Group-level dynamics
  • Heterogeneous animal group alignment
  • Wiener polynomial chaos

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