Continuum limit of self-driven particles with orientation interaction

Pierre Degond, Sébastien Motsch

Research output: Contribution to journalArticlepeer-review

268 Scopus citations


The discrete Couzin-Vicsek algorithm (CVA), which describes the interactions of individuals among animal societies such as fish schools is considered. In this paper, a kinetic (mean-field) version of the CVA model is proposed and its formal macroscopic limit is provided. The final macroscopic model involves a conservation equation for the density of the individuals and a non-conservative equation for the director of the mean velocity and is proved to be hyperbolic. The derivation is based on the introduction of a non-conventional concept of a collisional invariant of a collision operator.

Original languageEnglish (US)
Pages (from-to)1193-1215
Number of pages23
JournalMathematical Models and Methods in Applied Sciences
Issue numberSUPPL.
StatePublished - Aug 2008
Externally publishedYes


  • Asymptotic analysis
  • Collision invariants
  • Couzin-Vicsek algorithm
  • Fish behavior
  • Hydrodynamic limit
  • Individual based model
  • Orientation interaction

ASJC Scopus subject areas

  • Modeling and Simulation
  • Applied Mathematics


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