Kinetic hierarchy and propagation of chaos in biological swarm models

E. Carlen, R. Chatelin, P. Degond, B. Wennberg

Research output: Contribution to journalArticlepeer-review

25 Scopus citations

Abstract

Weconsider two models of biological swarm behavior. In these models, pairs of particles interact to adjust their velocities one to each other. In the first process, called 'BDG', they join their average velocity up to some noise. In the second process, called 'CL', one of the two particles tries to join the other one's velocity. This paper establishes the master equations and BBGKY hierarchies of these two processes. It investigates the infinite particle limit of the hierarchies at large time scales. It shows that the resulting kinetic hierarchy for the CL process does not satisfy propagation of chaos. Numerical simulations indicate that the BDG process has similar behavior to the CL process.

Original languageEnglish (US)
Pages (from-to)90-111
Number of pages22
JournalPhysica D: Nonlinear Phenomena
Volume260
DOIs
StatePublished - 2013

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

Keywords

  • BBGKY hierarchy
  • Correlation
  • Kinetic equations
  • Master equation
  • Propagation of chaos
  • Swarms

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