Kinetic hierarchy and propagation of chaos in biological swarm models
Journal article, 2013

We consider 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. (c) 2012 Elsevier B.V. All rights reserved.


Propagation of chaos


Master equation

Kinetic equations

BBGKY hierarchy


E. Carlen

Rutgers, The State University of New Jersey

R. Chatelin

Centre national de la recherche scientifique (CNRS)

University of Toulouse

P. Degond

University of Toulouse

Centre national de la recherche scientifique (CNRS)

Bernt Wennberg

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Physica D: Nonlinear Phenomena

0167-2789 (ISSN)

Vol. 260 90-111

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