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Kinetic hierarchy and propagation of chaos in biological swarm models

E. Carlen ; R. Chatelin ; P. Degond ; Bernt Wennberg (Institutionen för matematiska vetenskaper, matematik)
Physica D-Nonlinear Phenomena (0167-2789). Vol. 260 (2013), p. 90-111.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: Master equation, Kinetic equations, Propagation of chaos, BBGKY hierarchy; Swarms, Correlation

Denna post skapades 2013-11-11. Senast ändrad 2014-09-02.
CPL Pubid: 186378


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Institutionen för matematiska vetenskaper, matematik (2005-2016)



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