Emergence of time-asymptotic flocking in a stochastic Cucker-Smale system
Ha, Seung-Yeal ; Lee, Kiseop ; Levy, Doron
Commun. Math. Sci., Tome 7 (2009) no. 1, p. 453-469 / Harvested from Project Euclid
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We study a stochastic Cucker-Smale flocking system in which particles interact with the environment through white noise. We provide the definition of flocking for the stochastic system, and show that when the communication rate is constant, the system exhibits a flocking behavior independent of the initial configurations. For the case of a radially symmetric communication rate with a positive lower bound, we show that the relative fluctuations of the particle velocity around the mean velocity have a uniformly bounded variance in time. We conclude with numerical simulations that validate our analytical results.
Publié le : 2009-06-15
Classification:  Cucker-Smale model,  flocking,  kinetic models,  stochastic systems,  particle systems,  34F05,  82C22,  60H10 
@article{1243443989,
     author = {Ha, Seung-Yeal and Lee, Kiseop and Levy, Doron},
     title = {Emergence of time-asymptotic flocking in a stochastic Cucker-Smale system},
     journal = {Commun. Math. Sci.},
     volume = {7},
     number = {1},
     year = {2009},
     pages = { 453-469},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1243443989}
}

Ha, Seung-Yeal; Lee, Kiseop; Levy, Doron. Emergence of time-asymptotic flocking in a stochastic Cucker-Smale system. Commun. Math. Sci., Tome 7 (2009) no. 1, pp.  453-469. http://gdmltest.u-ga.fr/item/1243443989/