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June 2009 Emergence of time-asymptotic flocking in a stochastic Cucker-Smale system
Seung-Yeal Ha, Kiseop Lee, Doron Levy
Commun. Math. Sci. 7(2): 453-469 (June 2009).


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.


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Seung-Yeal Ha. Kiseop Lee. Doron Levy. "Emergence of time-asymptotic flocking in a stochastic Cucker-Smale system." Commun. Math. Sci. 7 (2) 453 - 469, June 2009.


Published: June 2009
First available in Project Euclid: 27 May 2009

zbMATH: 1192.34067
MathSciNet: MR2536447

Primary: 34F05
Secondary: 60H10 , 82C22

Keywords: Cucker-Smale model , flocking , kinetic models , Particle systems , stochastic systems

Rights: Copyright © 2009 International Press of Boston

Vol.7 • No. 2 • June 2009
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