Communications in Mathematical Sciences

Volume 7 (2009)

Number 2

Emergence of time-asymptotic flocking in a stochastic Cucker-Smale system

Pages: 453 – 469



Seung-Yeal Ha

Kiseop Lee

Doron Levy


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.


Cucker-Smale model, flocking, kinetic models, stochastic systems, particle systems

2010 Mathematics Subject Classification

Primary 34F05. Secondary 60H10, 82C22.

Published 1 January 2009