Emergence of time-asymptotic flocking in a stochastic Cucker-Smale system
Emergence of time-asymptotic flocking in a stochastic Cucker-Smale system
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DOI：
10.4310/cms.2009.v7.n2.a9
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发表时间：
2009-06
影响因子：
1
通讯作者：
Seung‐Yeal Ha;Kiseop Lee;D. Levy
中科院分区：
文献类型：
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作者：
Seung‐Yeal Ha;Kiseop Lee;D. Levy
抽象的。我们研究了一种随机 Cucker-Smale 植绒系统，其中粒子通过白噪声与环境相互作用。我们提供了随机系统的聚集定义，并表明当通信速率恒定时，系统表现出与初始配置无关的聚集行为。对于具有正下界的径向对称通信速率的情况，我们表明粒子速度围绕平均速度的相对波动在时间上具有一致有界方差。我们通过数值模拟来验证我们的分析结果。
Abstract. 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.