等级制度下带有白噪声的群集运动

Flocking under hierarchical leadership with white noise

研究了等级制度下带有白噪声的群集运动。首先提出了等级制度下带有白噪声的模型,然后利用伊藤公式、数学归纳法和数学期望的性质证明了当噪声强度满足一定的条件,时间趋于无穷大时,等级群体可以达到群集运动。最后,通过数值仿真给出了群集受到噪声影响后的状态图和误差图的例子。实验结果证明了结论的正确性。

The flocking under hierarchical leadership with white noise was mainly studied. First we proposed a model with white noise under the hierarchical leadership,and then use the properties of It8 formula,mathematical induction and mathematical expectation function to prove that when the noise intensity satisfies certain conditions and the time tends to infinity,the hierarchical group can reach the flocking. Finally,an example of state diagram and error graph after cluster is affected by noise is given by numerical simulation. The experimental results demonstrate the correctness of the conclusions.