一类受白噪声扰动群聚模型的动力学行为

吉林大学学报(理学版) ›› 2021, Vol. 59 ›› Issue (6): 1345-1350.

一类受白噪声扰动群聚模型的动力学行为

张艳妮¹, 周冉², 陈霄雨³

1. 吉林建筑科技学院基础科学部, 长春 130114； 2. 吉林大学数学学院, 长春 130012；3. 海军航空大学青岛校区基础教研室, 山东青岛 266041

收稿日期:2021-04-08 出版日期:2021-11-26 发布日期:2021-11-26
通讯作者: 周冉 E-mail:zhouran@jlu.edu.cn

Dynamic Behavior of a Class of Flocking Models Disturbed by White Noise

ZHANG Yanni¹, ZHOU Ran², CHEN Xiaoyu³

1. Department of Basic Science, Jilin University of Architecture and Technology, Changchun 130114, China;
2. College of Mathematics, Jilin University, Changchun 130012, China; 3. Teaching Section of Foundation, Qingdao Campus of Naval Aeronautical University, Qingdao 266041, Shandong Province, China

Received:2021-04-08 Online:2021-11-26 Published:2021-11-26

摘要/Abstract

摘要： 利用Ito公式和重对数律, 研究一类受白噪声扰动群聚模型的动力学行为. 首先, 证明两个个体的群聚模型呈无条件群聚现象; 其次, 对N个个体的群聚模型, 在一定条件下证明其系统发生强随机群聚现象.

关键词: 群聚模型, 白噪声, Ito公式, 动力学行为

Abstract: By using the Ito formula and the law of iterated logarithm, we studied the dynamic behavior of a class of flocking models disturbed by white noise. Firstly, we proved that the flocking model of two individuals presented unconditional flocking phenomenon. Secondly, for the flocking model of N individuals, we proved that the system had strong random flocking phenomenon under certain conditions.

Key words: flocking model, white noise, Ito formula, dynamic behavior

中图分类号:

O175.12

张艳妮, 周冉, 陈霄雨. 一类受白噪声扰动群聚模型的动力学行为[J]. 吉林大学学报(理学版), 2021, 59(6): 1345-1350.

ZHANG Yanni, ZHOU Ran, CHEN Xiaoyu. Dynamic Behavior of a Class of Flocking Models Disturbed by White Noise[J]. Journal of Jilin University Science Edition, 2021, 59(6): 1345-1350.