关于2类群体运动模型的综述:Cucker-Smale模型与Kuramoto模型  

A Survey on Two Types of Multi-agent Models:the Cucker-Smale Model and the Kuramoto Model

作　　者：薛小平[1] XUE Xiaoping(Department of Mathematics,Harbin Institute of Technology,Harbin 150001,Heilongjiang)

机构地区：[1]哈尔滨工业大学数学系,黑龙江哈尔滨150001

出　　处：《四川师范大学学报（自然科学版）》2017年第6期711-721,共11页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(11671109)

摘　　要：介绍2类重要的群体运动模型Cucker-Smale(简记(C-S))模型与Kuramoto(简记(K))模型的研究现状及发展动态.(C-S)模型是描述动物群体能如何成群的数学机制,(K)模型是揭示自然界中广泛存在的频率同步现象的形成机制.2个模型具有共同的特点,即群体效应,但研究的方法和手段却不相同.重点从数学方法上论述研究的成果及其未解决的问题,帮助有兴趣的读者能较快地进入这一领域.We introduce the recent research development about two types of multi-agent models： the Cucker-Smale（ C-S） model and the Kuramoto（ K） model.（ C-S） model is a mathematical model used to describe the flocking behavior of animals. K model reveals the mechanism of synchronization phenomenon in natural world. These two models have a common property,which is the group effect.But the methods to study these two models are quite different. We introduce not only the mathematical methods but also some open problems about these two models. We hope this survey can help the interested readers to enter this research area quickly.

关 键 词：Cucker-Smale模型 Kuramoto模型 成群 锁相 频率同步 

分 类 号：O175.14[理学—数学]