Configuration Analysis Of A Class Of Flocking Models

Self-organization phenomena are common in nature and human society,such as bird migration,ants building nests,and commodity price uniformity,these phenomena show self-organization patterns from different angles and forms.People think that flocking is a form of collective behavior of large number of interacting agents with a common group objective.It can be described as a group of individuals move in one direction in an orderly manner,making consistent behaviors like a super creature.For decades,the flocking problem has been applied in many research fields,such as self-organizing mobile sensor networks,intel-ligent body systems,UAV group flying in formation,and the implementation of surveillance and reconnaissance military missions.Thus,the research of the widespread phenomenon of flocking in the world and human society is of significance.Concretely,this article mainly considers the following n particle interaction model:where(?)qi,Pi?Rm,A=(aij)n×n is a non-negative symmetric matrix,Our main work is to analyze the asymptotic flocking behavior of the above model,First,use the LaSalle's principle of invariance to give the model's long-term unconditional flocking conclusion,and then analyze the geometric configuration during flocking,finally use Matlab software numerical simulation analyzes the corresponding stability problems.This article is divided into three chapters.The First chapter is an introduction,which introduces the research background of many-body problems,flocking models,and the main work of this article.The Second chapter is preliminary knowledge,a brief introduction to graph theory,Kronecker product,LaSalle's invariance principle and related concepts of flocking.Chapter 3 is the main work,First,use the principle of LaSalle's invariance to prove that the model has unconditional flocking for a long time,and then analyze the configuration of the corresponding flocking state under different numbers of individuals.it is proved that when the number of particles is 2,the corresponding configuration is only collinear,and when the number of particles is 3,the corresponding configuration there are only two cases:the collinear case and the equilateral triangle.When the number of particles is 4 or 5,we have found the collinear configuration,the regular polygon configuration,and the configuration that the particles distribute on the vertices and centers of the regular polygon.further,for any n particles,the collinear configuration and the polyhedral configuration are given,and finally use Matlab software to perform numerical simulation analysis on the corresponding dynamic asymptotic behavior.