Flocking Phenomena Of Two Classes Of Switched Cucker-Smale Models

Flocking phenomenon is a flock after a period of evolution of a kind of convergence of the collective behavior,which is universal in nature and human society.In recent years,this phenomenon has attracted the scholars of many fields to study.For example,in biology,flocks of birds migrate together,schools of fish forage;The regular motion of particle in physics,and a stable price system in financial markets,etc.For the generation of flocking phenomenon,there are many influencing factors,such as the interaction pattern between individuals,the reaction time of the interaction,and the noise produced by the environment disturbance factors,etc,which will have an impact on the behavioral evolution of the flocks.According to these typical influencing factors,people have established a variety of effective flocking models to study many phenomena in nature and human society.For example,Cucker-Smale model(C-S model),Motsch-Tadmor model(M-T model),Vicsek models,traffic flow models,etc,these models have been highly concerned by people and have gained a lot of important research and development in recent years.In this paper,based on the existing important results,we will consider the flocking phenomenon of two kinds of C-S models with special switching modes,and finally give some sufficient conditions for the corresponding models to achieve the flocking phenomenon by constructing the dissipative differential inequality and using the continuity theory.This paper is divided into four chapters.The first chapter is the introduction,which mainly introduces the research background of flocking phenomenon,several classical flocking models and the main work of this paper.In Chapter 2,the flocking of C-S models under a special switching mode is considered.Firstly,the existence and uniqueness of global solutions are proved,and then dissipative differential inequalities for displacement and velocity diameters are constructed.Finally,sufficient conditions for flocking of C-S models under a special switching mode are given.In Chapter 3,the flocking phenomenon of C-S model with time delay under a special switching mode is considered.The existence and uniqueness of the corresponding global solutions are proved respectively,and dissipative differential inequalities are constructed.Finally,sufficient conditions for the flocking phenomenon are given.Chapter 4 is a summary and discussion.Through the analysis of several classic models,the rationality of this paper’s work is demonstrated,and the comparison results between this model and several classic models are presented.