A Class Of Flocking Phenomena Under External Force

In many fields of natural science and human society,there are some com-mon phenomena,such as sheep moving in the same direction,migratory birds flying in the same direction at the same speed,bees collecting honey through close cooperation with each other,the evolution of human language and so on.The common feature of these phenomena is that a large number of interacting individuals conduct collective behavior with common group goals,this kind of phenomenon is called flocking.In recent decades,scientists from animal be-havior?biology?physics?artificial intelligence and other disciplines have done a lot of researches on the phenomenon of flocking,and widely used in eco-nomics?UAV formation control and other fields,it has important theoretical significance and application value.This paper considers the following system where qi,pi?Rm are the spatial position and velocity of the ith particle,is the derivative of t with respect to time,?·?? is ?-norm,(?)is a potential ability,(?)is a velocity consensus term,aij=?(?qj-qi?)is a general case of nonnegative and symmetric functions,nij is from qi points to qj,the direction vector of nij is defined as(?),0<?<1,qr,pr ?Rm are the position and speed of external control factors,c1>0,c2?0 are the influence coefficients.In this paper,we will analyze the clustering state of the system(1.3.1)under several kinds of forces.Firstly,we decompose the system(1.3.1)into a central system and a reduced central system,and give the theorem that the reduced central system can reach the clustering state.Secondly,we consid-er the asymptotic behavior of the solution of the system in four cases:fixed objective control,linear transportation control,periodic control and quasi pe-riodic control.Finally,we use matlab to simulate the clustering state of the system in four cases.This paper is divided into three chapters,the first chapter is the introduc-tion,which briefly introduces the clustering phenomenon and several classical clustering models.The second chapter is the establishment of the model,which introduces the basic knowledge and important properties of graph the-ory and norm,and analyzes the model.The third chapter is the main content of this paper,which discusses the dynamic properties of multi-body system with external force,and carries out numerical simulation by computer.