Flocking In The Coupled Multi-agent System With Non-uniform Mass

In recent years, studies on the phenomenon of group of organisms becomes more and more popular. Researchers are curious about the natural phenomenon, but more importantly because it has wide application prospects and great significance in robots,satellites and other fields. In 2007, Cucker and Smale proposed Cucker-Smale model which explains the group behavior of organisms. In the past few years, in order to facilitate the calculation and analysis of the model, researchers generally assumed that the mass of each individual are equal. However, this is not realistic. Therefore, this thesis will consider the flocking of the Cucker-Smale model with non-uniform mass.The main results of this study are as follows:1. We study the Cucker-Smale model with non-uniform mass. Firstly, the influence matrix between individuals is normalized. Secondly, we introduce the definitions of flocking, the diameter of relative position and velocity. Finally, we prove that flocking occurs when the diameter of the initial state satisfies certain conditions.2. We introduce the Cucker-Smale model under hierarchical leadership with non-uniform mass in noisy environments and present the definition of flocking of this special model firstly. Secondly, we introduce a new norm and an "error" system.Thirdly,we prove that flocking occurs under certain conditions when regarding noise as a certain kind of perturbation. Then, we estimate the probability of n-nearly-alignment after finite iterations when noise obeys uniform distribution or Gaussian distribution.