Collective Behavior in Systems within Confined Environments

Abstract

In this paper, we study the behavior of systems of individuals in confined environments that are driven by laws of self-organization. We propose that, under certain conditions, the long-term behavior of such systems will be global alignment. We study the result by Felipe Cucker and Steve Smale as well as their models describing the evolution of a flock in continuous and discrete time. Specifically, we will describe the models of Cucker-Smale on bounded domains $\mathbb{R}^+$ and on the interval $[a,b]$.