Emergence of flocks with local interactions

In a recent paper, Cucker and Smale proposed a multi-agent model to study the flocking behavior, where they assume that all agents can interact with all other agents. Though this model attracted much attention of researchers, the global interactions used in that paper changed the nature of multi-agent systems. In this paper we will investigate a new flocking model, in which the global interactions between agents are replaced by local interaction functions. We will provide necessary conditions and sufficient conditions for consensus.