How Does a Swarm Exhibit Emergent Behavior Through Synchronization?

A swarm of individuals often exhibits behaviors that are not possible for each individual. This phenomenon is called emergence, and this paper mathematically demonstrates that new dynamics can arise in swarm behavior that cannot be explained by the dynamics of individuals. In particular, we argue that emergence occurs when heterogeneity is coupled with synchronization. These two concepts may seem conflicting, as heterogeneity is the tendency to differ whereas synchronization is the tendency toward sameness. However, we show that emergent behavior arises from the interplay between the two.