Pattern formation in the interaction of Cucker–Smale ensembles

This paper investigates the spatial pattern formation problem arising from the interaction of two homogeneous Cucker–Smale ensembles, which models flock merging and separation. We show the emergence of global or local flocking and line-shaped motion patterns under the influence of driving forces. More precisely, we present sufficient conditions for the emergence of two distinct patterns: global flocking with a line-shaped motion pattern, and bi-cluster flocking with line-shaped motion patterns. An interesting thing we find is that the L2,2 norms works well for the global flocking and line-shaped motion pattern. However, L2,∞ works well for the bi-cluster flocking and line-shaped motion patterns.