Pattern formation in the Cucker-Smale model

Abstract

In this paper, we study the pattern formation phenomenon in the Cucker-Smale model with short-range communication weight under the interaction with introduced driving force. We show that the multi-cluster flocking and multi-cluster alignment emerge, and each flock achieves a line-shaped motion pattern for a given class of admissible initial configurations if the coupling strength and driving force strengths satisfy certain conditions. We also show the emergence of the global flocking, the global alignment, and the line-shaped motion pattern in the Cucker-Smale model with short-range communication weight if the coupling strength has a lower bound.