Flocking dynamics and pattern motion for the Cucker-Smale system with distributed delays.

In this paper, a new class of Cucker-Smale systems with distributed delays are developed from the measurement perspective. By combining dissipative differential inequalities with a continuity argument, some new sufficient criteria for the flocking dynamics of the proposed model with general communication rate, especially the non-normalized rate, are established. In order to achieve the prescribed pattern motion, the driving force term is incorporated into the delayed collective system. Lastly, some examples and simulations are provided to illustrate the validity of the theoretical results.