Flocking estimates for the Cucker-Smale model with time lag and hierarchical leadership

Abstract

We analyze the Cucker-Smale model under hierarchical leadership in presence of a time delay. By using a Lyapunov functional approach and some induction arguments we will prove convergence to consensus for every positive delay $\tau$. These results seem to point out the advantage of a hierarchical structure in order to contrast time delay effects that frequently appear in real situations.