The Cucker-Smale model with time delay

Abstract

We study the classical Cucker-Smale model in continuous time with a positive time delay $\tau$. As in the non-delayed case, unconditional flocking occurs when $\beta \le 1/2$ for every $\tau >0$. Furthermore, we prove the exponential decay for the diameter of the velocities.

19 pages, 2 figures