Collision-free flocking for a time-delay system
The authors studies a Cucker-Smale type model with two additional mechanism. One is time delay effect, and the other one is the repulsion force when two particles are close. Therefore, the inertial effect is stronger and oscillations appear in the system, which draws difficulty in analysis of large time behavior. Moreover, the mean velocity is no longer conservative, thus the flocking is described via vanishing of relative velocity. The authors first prove global existence of the solution by showing collision avoidance in finite time. Then, when delay is sufficiently small, the authors construct a proper Lyapunov functional to describe the decay structure, and show the emergence of asymptotical flocking based on Barbalat's lemma.
scientific article; zbMATH DE number 7354175
scientific article