Stability analysis of swarms with interaction time delays

This paper investigates the collective behavior of a general swarm model with communication time delays under different environment profiles, and the complex dynamic behavior of the delayed swarm model along a plane and a quadratic attractant/repellent profile are analyzed respectively too. It turns out that the swarm members can eventually converge to a finite region under certain conditions and the time delay plays an important role in the dynamic behavior of swarms. Finally numerical simulation results indicate that our theoretical analysis is correct.