Self-Organization of Swarms with Communication Delays under Disturbances

In this paper we establish a general swarm model with time delays under disturbances for the quadratic attractant/repellant profiles. It is proved that the swarm members will converge and form a cohesive cluster around the center in a finite time under certain conditions in the presence of communication delays and disturbances. For quadratic attractant/repellant profiles, all the swarm members will converge to more favorable areas in the presence of noise disturbances. Numerical simulations illustrate the theoretical results.