Abstract: This paper proposed a general delay swarm model and researched its collective behavior in the presence of communication time delays under general condition satisfied by several environment profiles. The results show that the swarm members can eventually converge to a finite region bound around swarm center along an attractant/repellent profile. Simulation proved the time delay swarm may display more complex dynamics, including stability and oscillation, depending on the delay values, the results also show the motion of the center.

Key words: Swarm, Collective behavior, Time delays, Quadratic environment profiles