Stability Analysis of Social Foraging Swarm with Interaction Time Delays

This paper considers a swarm model with an attraction-repulsion function involving variable communication time lags and an attractant/repellent. It is proved that for quadratic attractant/repellent profiles the members of the swarm with time delays will aggregate and form a cohesive cluster of finite size in a finite time. Moreover, all the swarm members will converge to more favorable areas of the quadratic attractant/repellent profiles under certain conditions in the presence of communication delays.