Stability Analysis of Swarm with Gaussian Attractant/Repellent Profiles

Abstract

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