Stability analysis of general swarm with Gaussian attractant/repellent profiles and interaction time delays

In this paper we consider a class of social foraging swarms with nutrient/toxic profiles and general nonlinear attraction and repulsion structure, as well as interaction constant time delays. The emergent behavior of the swarm motion is the result of a balance between inter-individuals interactions and the simultaneous interactions of the swarm with their environment. The paper considers some condition under which it shows 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 under some mild assumptions.