Stability analysis of social foraging swarm with general nonlinear attraction and repulsion forces 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 with constant time-delay. The paper considers the condition, which extends some existent results. 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. We show that the agents of social foraging swarm with interaction time-delay will asymptotically form a cohesive cluster with finite size for different profiles under some assumptions and we estimate the size of the bounded area. We give several numerical simulations demonstrating the validation of our results. Simulations also show that the swarm may display some complex dynamics behavior depending on different coupling matrices and time delays.