Aggregation stability of multiple agents with general nonlinear attraction/repulsion forces and interaction time delays

In this paper we consider the aggregation stability problem of a multi-agents system with general nonlinear attraction and repulsion forces and interaction constant time delays. The paper considers a general condition which extends the results provided in Shu and Zheng [1]. We show that the agents of multi-agents system with interaction time delays will asymptotically form a cohesive cluster with finite size and we estimate the size of the bounded area, if the nonlinear attraction and repulsion functions and interaction time delays satisfy some very mild assumptions. We give several numerical simulations demonstrate the validation of our results. Simulations also show that the swarm may display more complicated dynamics behavior depending on different values of delay.