Aggregation stability of multiple agents with general nonlinear attraction and repulsion forces

In this paper we consider the aggregation stability problem of a multi-agents system under network, among the agents there are nonlinear attactive/repulsive forces. Our work generalizes the results given by Gazi and Passino [1] and Chu, Wang and Chen [2], [3], [4] into a very general setting. It shows that the agents of multi-agents system in undirect communication network will asymptotically form a cohesive cluster with finite size if the nonlinear attraction and repulsion functions satisfy some very mild assumptions. We give several numerical simulations demonstrate that the collective behavior of system appear stable cohesion with finite size cohesive areas if the mild assumption is satisfied. We also study the system with directed networks. In such cases the swarms with same nonlinear attactive/repulsive forces may exhibit oscillation and dispersal phenomenon.