Collective behavior of swarms with general nonlinear attraction and repulsion functions

WE study the swarms (multi-agent systems in network) with general nonlinear attraction and repulsion functions. Our work generalizes the results given by Gazi and Passino [7] and Chu et al. [9, 11] into a more general setting. It is shown that the members of multi-agents system in reciprocal communication network will asymptotically form a cohesive cluster with finite size if the nonlinear attraction and repulsion functions satisfy some very mild assumptions. These results can be generalized into the case that the network is non-reciprocal with detailed balance condition. However, under general non-reciprocal networks the members of the system could appear some oscillatory or dispersed behavior depending on the choices of the nonlinear attraction and repulsion functions. We present several numerical simulations demonstrating the correctness of our theoretic results.