Self-organized motion in a class of anisotropic swarms: Convergence vs oscillation

We study an anisotropic swarm model with a class of attraction and repulsion functions. It is shown that the members of a reciprocal swarm will aggregate and eventually form a cohesive cluster of finite size around the swarm center within finite time. Under mild conditions on attraction and repulsion functions, the swarm is also completely stable, i.e., every motion converges to the equilibrium point set of the system. These results are further extended to a class of nonreciprocal swarms under the detailed balance condition on coupling weights. We also present numerical simulations demonstrating complex oscillatory behavior in general nonreciprocal swarms. These results provide more insight into the effect of the interaction pattern on collective behavior of swarms.