Complex collective dynamics of anisotropic swarms

An anisotropic swarm model with a new attraction and repulsion function is considered in this paper. It is shown that, when the coefficient matrix is symmetric, the swarm members will aggregate and eventually form a cohesive cluster around the swarm center. Moreover, the swarm system is completely stable and the swarm center keeps still for all time. Numerical simulations agree well with the theoretical results. In addition, for the case where the coupling weights satisfy detailed balance condition, these results are also valid, but the swarm center should be replaced by the weighted center. Finally, for general anisotropic swarms, the simulation results exhibit more complex collective oscillatory motions of all agents.