When Swarms Collide: Using one swarm to capture another*

Swarming patterns that emerge from the interaction of many mobile agents are a subject of great interest in fields ranging from biology to physics and robotics. In some application areas, multiple swarms effectively interact and collide, producing complex and chaotic spatio-temporal patterns. Recent studies of swarm-on-swarm dynamics deal with predicting the scattering of two large, colliding swarms with nonlinear interactions. By using a  combination of mean-field and time-series analysis techniques, we are able to predict physical parameters under which colliding swarms are  expected to form a combined milling state. That is, we predict when one swarm can capture another. Our semi-analytical methods rely on the  assumption that, upon collision, two swarms oscillate near a limit-cycle, where each swarm rotates around the other. Using this approach we are  able to predict the critical swarm-on-swarm interaction coupling, below which two colliding swarms merely scatter, for near head-on collisions as a  function of control parameters. In general, we show that the critical coupling corresponds to a saddle-node bifurcation of a stable limit cycle.