Modelling hierarchical flocking

We present a general framework for modeling a wide selection of flocking scenarios under free boundary conditions. Several variants have been considered-including examples for the widely observed behavior of hierarchically interacting units. The models we have simulated correspond to classes of various realistic situations. Our primary goal was to investigate the stability of a flock in the presence of noise. Some of our findings are counter-intuitive in the first approximation, e.g. if the hierarchy is based purely on dominance (an uneven contribution of the neighbors to the decision about the direction of flight of a given individual) the flock is more prone to loose coherence due to perturbations even when a comparison with the standard egalitarian flock is made. Thus, we concentrated on building models based on leader-follower relationships. And, indeed, our findings support the concept that hierarchical organization can be very efficient in important practical cases, especially if the leader-follower interactions (corresponding to an underlying directed network of interactions) have several levels. Efficiency here is associated with remaining stable (coherent and cohesive) even in cases when collective motion is destroyed by random perturbations. The framework we present allows allows the study of several further complex interactions among the members of flocking agents.