Radial and topological interactions generate dynamic emergence

Abstract A natural feature of a flock of birds is to develop time-dependent coherent patterns that spontaneously emerge during their flight. The origins and quantification of this phenomenon have been less studied. Here, we computationally show that this state can be reproduced by employing canonic interaction rules (radial and topological) together with a simple frustration rule; and characterize it introducing global and local order parameters. Using these parameters, we prove that both canonic interactions are able to generate this state; although it is observed that a topological interaction rule is more effective in reproducing it. Extra information is obtained after uncovering their respective interaction networks in time. In particular, the network efficiency measure in time for radial and topological rules is found and used to show that networks following topological interactions are more efficient through time. The presented analysis is general and can be used to quantify emergent phenomena in other groups of animals like fish, insects, ants or even humans performing collective motion.

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