Learning to flock in open space by avoiding collisions and staying together

The synchronized flight of bird flocks, exemplified by starling murmurations, is perhaps the most striking example of collective behavior in natural systems, which fascinated scholars for quite a long time [1]. Evolutionary biologists, for instance, have long debated the advantages of living in groups [2], which should offer increased protection from predation by diluting the individual risk and 1 possibly confusing the attackers by the sheer size of the assembly. Flocking behavior involves a high degree of order in the individual directions of motion [3], and has been reproduced by minimal models of self-propelling particles (SPPs), such as Craig Reynolds Boids [4] or the celebrated Vicsek model [5] that has long captivated the attention of statistical physicists and played a pivotal role in the birth of the active matter research field. The essential ingredient of these models is the tendency of individual particles to align their direction of motion with those of their local neighbours, which is enough to promote long range order in systems with finite density (even in two spatial dimensions, due to the non-equilibrium nature of self-propelled particles) such as in toy models with periodic boundary conditions. In open systems, constituted by a finite number of individuals in an open, infinite space, purely alignment interactions are however not enough to maintain group cohesion.