Non-Reciprocity in Metric and Topological Models of Flocking

Hydrodynamic models based on the symmetries (or lack thereof) of self-propelling agents have been a powerful tool in studying the large-scale collective motion of organisms such as flocks of birds. Recently, there has been an interest in understanding systems where, due to the level of description chosen, violations of the action-reaction symmetry of Newton's third law can be found. In this work we study the non-reciprocity embedded in the many-body interactions of the classic Vicsek model of flocking. We propose coarse-graining the non-reciprocal interactions into hydrodynamic couplings between density and velocity fields that would be normally forbidden in equilibrium systems, and explore the role of these "non-reciprocal" coupling constants on inhomogeneous pattern formation in the model. Our results suggest that the qualitative role of these couplings depend sensitively on whether interacting neighbors are chosen based on metric or topological considerations.