Topological Active Matter in Complex Environments.

Flocking models with metric and topological interactions are supposed to exhibit very distinct features, as for instance the presence and absence, respectively, of moving polar bands. By using Voronoi and k-nearest neighbors (kNN) interaction rules, we show that topological models recover several features of metric ones in homogeneous media, when placed in a complex environment. In particular, we find that order is long-ranged even in the presence of spatial heterogeneities, and that the environment induces an effective density-order coupling that allows the formation of traveling bands.