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 in a complex environment recover several features of metric models in homogeneous media. In particular, we find that order is long-ranged even in the presence of spatial heterogeneities, and that the environment facilitates an effective density-order coupling that allows the formation of traveling bands.