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.