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Flocking models with metric and topological interactions are supposed to exhibit distinct features, as for instance the presence and absence of moving polar bands. On the other hand, quenched disorder (spatial heterogeneities) has been shown to dramatically affect large-scale properties of active systems with metric interactions, while the impact of quenched disorder on active systems with metric-free interactions has remained, until now, unexplored. Here, we show that topological flocking models recover several features of metric ones in homogeneous media, when placed in a heterogeneous environment. In particular, we find that order is long-ranged even in the presence of spatial heterogeneities, and that the heterogeneous environment induces an effective density-order coupling facilitating emergence of traveling bands, which are observed in wide regions of parameter space. We argue that such a coupling results from a fluctuation-induced rewiring of the topological interaction network, strongly enhanced by the presence of spatial heterogeneities.

Topological flocking models in spatially heterogeneous environments