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.

具有度量和拓扑相互作用的植绒模型应该表现出不同的特征，例如移动极带的存在和不存在。另一方面，淬灭无序（空间异质性）已被证明会显着影响具有度量相互作用的活性系统的大规模特性，而淬灭无序对具有无度量相互作用的活性系统的影响至今仍未得到探索。在这里，我们展示了当放置在异质环境中时，拓扑植绒模型可以恢复同质媒体中度量特征的几个特征。特别是，我们发现即使存在空间异质性，有序也是长程的，并且异质环境诱导了有效的密度-有序耦合，促进了行带的出现，在参数空间的广泛区域中观察到。我们认为这种耦合是由波动引起的拓扑相互作用网络重新布线的结果，空间异质性的存在大大增强了这种耦合。