Topological flocking models in spatially heterogeneous environments

TL;DR

This paper investigates how topological flocking models behave in spatially heterogeneous environments, revealing that they maintain long-range order and form traveling bands due to environment-induced network rewiring.

Contribution

It demonstrates that topological flocking models recover key features of metric models in heterogeneous media, highlighting the role of spatial heterogeneities in collective behavior.

Findings

Order remains long-ranged despite heterogeneities.

Heterogeneous environments induce effective density-order coupling.

Traveling bands emerge across wide parameter regions.

Abstract

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.