Emergent rotational order and reentrant global order of Vicsek agents in a complex noise environment

Noisy pursuit in complex environments drives the emergence of collective behaviors in active matter systems. A compelling, minimal framework for studying the impact of spatially heterogeneous noise on collective motion is provided by the standard Vicsek model. In this study, we investigate the collective dynamics of Vicsek agents in a complex noise environment, comprising a central noiseless circular region surrounded by a tunable noisy outer zone with short-range mutual repulsion. By varying the outer noise intensity, we observe an emergent rotational order that peaks at higher noise levels, as revealed by phase and susceptibility plots. Global translational order follows a distinctive "U-shaped" curve: near-perfect alignment at zero outer noise, which dies down to a deep minimum around intermediate noise and reenters at high noise. The latter rise is attributed to an increase in rotational order. Strong rotational order effectively confines slower agents within the noiseless core, while faster agents escape more readily. We quantify escape dynamics through time-averaged and first-passage escape rates, demonstrating velocity-dependent retention on the probability of finding the bimotility agent flocks at a given time, resulting in segregation and trapping. Introducing a gradual noise increase from the circle's center to its outer region reduces both translational and rotational order, underscoring the impact of environmental heterogeneity and sudden annealing over gradual change. These findings offer insights into predicting and manipulating the dynamics of active agents in complex environments, with applications in both biological and synthetic swarming systems.