Stability and breakdown of chiral motion in nonreciprocal flocking

We study a two-species Vicsek model with intraspecies alignment and asymmetric interspecies couplings, where one species aligns with the other while the latter antialigns. Motivated by recent results showing that globally coherent chiral motion is not a generic large-scale state of finite-range nonreciprocal flocking, we ask whether a chiral state can nevertheless be stabilized in the discrete-time, metric, nonreciprocal two-species Vicsek model, and if so, under what conditions. For equal populations and motilities, we find that the global chiral state is a long-lived finite-time state rather than an asymptotically stable phase at nonzero motility. Its breaking time increases rapidly as the self-propulsion speed is reduced or the strength of the nonreciprocal coupling is enhanced, explaining why systems with very low motility can appear stably chiral over conventional simulation timescales. This finite-time chiral regime is further limited to high-density systems and to system sizes that are small relative to the interaction range. Within this window, we also find that chirality appears primarily when aligning interactions dominate over antialignment, whereas stronger antialignment leads to species segregation and suppresses chirality. Conversely, introducing species asymmetry through population imbalance drives transitions from the finite-time chiral regime to porous parallel-flocking or antiparallel-flocking liquids; motility imbalance induces asynchronous oscillations and, in extreme cases, leads to segregation into moving clusters of the faster species within a more dispersed background of slower particles. Overall, these results indicate that chirality in the nonreciprocal two-species Vicsek model arises within a restricted regime set by density, motility, interspecies coupling, and system size, rather than being a generic outcome of nonreciprocal interactions.