Stability and breakdown of chiral motion in non-reciprocal flocking
We study a two-species Vicsek model with intra-species alignment and asymmetric inter-species couplings, where one species aligns with the other while the latter anti-aligns. 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 anti-alignment, whereas stronger anti-alignment 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 anti-parallel-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, inter-species coupling, and system size, rather than being a generic outcome of nonreciprocal interactions.