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 non-reciprocal flocking, we ask whether a chiral state can nevertheless be stabilized in the discrete-time, metric, non-reciprocal two-species Vicsek model, and if so, under what conditions. For equal populations and motilities, we show that such a state exists only within a restricted window characterized by high density, very low self-propulsion speed, and small system size 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 chiral states 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 non-reciprocal 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 non-reciprocal interactions.